Valuation of preference-based measures: can existing preference data be used to generate better estimates?

Valuation of preference-based measures: can existing preference data be used to generate better... Background: Experimental studies to develop valuations of health state descriptive systems like EQ-5D or SF-6D need to be conducted in different countries, because social and cultural differences are likely to lead to systematically different valuations. There is a scope utilize the evidence in one country to help with the design and the analysis of a study in another, for this to enable the generation of utility estimates of the second country much more precisely than would have been possible when collecting and analyzing the country’s data alone. Methods: We analyze SF-6D valuation data elicited from representative samples corresponding to the Hong Kong (HK) and United Kingdom (UK) general adult populations through the use of the standard gamble technique to value 197 and 249 health states respectively. We apply a nonparametric Bayesian model to estimate a HK value set using the UK dataset as informative prior to improve its estimation. Estimates are compared to a HK value set estimated using HK values alone using mean predictions and root mean square error. Results: The novel method of modelling utility functions permitted the UK valuations to contribute significant prior information to the Hong Kong analysis. The results suggest that using HK data alongside the existing UK data produces HK utility estimates better than using the HK study data by itself. Conclusion: The promising results suggest that existing preference data could be combined with valuation study in a new country to generate preference weights, making own country value sets more achievable for low and middle income countries. Further research is encouraged. Keywords: Preference-based health measure, Non-parametric Bayesian methods, Time trade-off, EQ-5D Background preference-based measure. Such a measure consists of a Health resource allocation is becoming increasingly im- classification system used to describe health (patients re- portant in an economic climate of increasing demands port their own health and this is assigned to a health on healthcare systems with constrained budgets. state using a classification system) and a value set that Economic evaluation using cost-utility analysis has generates a utility value for every health state defined by become widely popular technique internationally to the classification system. inform resource allocation decisions. Cost-utility analysis Among the large number of currently available measures benefits using Quality Adjusted Life Years preference-based measures of health-related quality of (QALYs), a measure that multiples a quality adjustment life (HRQoL) are the generic EuroQol five dimensional for health by the duration of that state of health [1]. The (EQ-5D) questionnaire [2], health utilities index 2 quality adjustment weight is generated using utility (HUI2) and 3 [3, 4], Assessment of Quality of Life values where 1 denotes full health and 0 denotes dead, (AQoL) [5], Quality of Well-being scale (QWB) [6], and and is most often generated using an existing the six-dimensional health state short form (derived from short-form 36 health survey) (SF- 6D) [7], though there are an increasing number of condition-specific Correspondence: sk157@aub.edu.lb measures available [8]. Department of Nutrition and Food Sciences, Faculty of Agricultural and Food Sciences, American University of Beirut, Beirut, Lebanon © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 2 of 13 There is now an increasing number of datasets of pref- does not present new methodological developments, it erence data, where preferences have been elicited for the further accentuates the key point made in the Kharroubi same measure for different countries. Kharroubi et al. et al. [14, 15] articles, i.e. the good performance of the [9] use a novel nonparametric Bayesian approach to new modelling approach. model the disparities between the United States (US) First, SF-6D valuation surveys along with employed and UK which is simpler, better fitting and more appro- data corresponding to UK and HK are summarized here. priate for the data than the previously adopted conven- Second the Bayesian non-parametric model is described tional parametric model of Johnson et al. [10]. Such an and third the results are presented. Finally, the results approach has also been applied to the joint UK-Hong are discussed, including limitations and suggestions of Kong and UK-Japan SF-6D data set ([11], [12]). The possible future outlooks. nonparametric Bayesian model offers a major added ad- vantage as it permits the utilization of findings of coun- Methods try 1 to improve those of country 2, and as such The SF-6D generated utility estimates of the second country will be The SF-6D includes six health dimensions: physical more precise than would have been the case if that functioning, role limitation, social functioning, bodily country’s data was collected and analyzed on its own. pain, mental health and vitality, each with between four There are two distinct ways in which such a model and six levels [7]. Through the selection of one level may be useful. In the existence of large quantity of data from each dimension, physical functioning being the first pertaining to two countries, good estimates of popula- and vitality being the last, an SF-6D health state is de- tion utility functions corresponding to each country can fined. Different combinations result in 18,000 possible be generated through the analysis of data from each health states, which are associated with a six-digit de- country on its own (using the model of [13]) and this is scriptor ranging from 111,111 representing full health the best option. However, in case where a significant and 645,655 representing the worst possible state called quantity of data is available in one country but limited “the pits”. in another, there is a scope to borrow strength from country 1 in an effort to obtain better population utility The valuation survey and data set estimates for the second country than those generated UK when analyzing that second country’s data on its own. A sample of 249 health states is described through the Recently, Kharroubi [14, 15] developed a modified SF-6D and then valued by a representative sample of the nonparametric Bayesian statistical method that permits UK population (n = 836). Selection methods of respon- the utilization of evidence from one country as substan- dents along with health states are discussed elsewhere tial prior information for a study in another, and [7]. All the selected respondents have been asked to rank employed this method in the analysis of a valuation and value six health states according to the McMaster study for EQ-5D in US using the already existing UK ‘ping pong’ variant of the standard gamble (SG) tech- data. Crucial assumption underlying this analysis was nique. Accordingly, each of the five SF-6D health states that preferences of the UK population are in essence the was valued against the perfect health state and against same as those of the US in addition to that both coun- the “pits” by the respondents. As for the sixth question, tries have plenty of data. However, different countries it consisted of valuing the “pits” by determining whether have different population compositions, work, cultures they perceived it as worse or better than death by consid- and language. These can all impact on the relative values ering one of the following choices: (i) the certain prospect given to different dimensions of health (for example, of being in the “pits” state and the uncertain prospect of self-care and anxiety/depression) as well as where on the full health or immediate death; or (ii) the certain prospect 1-0 full health-dead scale each health state lies. of death and the uncertain prospect of full health or the The present paper seeks to explore the use of such a “pits” state [16]. Negative values were bounded at − 1, and model in the context of smaller countries with different they designate the states value as worse than death [17]. cultures. This is explored using a case study for SF-6D Then, the other 5 health states were chained onto the zero HK and UK data, where the health states valued in the to one scale, where 0 s designates the perceived equivalent HK valuation study are modelled using the already exist- to being dead, and 1 corresponds to perfect health [7]. As ing UK dataset, and the estimates are compared to the such, the dependent variables (y) in the models below cor- estimates generated modelling HK data alone. It should respond to the adjusted SG values. be noted that this method was used to model the US/ Of the original 836 respondents, a total of 225 respon- UK data (the Kharroubi et al. [14, 15] articles describe dents had to be excluded for several reasons. For in- this at length), and as such the method given in this art- stance, 130 respondents failed to value the “pits” state; icle is a replication of that method. Hence, though it consequently, the corresponding data couldn’tbe Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 3 of 13 processed any further [10]. Of the total 611 included re- We next let u(x) and u (x) be the utility functions UK spondents, 148 missing values from 117 respondents for health state x valued in the HK and UK experiments were present thereby resulting in a total of 3518 ob- respectively, Kharroubi [14] then model the prior distri- served SG valuations across the 249 health states. Details bution for u(x) as multivariate normal with mean de- pertaining to the valuation of the 249 SF-6D UK health fined as states can be found in [7]. EuðÞ ðÞ x ¼ EuðÞ ðÞ x þ γ þ β x ð2Þ UK Hong Kong and variance-covariance matrix The HK study comprised of a sample of 197 health states (selected according to the UK procedures) which were val- 0 2 0 covðÞ u ðÞ x ; u ðÞ xþσ cðÞ x; x ð3Þ UK UK ued using the same valuation procedures as those in the UK study [18]. Each respondent was asked to rank and where E(u (x)) is the expected value of the utility of UK value eight health states, and the interview procedure was health state x and cov(u (x), u (x′)) is the variance- UK UK modelled on the basis of that in the UK study. covariance matrix between u (x)and u (x′) for two dif- UK UK Out of the original 641 respondents, a total of 59 re- ferent states x and x′ in the UK experiment, both of which spondents were disqualified from the analysis according are readily available from the analysis of the UK study. to the same exclusion conditions as in the UK study [6] Given Eqs. 2 and 3, note that x represents a vector leaving 582 respondents’ data for analysis. Each of the consisting of discrete levels on each of the six health di- 582 respondents made 8 SG valuations, giving 4596 val- mensions and γ, β and σ are unknown parameters. If uations. Of these, 60 missing health state values were follows from Kharroubi [14] that the mean function of present and so 4596 observed SG valuations across 197 u(x) represents a prior expectation that the utility will health states were finally included in the analysis. Details be approximately a simple additive linear function of the pertaining to the valuation of the 197 SF-6D HK health dimension level in x. Additionally, the true function is states can be found in [18]. allowed to deviate around this mean according to its multivariate normal distribution, and so it can as a result Modelling assume any form. It is in this sense that the Bayesian The modelling approach is described in Kharroubi [14], model is described as nonparametric. Furthermore, there where a nonparametric Bayesian model was employed in seem to be a high correlation c(x,x′) between u(x) and the modelling of the US EQ-5D dataset using the already u(x′) when x and x′ are close enough, and is given by existing UK dataset as informative prior. In this article, no we follow on from its work to examine whether the X 0 0 cðÞ x; x ¼ exp − b x −x ð4Þ d d adoption of HK health states, while drawing extra infor- d mation from the UK data, generates better estimation than analyzing the HK sample by itself. The estimates where b is a roughness parameter in the dimension d are compared using different prediction criterion, in- that controls the extent to which the true utility function cluding predicted versus actual mean health states valua- is anticipated to adhere to a linear form in a dimension tions, mean predicted error and root mean square error. d. It is to be noted that many other choices have been Kharroubi [14] propose the following model made for this covariance matrix; see for example [19]or [20], but the resulting estimates are not generally sensi- y ¼ 1−α 1−u x þ ε ð1Þ j ij ij tive to the change of this function. However, the pro- ij posed form is appropriate here [13]. See Kharroubi et al. Where, for i = 1,2,…,I and j = 1,2,…,J, x is the i-th j ij [14] for more details on this. health state valued by the respondent j in the HK experi- Finally, it is to be noted that the novel method of ment,y is the respondent j’s time trade-off (TTO) valu- ij modelling utility function u(x), represented by adding ation for that health state i, α is a term to allow for the two terms E(u (x)) and cov(u (x), u (x′)) in Eqs. UK UK UK individual characteristics of respondent j and ε is a ran- ij 2 and 3, allows the already existing UK evidence to con- dom error term. Let t be a vector of covariates repre- tribute significant prior knowledge to the HK study. In senting individual characteristics of respondent j, other words, the posterior density of the UK utility func- Kharroubi [14] propose the following distributions: tion was treated as a prior density to analyse the new study in the HK. T 2 2 α  LN t γ; τ and ε  N 0; υ : j ij Full theory of the Bayesian approach here is dis- cussed in Kharroubi [14]. Programs to undertake the where γ is the vector of coefficients for the covariates Bayesian approach were written in Matlab and are 2 2 and τ and v are further parameters to be estimated. available on request. Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 4 of 13 Results in the sample along with the perfect health, sorted via the The new modelling approach is now applied to the ana- predicted valuations. Figure 1a shows the predicted lysis of SF-6D HK study using the previously existing (squared line) and actual (diamond marked line) mean val- UK study (to be indicated by HK/UK model hereinafter). uations using the HK model. The line marked with trian- From a Bayesian prospective, the old posterior contains gles denotes the errors computed based on the difference all that we know before seeing the new data, and so be- between the two valuations. Figure 1b shows the corre- comes the new prior distribution. Thus for our analysis, sponding results obtained using HK/UK model. Based on the posterior of the UK utility function becomes our the plots it is apparent that the estimates of the HK/UK prior for the analysis of the HK study. The estimates are utilities for the various SF-6D health states are much more compared to those estimated using the HK data exclud- precise than those corresponding to the HK only results. ing the UK data (to be indicated by HK model herein- These plots also reveal the HK model tends to under pre- after) using different prediction criterion, including dict at low health state values (meaning the poor health predicted versus actual mean health states valuations, states). However, this is not the case for the HK/UK model. mean predicted error, root mean square error along with Additionally, the plots suggest that the variations of the the Bland-Altman agreement plots [21]. predictions are larger and so a high fluctuation and Figure 1 shows the HK predicted and observed mean non-steady trend of the difference line, so this suggests that valuations corresponding to the 197 health states evaluated the HK/UK model is less susceptible to systematic bias. Fig. 1 Sample mean and predicted health states valuations for a the HK model and b the HK/UK model Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 5 of 13 Figure 2a and b depict the Bland–Altman agreement the HK/UK model is much smaller (0.0416) as compared plots for HK and HK/UK models. In this context, the dif- to that corresponding to the HK model (0.0503), thereby ference between the observed and predicted mean valua- vindicating the variations of the differences in Fig. 2a.On tions is plotted against the mean of the difference (or the the other hand, the HK/UK model differences are well val- average bias). The solid line corresponds to the mean bias, idated as observed in Fig. 2b. whereas the dotted lines depict the 95% limits of agree- Table 1 provides the inferences for the utilities of the ment. For better visual judgment of how good the two val- 197 states evaluated in the study along with the perfect uations agree, the 95% limits-of-agreement lines are health. Table 1 displays the actual mean, the standard error drawn. The narrower the range between these two limits, corresponding to each health state for both models. The the better the agreement is. When comparing these two results for the population utilities from the UK that were figures, we see that the HK/UK model reveals a better treated as prior information in the HK/UK model are also agreement as the length of the 95% limits of agreement is provided. As depicted all through the 197 health states 0.163, i.e. narrower than that of the HK model of length (excluding the perfect health state) presented in Table 1,it 0.197. Additionally, the difference in mean bias between is evident that the HK/UK model has a better predictive the two models is also obvious, with values of 0.0116 for performance compared to the HK model overall, and as a the HK/UK model and 0.0175 for the HK model. More- results it has a root mean square error (RMSE) of 0.045 over, the differences standard deviation corresponding to whereas the HK model has an RMSE of 0. 051. Fig. 2 Bland-Altman agreement plots for a the HK model and b the HK/UK model Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 6 of 13 Table 1 Posterior inferences for utilities of the 197 health states valued in the empirical survey along with the perfect health State X Observed mean UK results HK Model HK/UK Model Posterior mean Posterior SD Posterior mean Posterior SD Posterior mean Posterior SD 111111 1 1 0 1 0 1 0 111621 0.6492 0.7482 0.0345 0.6322 0.029 0.6652 0.0267 111645 0.5055 0.6169 0.0586 0.5568 0.0281 0.5384 0.0316 112153 0.6519 0.691 0.0577 0.6681 0.0293 0.6524 0.0326 112455 0.6777 0.6078 0.0515 0.635 0.0298 0.6274 0.0325 112613 0.7305 0.7049 0.0612 0.6636 0.0321 0.674 0.0364 112651 0.6288 0.6342 0.0614 0.6182 0.0335 0.5919 0.0366 113141 0.8022 0.7581 0.0643 0.7665 0.0287 0.7633 0.0322 113352 0.7441 0.6776 0.0523 0.7304 0.0262 0.7253 0.0282 113411 0.7324 0.7284 0.031 0.7208 0.0287 0.701 0.0255 113615 0.6685 0.6415 0.0677 0.6308 0.0334 0.6125 0.0401 113634 0.64 0.6017 0.0535 0.5971 0.0305 0.5902 0.0352 114631 0.7057 0.6754 0.056 0.6418 0.0343 0.6467 0.0376 115131 0.7243 0.7695 0.0704 0.7203 0.029 0.7193 0.0317 115211 0.7951 0.7738 0.0561 0.7739 0.0309 0.7802 0.0327 115251 0.6223 0.7148 0.074 0.6427 0.0287 0.6329 0.0318 115314 0.6788 0.779 0.0545 0.6585 0.0312 0.6731 0.0347 115355 0.5346 0.5859 0.0563 0.5649 0.0306 0.5396 0.0347 115432 0.6201 0.7091 0.06 0.6673 0.0265 0.6696 0.0287 115653 0.5728 0.5652 0.0561 0.5189 0.0308 0.494 0.0325 121212 0.8253 0.8275 0.0261 0.8452 0.0249 0.8259 0.0233 122233 0.6894 0.7475 0.034 0.6882 0.0273 0.6888 0.0273 122425 0.704 0.6784 0.0353 0.6764 0.0262 0.683 0.0268 124125 0.612 0.7292 0.0475 0.6194 0.0279 0.6158 0.029 125143 0.6505 0.6892 0.053 0.6515 0.0284 0.649 0.0301 125625 0.5478 0.5779 0.0663 0.5187 0.0326 0.4992 0.0374 131151 0.7621 0.7402 0.0725 0.7591 0.0293 0.767 0.0331 131331 0.7638 0.7629 0.0522 0.7103 0.0292 0.7071 0.0326 131542 0.7067 0.6181 0.0304 0.6407 0.0276 0.6118 0.0269 131555 0.5327 0.5832 0.0544 0.5345 0.0313 0.521 0.0349 132524 0.5983 0.6574 0.037 0.5944 0.0265 0.5819 0.0274 133132 0.7425 0.6942 0.0343 0.7093 0.0266 0.6978 0.0263 135155 0.6251 0.5947 0.0639 0.5928 0.032 0.5747 0.0365 135312 0.7 0.6992 0.0488 0.6814 0.0272 0.6802 0.0283 135435 0.655 0.5664 0.063 0.6194 0.0291 0.6114 0.0327 135633 0.5085 0.5848 0.0613 0.5205 0.0304 0.5014 0.0353 141215 0.7089 0.7227 0.0698 0.6916 0.0303 0.6843 0.035 142113 0.6585 0.6911 0.0543 0.7071 0.0277 0.6917 0.0294 142154 0.6821 0.6844 0.0373 0.6494 0.0281 0.6444 0.0274 142335 0.6654 0.6536 0.0529 0.6164 0.0294 0.6 0.0332 143641 0.5733 0.6151 0.0506 0.5495 0.0329 0.5461 0.0349 143654 0.5028 0.5487 0.0585 0.5145 0.0306 0.5018 0.0341 144341 0.5565 0.72 0.0279 0.5856 0.0275 0.6026 0.0243 Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 7 of 13 Table 1 Posterior inferences for utilities of the 197 health states valued in the empirical survey along with the perfect health (Continued) State X Observed mean UK results HK Model HK/UK Model Posterior mean Posterior SD Posterior mean Posterior SD Posterior mean Posterior SD 144455 0.5676 0.5356 0.0643 0.5839 0.0299 0.5768 0.0352 144613 0.6916 0.6501 0.0583 0.6136 0.0334 0.6147 0.0385 145515 0.5903 0.617 0.0735 0.5834 0.0322 0.5786 0.0371 145621 0.6093 0.6233 0.0645 0.6026 0.0315 0.5952 0.0361 145645 0.5814 0.5077 0.0715 0.5391 0.0316 0.5427 0.0347 145652 0.5291 0.5334 0.0678 0.4771 0.0328 0.4634 0.0385 211111 0.8584 0.9197 0.0215 0.9219 0.0181 0.836 0.0205 211251 0.6738 0.7049 0.0631 0.6901 0.0278 0.6763 0.0299 211615 0.6206 0.6781 0.0713 0.6458 0.0307 0.6372 0.0357 211633 0.7051 0.6622 0.0527 0.62 0.0319 0.6129 0.0354 212145 0.6188 0.6927 0.0446 0.5961 0.0277 0.5851 0.0279 213323 0.6571 0.7761 0.0296 0.6767 0.0228 0.6946 0.0226 214435 0.5943 0.6291 0.0401 0.6097 0.0272 0.5997 0.0293 221452 0.6627 0.6237 0.0459 0.6727 0.0261 0.6585 0.0279 224612 0.6385 0.6256 0.0392 0.6217 0.0288 0.5986 0.0298 232111 0.7796 0.6987 0.0377 0.7564 0.0273 0.7304 0.0264 235224 0.6506 0.6486 0.0335 0.632 0.0271 0.6042 0.0274 241135 0.5824 0.702 0.0601 0.5989 0.0297 0.5758 0.0327 241531 0.6643 0.702 0.0352 0.6189 0.0275 0.625 0.027 243433 0.5053 0.702 0.0351 0.5941 0.0259 0.6017 0.026 243615 0.5913 0.6257 0.0643 0.5651 0.0301 0.5659 0.0332 244353 0.6976 0.61 0.0413 0.5863 0.0307 0.6613 0.034 311654 0.6581 0.5391 0.0452 0.5414 0.0336 0.6066 0.0365 312332 0.701 0.7472 0.0285 0.7068 0.0241 0.7146 0.0229 315123 0.5582 0.8043 0.0542 0.5361 0.0312 0.531 0.0325 315235 0.6161 0.7018 0.0542 0.5866 0.0291 0.585 0.0329 315341 0.6486 0.7105 0.0618 0.592 0.0307 0.5796 0.0359 315515 0.6064 0.6642 0.0363 0.5686 0.0295 0.5675 0.029 321122 0.7987 0.7638 0.0266 0.7525 0.0256 0.7451 0.0239 323644 0.4377 0.5362 0.0287 0.4567 0.0298 0.4148 0.0269 324155 0.6248 0.6015 0.0479 0.5536 0.0334 0.6095 0.0374 325433 0.5685 0.6875 0.0451 0.5845 0.0262 0.5754 0.0294 331115 0.6584 0.7288 0.0598 0.6649 0.0275 0.6621 0.0297 332411 0.6152 0.7217 0.0376 0.6523 0.0246 0.6607 0.0246 333135 0.631 0.6657 0.0349 0.6219 0.0284 0.6249 0.0278 333455 0.6131 0.5504 0.0448 0.5588 0.0315 0.5438 0.0352 334251 0.5031 0.6761 0.0532 0.5621 0.0266 0.5547 0.0289 341123 0.7389 0.7009 0.0393 0.6653 0.0296 0.6685 0.0289 341251 0.6023 0.679 0.067 0.6064 0.0307 0.59 0.0339 341414 0.7513 0.6751 0.0574 0.6503 0.0317 0.6535 0.0363 341634 0.5209 0.6174 0.0409 0.5463 0.0297 0.5454 0.0295 341651 0.6015 0.5904 0.0633 0.5401 0.0325 0.5338 0.0352 Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 8 of 13 Table 1 Posterior inferences for utilities of the 197 health states valued in the empirical survey along with the perfect health (Continued) State X Observed mean UK results HK Model HK/UK Model Posterior mean Posterior SD Posterior mean Posterior SD Posterior mean Posterior SD 342613 0.6672 0.6342 0.0526 0.589 0.0299 0.583 0.0334 343425 0.6307 0.6443 0.0405 0.5981 0.0284 0.5881 0.0303 344633 0.5002 0.6267 0.0395 0.493 0.0299 0.4787 0.0319 345153 0.4966 0.5875 0.0578 0.5378 0.0287 0.5242 0.0311 345355 0.4751 0.5101 0.0557 0.5036 0.0285 0.4895 0.0321 345411 0.6347 0.6506 0.0533 0.6302 0.0303 0.6019 0.0344 345535 0.6564 0.5436 0.0561 0.5377 0.0317 0.6356 0.036 345553 0.4538 0.5276 0.0527 0.4548 0.0307 0.4436 0.0345 411612 0.6595 0.6584 0.0634 0.6355 0.0305 0.6314 0.0332 412152 0.608 0.6558 0.0371 0.5804 0.0254 0.5715 0.0256 413212 0.6879 0.7402 0.0485 0.678 0.028 0.6757 0.0298 414355 0.5976 0.6335 0.0478 0.5634 0.0294 0.5588 0.0317 414522 0.7007 0.6612 0.0301 0.626 0.0303 0.6929 0.0299 415115 0.6264 0.7271 0.0617 0.5911 0.0321 0.592 0.0359 415313 0.5055 0.7889 0.0501 0.5672 0.0263 0.5795 0.0289 415453 0.5826 0.6483 0.0557 0.5458 0.0301 0.5477 0.0328 415651 0.5347 0.5696 0.069 0.4882 0.0334 0.474 0.0377 415655 0.4739 0.5087 0.0623 0.4259 0.0347 0.4026 0.0396 421314 0.6607 0.6689 0.0368 0.658 0.0253 0.6495 0.0261 421455 0.4016 0.6127 0.0383 0.5198 0.0275 0.4093 0.0286 421641 0.6118 0.635 0.0577 0.5533 0.0316 0.5464 0.0354 423435 0.6172 0.5985 0.0435 0.5564 0.0297 0.5321 0.0338 423615 0.6373 0.5506 0.0581 0.5312 0.0323 0.6111 0.038 425131 0.5312 0.6771 0.0551 0.5876 0.0253 0.5817 0.0273 431443 0.5838 0.638 0.0339 0.5927 0.0261 0.5889 0.0261 432621 0.6423 0.6468 0.0487 0.5754 0.0292 0.5735 0.0337 434211 0.6601 0.7068 0.0466 0.6409 0.0302 0.6375 0.0327 435335 0.6579 0.57 0.0499 0.5929 0.0295 0.5788 0.0337 441255 0.5133 0.5918 0.0522 0.5271 0.0324 0.5042 0.0346 441331 0.557 0.7049 0.0434 0.5765 0.0277 0.5772 0.0282 441615 0.4883 0.5871 0.0633 0.5209 0.0303 0.5033 0.0334 442655 0.353 0.5227 0.0536 0.4346 0.0301 0.4359 0.0327 443215 0.5719 0.6548 0.0352 0.5981 0.0272 0.5845 0.0267 443652 0.4431 0.5548 0.0564 0.4242 0.0312 0.4127 0.0353 444611 0.6854 0.6028 0.0592 0.5974 0.0312 0.5983 0.0345 445145 0.3405 0.552 0.0525 0.4903 0.0273 0.3726 0.0307 445233 0.4914 0.6384 0.0434 0.5801 0.0267 0.5741 0.0282 445615 0.4775 0.5487 0.0653 0.4665 0.0327 0.4409 0.0363 445641 0.5364 0.5241 0.0641 0.4739 0.033 0.4687 0.0378 511114 0.6239 0.6993 0.0379 0.64 0.0281 0.6376 0.0276 511435 0.6804 0.654 0.0546 0.6422 0.0298 0.6613 0.0306 511615 0.5991 0.5818 0.0725 0.5918 0.0313 0.5879 0.0372 Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 9 of 13 Table 1 Posterior inferences for utilities of the 197 health states valued in the empirical survey along with the perfect health (Continued) State X Observed mean UK results HK Model HK/UK Model Posterior mean Posterior SD Posterior mean Posterior SD Posterior mean Posterior SD 511633 0.5805 0.5918 0.0611 0.5599 0.0298 0.5497 0.0349 512242 0.6013 0.6906 0.0324 0.5932 0.0255 0.5972 0.0261 513654 0.4584 0.5474 0.0525 0.4182 0.0328 0.4126 0.0361 515155 0.6677 0.5927 0.0618 0.5675 0.0348 0.6586 0.0395 522321 0.7164 0.6846 0.0324 0.6844 0.0264 0.6776 0.026 523551 0.6141 0.6201 0.0471 0.5167 0.0314 0.5206 0.0334 531635 0.5015 0.5323 0.0345 0.5003 0.0292 0.4633 0.0299 533415 0.5342 0.5848 0.0533 0.5228 0.0288 0.5086 0.0329 534113 0.5076 0.7106 0.0437 0.5266 0.0283 0.528 0.0293 541451 0.5194 0.6153 0.0626 0.5266 0.0286 0.5256 0.0325 543533 0.4771 0.674 0.0365 0.4745 0.0293 0.4834 0.0303 545115 0.5171 0.6074 0.0662 0.5582 0.0295 0.5545 0.0325 545151 0.5136 0.5474 0.0686 0.5256 0.0291 0.5225 0.0329 545353 0.5103 0.5243 0.0492 0.4303 0.0326 0.4147 0.0358 545422 0.6088 0.6351 0.0322 0.5954 0.0253 0.5688 0.0276 611154 0.5961 0.658 0.0636 0.5557 0.0329 0.5629 0.0354 611221 0.681 0.6667 0.0521 0.654 0.0319 0.6183 0.0344 611432 0.4712 0.6454 0.05 0.5706 0.0267 0.5654 0.0281 611454 0.3346 0.6146 0.0608 0.4466 0.0286 0.3353 0.0316 611621 0.5816 0.6112 0.0699 0.5529 0.0319 0.5447 0.0349 611645 0.4649 0.5249 0.0688 0.4731 0.031 0.4577 0.0354 611652 0.5207 0.5638 0.0616 0.437 0.034 0.4247 0.0383 612415 0.4566 0.5872 0.0632 0.5267 0.0292 0.5128 0.0327 613625 0.3453 0.5321 0.0646 0.4299 0.0298 0.4105 0.0345 614135 0.5587 0.6619 0.057 0.5224 0.0331 0.5247 0.0368 614434 0.4449 0.6497 0.0383 0.4615 0.0281 0.4682 0.0286 615253 0.6248 0.5737 0.0566 0.5308 0.0342 0.5269 0.0391 615315 0.5634 0.642 0.0628 0.5097 0.0334 0.5097 0.0369 615412 0.4129 0.6469 0.0544 0.5182 0.0282 0.5084 0.031 615451 0.4431 0.5666 0.0689 0.4499 0.0324 0.4353 0.0362 615455 0.4993 0.5404 0.0645 0.4753 0.0327 0.4723 0.0373 615614 0.4344 0.5683 0.0701 0.4885 0.0317 0.4952 0.0343 615631 0.5056 0.5247 0.0664 0.4574 0.0347 0.4338 0.0397 615653 0.381 0.5127 0.0681 0.356 0.0349 0.3388 0.039 621135 0.4934 0.6645 0.0605 0.5417 0.0291 0.535 0.032 622513 0.5108 0.5809 0.0392 0.529 0.0265 0.5069 0.0276 623155 0.4501 0.5938 0.0598 0.4784 0.0315 0.4631 0.0356 623353 0.4256 0.5718 0.043 0.4528 0.0318 0.4181 0.0346 624431 0.5694 0.5912 0.0379 0.53 0.0319 0.4933 0.033 624633 0.3082 0.551 0.0475 0.4345 0.0291 0.3316 0.0317 625141 0.5605 0.5561 0.0466 0.5398 0.0287 0.5047 0.0316 631315 0.5806 0.6157 0.0577 0.5403 0.0326 0.5223 0.0353 Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 10 of 13 Table 1 Posterior inferences for utilities of the 197 health states valued in the empirical survey along with the perfect health (Continued) State X Observed mean UK results HK Model HK/UK Model Posterior mean Posterior SD Posterior mean Posterior SD Posterior mean Posterior SD 631333 0.6175 0.6386 0.0462 0.5443 0.0315 0.5336 0.0354 631355 0.4479 0.5823 0.0354 0.4765 0.0287 0.4666 0.0285 631632 0.4974 0.5525 0.0519 0.5252 0.0307 0.5102 0.0345 632615 0.5484 0.5202 0.0608 0.4831 0.0307 0.4872 0.0349 633122 0.4986 0.6515 0.0338 0.5131 0.0278 0.5084 0.0266 633535 0.3343 0.5378 0.0419 0.3942 0.0303 0.3791 0.0336 633653 0.4335 0.5395 0.0522 0.3644 0.0335 0.3776 0.0378 635611 0.4001 0.5522 0.0674 0.4736 0.0314 0.4538 0.0347 635651 0.4884 0.4829 0.0732 0.3799 0.0378 0.4841 0.044 641114 0.6165 0.6874 0.0653 0.6008 0.0313 0.6049 0.0335 641132 0.4794 0.6094 0.0542 0.5182 0.0312 0.4904 0.034 641154 0.545 0.5742 0.064 0.5188 0.0339 0.5143 0.0374 641211 0.6294 0.6567 0.0652 0.5718 0.0348 0.5505 0.0385 641654 0.4842 0.5225 0.0658 0.4347 0.0348 0.4418 0.0392 642151 0.5356 0.5776 0.0712 0.5119 0.0318 0.5009 0.0351 642313 0.5499 0.6834 0.0541 0.5278 0.0311 0.5332 0.0334 642453 0.5104 0.5844 0.054 0.4419 0.0326 0.4334 0.0366 642612 0.4496 0.5594 0.0336 0.4965 0.0282 0.4698 0.0289 642651 0.3731 0.5104 0.0707 0.4346 0.0308 0.4282 0.035 643,125 0.5007 0.6217 0.0556 0.4801 0.033 0.4661 0.0371 643143 0.463 0.6039 0.0531 0.4581 0.0321 0.4588 0.0333 644614 0.4387 0.5614 0.0573 0.4161 0.0321 0.4004 0.0376 644631 0.416 0.533 0.0623 0.4415 0.0313 0.4276 0.0352 645132 0.601 0.577 0.0517 0.5009 0.0352 0.5749 0.0384 645154 0.4948 0.5184 0.0614 0.396 0.0334 0.4765 0.0379 645235 0.3724 0.551 0.0592 0.4562 0.0299 0.4649 0.0339 645415 0.6023 0.5517 0.069 0.4761 0.0354 0.5666 0.0407 645441 0.4085 0.5106 0.0632 0.4309 0.0314 0.4094 0.0351 645655 0.067 0.3575 0.0186 0.0983 0.0226 0.0708 0.0251 SD Standard Deviation Additionally, Table 1 indicates other noteworthy dif- a result of selecting one health state at random from ferences between the HK and HK/UK models. For the these 6-12 states, 10,000 adjacent pairs were obtained. pits state, for instance, the HK model predicts a value Out of these 10,000 adjacent pairs, 20% display of 0.0983 albeit the actual average for this state is non-monotonicity in the HK model compared to 10% 0.067, whereas the HK/UK model attains a value of for the HK/UK model. 0.0708. Furthermore, the standard deviations corre- A more apparent presentation of the differences be- sponding to the HK/UK model are smaller as a result tween the HK and HK/UK models is shown in Fig. 3, of using the UK results as priors thereby providing a which depicts the fitted values corresponding to the HK better estimate. Differences in performance based on model (Fig. 3a) and the HK/UK model (Fig. 3b) against monotonicity are also apparent. Of the total 18,000 the observed of the 198 health states, as well as the per- health states defined by the SF-6D descriptive system, fect predictions given by a 45° unity line (solid line). 10,000 health states were sampled at random without Theoretically, the fitted values from the two models are replacement. In theory, there are 6–12 health states expected to lie roughly on the unity line. When compar- adjacent to each state of the 10,000 health. Then, as ing these two plots, it is clear from Fig. 3b that estimates Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 11 of 13 Fig. 3 Sample mean and predicted health states valuations for a the HK model and b the HK/UK model from the HK/UK model tend to be more proximate to evaluate the new HK study. The method given here is a the perfect predictions line, in contrast to Fig. 3a, which replication of that used in modelling the US/UK data depicts a larger scatter and the valuations deviate largely (the Kharroubi et al. [14, 15] articles describe this fully). from the 45°theoretical line. As a result, we emphasize Hence, though it does not present new methodological the fact that the HK/UK model provides predictions developments, it further accentuates the key point made much more precisely than the HK model. in the Kharroubi et al. [14, 15] articles, i.e. the good per- formance of the new modelling approach. Discussion Crucial assumption underlying the US/UK analyses In this paper, we have applied a nonparametric Bayesian (Kharroubi et al. [14, 15]) was that preferences of the model to estimate the utility values of health states UK population are in essence the same as those of the based on the SF-6D descriptive system. This model was US; in addition to that both countries have plenty of undertaken in an effort to use the already existing infor- data. The novelty of the analysis presented here was to mation from one country to serve as an informative explore the use of new modelling in the context of prior for a study in another. The methodology was ap- smaller countries with different population composi- plied to the HK SF-6D data set using the already avail- tions, work, cultures, language, all of which can impact able UK valuation, whereby the posterior of the UK on the relative values given to different dimensions of utility function was used as a substantial prior to health (for example, self-care and anxiety/depression) as Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 12 of 13 well as where on the 1-0 full health-dead scale each would be possible to generalize Eqs. 2 and 3 to handle health state lies. This is explored using a case study for more than two countries. Indeed, we can generalize fur- SF-6D HK and UK data, where the HK valuations are ther to a generic form modelled using the already existing UK dataset and the X n 0 EuðÞ ðÞ x ¼ EuðÞ ðÞ x þ γ þ β x estimates are compared to the estimates generated mod- k¼1 elling HK data alone. It is shown that the new modelling and variance-covariance matrix of the utility function permitted the already existing UK dataset to contribute significant prior belief to the HK n 0 2 0 covðÞ u ðÞ x ; u ðÞ xþ σ cðÞ x; x k k k¼1 analysis, and for this to enable the generalisability of this approach by making use of experience in a European where Eðu ðxÞÞ is the total mean utility of health k¼1 country to aid the analysis of a study in another Asian state x and covðu ðxÞ; u ðx ÞÞ is the total variance- k k k¼1 country. Consequently, much more precise estimates of covariance matrix between u (x)and u (x′)fortwodiffer- k k the HK utilities corresponding to the various SF-6D ent states x and x′, all of which are readily available from health states were obtained using the HK/UK model the analysis of the n available countries data. than would have been the case if the data from HK study A final note regarding the potential impact of our was used on its own, yet respect the inherent monoton- study in terms of health and quality of life gains: Note icity of the underlying utility measure even further. from Table 1 that health state 635,651, for instance, has Cautious model diagnostics affirm that the HK/UK an estimated health state utility value of 0.3799 from the model performs well and better than the HK model. HK model and 0.4841 from the HK/UK model. Thus, The nonparametric Bayesian model offers a major the difference in utility estimates is nearly 0.11. This added advantage: in the existence of lots of data on one could bring about an shift in QALYs from a treatment country and limited on another, it permits the utilization that prolongs life by 1 yr from 0.5 to 0.61. This implies of results of country 1 to improve those of country 2, that if a treatment costs 12,000, for example, the cost and as such generated utility estimates of the second per QALY would decrease from £24,000 to £19,672, country will be much more precise than would have thereby it below the cost effectiveness threshold used by been the case if that country’s data was collected and an- National Institute for Health and Clinical Excellence. In alyzed on its own. This in turn reduces the need for other words, it could influence whether or not a treat- undertaking large surveys in every country using costly ment is funded. Heijink et al. [22] found analogous im- and more often time-consuming face to face interviews pact of different valuation functions on QALYs. with techniques such as SG and TTO. To our know- ledge, this concept hasn’t been investigated properly yet, Conclusion but clearly it has a lot of potential value. Further re- In conclusion, this novel method of modelling utility func- search is underway to assess this. tions permitted the UK data to contribute considerable Experimental studies to develop valuations of health prior to the HK analysis. Consequently, estimates of the state descriptive systems like EQ-5D, HUI or SF-6D HK utilities for the various SF-6D health states could be need to be conducted in different countries and such generated much more precisely than would have been the work is costly and is potentially wasteful. The work pre- case if the data from HK study was used alone. It is likely sented here suggests how making use of the already that this will prove to allow the need for much smaller existing data as substantial prior information improve studies compared to what has been employed when devel- the accuracy of prediction, thereby reducing the number oping valuations for new countries. The promising results of states to be valued which in turn reduces the cost of suggest that existing preference data could be combined cross-country valuation. Work on the demonstration of with valuation study in a new country to generate prefer- this idea in a smaller country setting is still in progress. ence weights, making own country value sets more One limitation of this study is that, as many inter- achievable for low and middle income countries. national agencies recommend the use of country own Abbreviations value sets to generate QALYs, it is unclear whether a AQoL: Assessment of Quality of Life; EQ-5D: The EuroQol; HK: Hong Kong; value set generated using own country data modelled HRQoL: Health-related quality of life; HUI: Health Utilities Index; LN(.,.): Log- alongside another country’s dataset would be acceptable. Normal distribution; MLE: maximum likelihood estimator; MVH: Measurement and Valuation of Health; N(.,.): Normal distribution; QALYs: Quality adjusted life However, this may not be a concern if the estimates are years; QWB: Quality of well-being; RMSE: Root mean square error; SD: Standard accurate and the ordering of health states and location deviation; SF-6D: Short form 6 dimensions health survey; SG: Standard gamble; on the 1-0 full health-dead scale is similar to those TTO: Time trade-off; UK: United Kingdom; VAS: visual analogue scale achieved using a large scale valuation study. Acknowledgements Our basic model Eq. 1 has the potential to allow for SAK would like to thank the University Research Bureau at the American more than two countries to be analysed. Additionally, it University of Beirut, Lebanon for funding this study. Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 13 of 13 Funding 15. Kharroubi SA. Bayesian nonparametric estimation of EQ-5D utilities for This study was funded by the University Research Bureau at the American United States using the existing United Kingdom data. Health Qual Life University of Beirut, Lebanon. Outcomes. 2017;15:195. https://doi.org/10.1186/s12955-017-0770-1. 16. Brazier JE, Kolotkin RL, Crosby RD, Williams GR. Estimating a preference- Availability of data and materials based single index for the impact of weight on quality of life-lite (IWQOL- Publicly available datasets have been used for this study. lite) instrument from the SF-6D. Value Health. 2004;7(4):490–8. 17. Patrick DL, Starks HE, Cain KC, Uhlmann RF, Pearlman RA. Measuring Author’s contributions preferences for health states worse than death. Med Decis Mak. 1994;14:9–18. SAK has solely carried out the data analysis, wrote and approved the manuscript. 18. McGhee SM, Brazier J, CLK L, et al. Quality adjusted life years: population specific measurement of the quality component. Hong Kong Med. 2011; Authors’ information 17(Suppl.6):S17–21. SAK is an associate professor in Biostatistics based in the Department of 19. Kennedy MC, O’Hagan A. Bayesian calibration of computer models (with Nutrition and Food Sciences at the American University of Beirut. SAK’s discussion). J R Statist Soc B. 2001;63:425–64. research is in the theory and applications of Bayesian statistics. His main area 20. Schmidt AM, O’Hagan A. Bayesian inference for non-stationary spatial of research and consulting activity is in the theory of inference, covariance structure via spatial deformations. J R Stat Soc B. 2003;65:743–58. computational aspects of Bayesian statistics and in Bayesian modelling 21. Bland JM, Altman D. Statistical methods for assessing agreement between generally. He has been involved in many application areas, particularly in two methods of clinical measurement. Lancet. 1986;327(8476):307–10. medicine and Health Economics. 22. Heijink R, van Baal P, Opp M, Koolman X, Westert G. Decomposing cross- country differences in quality adjusted life expectancy: the impact of value Ethics approval and consent to participate sets. Popul Health Metrics. 2011;9:17. Secondary publicly available data were used in this study. Competing interests The author declares that he has no competing interests. Publisher’sNote Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Received: 3 January 2018 Accepted: 23 May 2018 References 1. Drummond MF, Sculpher M, O’Brien B, Stoddart GL, Torrance GW. Methods for the economic evaluation of health care programs. Oxford: Oxford medical publications; 2005. 2. Brooks R. EuroQol: the current state of play. Health Policy. 1996;37:53–72. 3. Torrance GW, Feeny DH, Furlong WJ, Barr RD, Zhang Y, Wang QA. Multi- attribute utility function for a comprehensive health status classification system: health utilities index mark 2. Med Care. 1996;34:702–22. 4. Feeny DH, Furlong WJ, Torrance GW, et al. Multi-attribute and single- attribute utility function for the health utility index mark 3 system. Med Care. 2002;40:113–28. 5. Hawthorne G, Richardson G, Atherton-Day N. A comparison of the assessment of quality of life (AQoL) with four other generic utility instruments. Ann Med. 2001;33:358–70. 6. Kaplan RM, Anderson JP. A general health policy model: update and application. Health Serv Res. 1988;23:203–35. 7. Brazier JE, Roberts J, Deverill M. The estimation of a preference-based measure of health from the SF-36. J Health Econ. 2002;21:271–92. 8. Rowen DL, Brazier J, Ara R, Azzabi Zouraq I. The role of condition-specific preference-based measures in health technology assessment. PharmacoEconomics. 2017;35(Suppl 1):33–41. 9. Kharroubi SA, O’Hagan A, Brazier J. A comparison of United States and United Kingdom EQ-5D health states valuations using a nonparametric Bayesian method. Stat Med. 2010;29(15):1622–34. 10. Johnson JA, Luo N, Shaw JW, Kind P, Coons SJ. Valuations of EQ-5D health states: are the United States and United Kingdom different? Med Care. 2005; 43:221–8. 11. Kharroubi SA, Brazier J, McGhee S. A comparison of Hong Kong and United Kingdom SF-6D health states valuations using a nonparametric Bayesian method. Value Health. 2014;17(4):397–405. 12. Kharroubi SA. A comparison of Japan and United Kingdom SF-6D health states valuations using a nonparametric Bayesian method. Applied Health Economics and Health Policy. 2015;13(4):409–20. 13. Kharroubi SA, O’Hagan A, Brazier JE. Estimating utilities from individual health state preference data: a nonparametric Bayesian approach. Appl Stat. 2005;54:879–95. 14. Kharroubi SA. Valuations of EQ-5D health states: could United Kingdom results be used as informative priors for United States. J Appl Stat. 2017; https://doi.org/10.1080/02664763.2017.1386770. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Health and Quality of Life Outcomes Springer Journals

Valuation of preference-based measures: can existing preference data be used to generate better estimates?

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Medicine & Public Health; Quality of Life Research; Quality of Life Research
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Abstract

Background: Experimental studies to develop valuations of health state descriptive systems like EQ-5D or SF-6D need to be conducted in different countries, because social and cultural differences are likely to lead to systematically different valuations. There is a scope utilize the evidence in one country to help with the design and the analysis of a study in another, for this to enable the generation of utility estimates of the second country much more precisely than would have been possible when collecting and analyzing the country’s data alone. Methods: We analyze SF-6D valuation data elicited from representative samples corresponding to the Hong Kong (HK) and United Kingdom (UK) general adult populations through the use of the standard gamble technique to value 197 and 249 health states respectively. We apply a nonparametric Bayesian model to estimate a HK value set using the UK dataset as informative prior to improve its estimation. Estimates are compared to a HK value set estimated using HK values alone using mean predictions and root mean square error. Results: The novel method of modelling utility functions permitted the UK valuations to contribute significant prior information to the Hong Kong analysis. The results suggest that using HK data alongside the existing UK data produces HK utility estimates better than using the HK study data by itself. Conclusion: The promising results suggest that existing preference data could be combined with valuation study in a new country to generate preference weights, making own country value sets more achievable for low and middle income countries. Further research is encouraged. Keywords: Preference-based health measure, Non-parametric Bayesian methods, Time trade-off, EQ-5D Background preference-based measure. Such a measure consists of a Health resource allocation is becoming increasingly im- classification system used to describe health (patients re- portant in an economic climate of increasing demands port their own health and this is assigned to a health on healthcare systems with constrained budgets. state using a classification system) and a value set that Economic evaluation using cost-utility analysis has generates a utility value for every health state defined by become widely popular technique internationally to the classification system. inform resource allocation decisions. Cost-utility analysis Among the large number of currently available measures benefits using Quality Adjusted Life Years preference-based measures of health-related quality of (QALYs), a measure that multiples a quality adjustment life (HRQoL) are the generic EuroQol five dimensional for health by the duration of that state of health [1]. The (EQ-5D) questionnaire [2], health utilities index 2 quality adjustment weight is generated using utility (HUI2) and 3 [3, 4], Assessment of Quality of Life values where 1 denotes full health and 0 denotes dead, (AQoL) [5], Quality of Well-being scale (QWB) [6], and and is most often generated using an existing the six-dimensional health state short form (derived from short-form 36 health survey) (SF- 6D) [7], though there are an increasing number of condition-specific Correspondence: sk157@aub.edu.lb measures available [8]. Department of Nutrition and Food Sciences, Faculty of Agricultural and Food Sciences, American University of Beirut, Beirut, Lebanon © The Author(s). 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated. Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 2 of 13 There is now an increasing number of datasets of pref- does not present new methodological developments, it erence data, where preferences have been elicited for the further accentuates the key point made in the Kharroubi same measure for different countries. Kharroubi et al. et al. [14, 15] articles, i.e. the good performance of the [9] use a novel nonparametric Bayesian approach to new modelling approach. model the disparities between the United States (US) First, SF-6D valuation surveys along with employed and UK which is simpler, better fitting and more appro- data corresponding to UK and HK are summarized here. priate for the data than the previously adopted conven- Second the Bayesian non-parametric model is described tional parametric model of Johnson et al. [10]. Such an and third the results are presented. Finally, the results approach has also been applied to the joint UK-Hong are discussed, including limitations and suggestions of Kong and UK-Japan SF-6D data set ([11], [12]). The possible future outlooks. nonparametric Bayesian model offers a major added ad- vantage as it permits the utilization of findings of coun- Methods try 1 to improve those of country 2, and as such The SF-6D generated utility estimates of the second country will be The SF-6D includes six health dimensions: physical more precise than would have been the case if that functioning, role limitation, social functioning, bodily country’s data was collected and analyzed on its own. pain, mental health and vitality, each with between four There are two distinct ways in which such a model and six levels [7]. Through the selection of one level may be useful. In the existence of large quantity of data from each dimension, physical functioning being the first pertaining to two countries, good estimates of popula- and vitality being the last, an SF-6D health state is de- tion utility functions corresponding to each country can fined. Different combinations result in 18,000 possible be generated through the analysis of data from each health states, which are associated with a six-digit de- country on its own (using the model of [13]) and this is scriptor ranging from 111,111 representing full health the best option. However, in case where a significant and 645,655 representing the worst possible state called quantity of data is available in one country but limited “the pits”. in another, there is a scope to borrow strength from country 1 in an effort to obtain better population utility The valuation survey and data set estimates for the second country than those generated UK when analyzing that second country’s data on its own. A sample of 249 health states is described through the Recently, Kharroubi [14, 15] developed a modified SF-6D and then valued by a representative sample of the nonparametric Bayesian statistical method that permits UK population (n = 836). Selection methods of respon- the utilization of evidence from one country as substan- dents along with health states are discussed elsewhere tial prior information for a study in another, and [7]. All the selected respondents have been asked to rank employed this method in the analysis of a valuation and value six health states according to the McMaster study for EQ-5D in US using the already existing UK ‘ping pong’ variant of the standard gamble (SG) tech- data. Crucial assumption underlying this analysis was nique. Accordingly, each of the five SF-6D health states that preferences of the UK population are in essence the was valued against the perfect health state and against same as those of the US in addition to that both coun- the “pits” by the respondents. As for the sixth question, tries have plenty of data. However, different countries it consisted of valuing the “pits” by determining whether have different population compositions, work, cultures they perceived it as worse or better than death by consid- and language. These can all impact on the relative values ering one of the following choices: (i) the certain prospect given to different dimensions of health (for example, of being in the “pits” state and the uncertain prospect of self-care and anxiety/depression) as well as where on the full health or immediate death; or (ii) the certain prospect 1-0 full health-dead scale each health state lies. of death and the uncertain prospect of full health or the The present paper seeks to explore the use of such a “pits” state [16]. Negative values were bounded at − 1, and model in the context of smaller countries with different they designate the states value as worse than death [17]. cultures. This is explored using a case study for SF-6D Then, the other 5 health states were chained onto the zero HK and UK data, where the health states valued in the to one scale, where 0 s designates the perceived equivalent HK valuation study are modelled using the already exist- to being dead, and 1 corresponds to perfect health [7]. As ing UK dataset, and the estimates are compared to the such, the dependent variables (y) in the models below cor- estimates generated modelling HK data alone. It should respond to the adjusted SG values. be noted that this method was used to model the US/ Of the original 836 respondents, a total of 225 respon- UK data (the Kharroubi et al. [14, 15] articles describe dents had to be excluded for several reasons. For in- this at length), and as such the method given in this art- stance, 130 respondents failed to value the “pits” state; icle is a replication of that method. Hence, though it consequently, the corresponding data couldn’tbe Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 3 of 13 processed any further [10]. Of the total 611 included re- We next let u(x) and u (x) be the utility functions UK spondents, 148 missing values from 117 respondents for health state x valued in the HK and UK experiments were present thereby resulting in a total of 3518 ob- respectively, Kharroubi [14] then model the prior distri- served SG valuations across the 249 health states. Details bution for u(x) as multivariate normal with mean de- pertaining to the valuation of the 249 SF-6D UK health fined as states can be found in [7]. EuðÞ ðÞ x ¼ EuðÞ ðÞ x þ γ þ β x ð2Þ UK Hong Kong and variance-covariance matrix The HK study comprised of a sample of 197 health states (selected according to the UK procedures) which were val- 0 2 0 covðÞ u ðÞ x ; u ðÞ xþσ cðÞ x; x ð3Þ UK UK ued using the same valuation procedures as those in the UK study [18]. Each respondent was asked to rank and where E(u (x)) is the expected value of the utility of UK value eight health states, and the interview procedure was health state x and cov(u (x), u (x′)) is the variance- UK UK modelled on the basis of that in the UK study. covariance matrix between u (x)and u (x′) for two dif- UK UK Out of the original 641 respondents, a total of 59 re- ferent states x and x′ in the UK experiment, both of which spondents were disqualified from the analysis according are readily available from the analysis of the UK study. to the same exclusion conditions as in the UK study [6] Given Eqs. 2 and 3, note that x represents a vector leaving 582 respondents’ data for analysis. Each of the consisting of discrete levels on each of the six health di- 582 respondents made 8 SG valuations, giving 4596 val- mensions and γ, β and σ are unknown parameters. If uations. Of these, 60 missing health state values were follows from Kharroubi [14] that the mean function of present and so 4596 observed SG valuations across 197 u(x) represents a prior expectation that the utility will health states were finally included in the analysis. Details be approximately a simple additive linear function of the pertaining to the valuation of the 197 SF-6D HK health dimension level in x. Additionally, the true function is states can be found in [18]. allowed to deviate around this mean according to its multivariate normal distribution, and so it can as a result Modelling assume any form. It is in this sense that the Bayesian The modelling approach is described in Kharroubi [14], model is described as nonparametric. Furthermore, there where a nonparametric Bayesian model was employed in seem to be a high correlation c(x,x′) between u(x) and the modelling of the US EQ-5D dataset using the already u(x′) when x and x′ are close enough, and is given by existing UK dataset as informative prior. In this article, no we follow on from its work to examine whether the X 0 0 cðÞ x; x ¼ exp − b x −x ð4Þ d d adoption of HK health states, while drawing extra infor- d mation from the UK data, generates better estimation than analyzing the HK sample by itself. The estimates where b is a roughness parameter in the dimension d are compared using different prediction criterion, in- that controls the extent to which the true utility function cluding predicted versus actual mean health states valua- is anticipated to adhere to a linear form in a dimension tions, mean predicted error and root mean square error. d. It is to be noted that many other choices have been Kharroubi [14] propose the following model made for this covariance matrix; see for example [19]or [20], but the resulting estimates are not generally sensi- y ¼ 1−α 1−u x þ ε ð1Þ j ij ij tive to the change of this function. However, the pro- ij posed form is appropriate here [13]. See Kharroubi et al. Where, for i = 1,2,…,I and j = 1,2,…,J, x is the i-th j ij [14] for more details on this. health state valued by the respondent j in the HK experi- Finally, it is to be noted that the novel method of ment,y is the respondent j’s time trade-off (TTO) valu- ij modelling utility function u(x), represented by adding ation for that health state i, α is a term to allow for the two terms E(u (x)) and cov(u (x), u (x′)) in Eqs. UK UK UK individual characteristics of respondent j and ε is a ran- ij 2 and 3, allows the already existing UK evidence to con- dom error term. Let t be a vector of covariates repre- tribute significant prior knowledge to the HK study. In senting individual characteristics of respondent j, other words, the posterior density of the UK utility func- Kharroubi [14] propose the following distributions: tion was treated as a prior density to analyse the new study in the HK. T 2 2 α  LN t γ; τ and ε  N 0; υ : j ij Full theory of the Bayesian approach here is dis- cussed in Kharroubi [14]. Programs to undertake the where γ is the vector of coefficients for the covariates Bayesian approach were written in Matlab and are 2 2 and τ and v are further parameters to be estimated. available on request. Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 4 of 13 Results in the sample along with the perfect health, sorted via the The new modelling approach is now applied to the ana- predicted valuations. Figure 1a shows the predicted lysis of SF-6D HK study using the previously existing (squared line) and actual (diamond marked line) mean val- UK study (to be indicated by HK/UK model hereinafter). uations using the HK model. The line marked with trian- From a Bayesian prospective, the old posterior contains gles denotes the errors computed based on the difference all that we know before seeing the new data, and so be- between the two valuations. Figure 1b shows the corre- comes the new prior distribution. Thus for our analysis, sponding results obtained using HK/UK model. Based on the posterior of the UK utility function becomes our the plots it is apparent that the estimates of the HK/UK prior for the analysis of the HK study. The estimates are utilities for the various SF-6D health states are much more compared to those estimated using the HK data exclud- precise than those corresponding to the HK only results. ing the UK data (to be indicated by HK model herein- These plots also reveal the HK model tends to under pre- after) using different prediction criterion, including dict at low health state values (meaning the poor health predicted versus actual mean health states valuations, states). However, this is not the case for the HK/UK model. mean predicted error, root mean square error along with Additionally, the plots suggest that the variations of the the Bland-Altman agreement plots [21]. predictions are larger and so a high fluctuation and Figure 1 shows the HK predicted and observed mean non-steady trend of the difference line, so this suggests that valuations corresponding to the 197 health states evaluated the HK/UK model is less susceptible to systematic bias. Fig. 1 Sample mean and predicted health states valuations for a the HK model and b the HK/UK model Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 5 of 13 Figure 2a and b depict the Bland–Altman agreement the HK/UK model is much smaller (0.0416) as compared plots for HK and HK/UK models. In this context, the dif- to that corresponding to the HK model (0.0503), thereby ference between the observed and predicted mean valua- vindicating the variations of the differences in Fig. 2a.On tions is plotted against the mean of the difference (or the the other hand, the HK/UK model differences are well val- average bias). The solid line corresponds to the mean bias, idated as observed in Fig. 2b. whereas the dotted lines depict the 95% limits of agree- Table 1 provides the inferences for the utilities of the ment. For better visual judgment of how good the two val- 197 states evaluated in the study along with the perfect uations agree, the 95% limits-of-agreement lines are health. Table 1 displays the actual mean, the standard error drawn. The narrower the range between these two limits, corresponding to each health state for both models. The the better the agreement is. When comparing these two results for the population utilities from the UK that were figures, we see that the HK/UK model reveals a better treated as prior information in the HK/UK model are also agreement as the length of the 95% limits of agreement is provided. As depicted all through the 197 health states 0.163, i.e. narrower than that of the HK model of length (excluding the perfect health state) presented in Table 1,it 0.197. Additionally, the difference in mean bias between is evident that the HK/UK model has a better predictive the two models is also obvious, with values of 0.0116 for performance compared to the HK model overall, and as a the HK/UK model and 0.0175 for the HK model. More- results it has a root mean square error (RMSE) of 0.045 over, the differences standard deviation corresponding to whereas the HK model has an RMSE of 0. 051. Fig. 2 Bland-Altman agreement plots for a the HK model and b the HK/UK model Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 6 of 13 Table 1 Posterior inferences for utilities of the 197 health states valued in the empirical survey along with the perfect health State X Observed mean UK results HK Model HK/UK Model Posterior mean Posterior SD Posterior mean Posterior SD Posterior mean Posterior SD 111111 1 1 0 1 0 1 0 111621 0.6492 0.7482 0.0345 0.6322 0.029 0.6652 0.0267 111645 0.5055 0.6169 0.0586 0.5568 0.0281 0.5384 0.0316 112153 0.6519 0.691 0.0577 0.6681 0.0293 0.6524 0.0326 112455 0.6777 0.6078 0.0515 0.635 0.0298 0.6274 0.0325 112613 0.7305 0.7049 0.0612 0.6636 0.0321 0.674 0.0364 112651 0.6288 0.6342 0.0614 0.6182 0.0335 0.5919 0.0366 113141 0.8022 0.7581 0.0643 0.7665 0.0287 0.7633 0.0322 113352 0.7441 0.6776 0.0523 0.7304 0.0262 0.7253 0.0282 113411 0.7324 0.7284 0.031 0.7208 0.0287 0.701 0.0255 113615 0.6685 0.6415 0.0677 0.6308 0.0334 0.6125 0.0401 113634 0.64 0.6017 0.0535 0.5971 0.0305 0.5902 0.0352 114631 0.7057 0.6754 0.056 0.6418 0.0343 0.6467 0.0376 115131 0.7243 0.7695 0.0704 0.7203 0.029 0.7193 0.0317 115211 0.7951 0.7738 0.0561 0.7739 0.0309 0.7802 0.0327 115251 0.6223 0.7148 0.074 0.6427 0.0287 0.6329 0.0318 115314 0.6788 0.779 0.0545 0.6585 0.0312 0.6731 0.0347 115355 0.5346 0.5859 0.0563 0.5649 0.0306 0.5396 0.0347 115432 0.6201 0.7091 0.06 0.6673 0.0265 0.6696 0.0287 115653 0.5728 0.5652 0.0561 0.5189 0.0308 0.494 0.0325 121212 0.8253 0.8275 0.0261 0.8452 0.0249 0.8259 0.0233 122233 0.6894 0.7475 0.034 0.6882 0.0273 0.6888 0.0273 122425 0.704 0.6784 0.0353 0.6764 0.0262 0.683 0.0268 124125 0.612 0.7292 0.0475 0.6194 0.0279 0.6158 0.029 125143 0.6505 0.6892 0.053 0.6515 0.0284 0.649 0.0301 125625 0.5478 0.5779 0.0663 0.5187 0.0326 0.4992 0.0374 131151 0.7621 0.7402 0.0725 0.7591 0.0293 0.767 0.0331 131331 0.7638 0.7629 0.0522 0.7103 0.0292 0.7071 0.0326 131542 0.7067 0.6181 0.0304 0.6407 0.0276 0.6118 0.0269 131555 0.5327 0.5832 0.0544 0.5345 0.0313 0.521 0.0349 132524 0.5983 0.6574 0.037 0.5944 0.0265 0.5819 0.0274 133132 0.7425 0.6942 0.0343 0.7093 0.0266 0.6978 0.0263 135155 0.6251 0.5947 0.0639 0.5928 0.032 0.5747 0.0365 135312 0.7 0.6992 0.0488 0.6814 0.0272 0.6802 0.0283 135435 0.655 0.5664 0.063 0.6194 0.0291 0.6114 0.0327 135633 0.5085 0.5848 0.0613 0.5205 0.0304 0.5014 0.0353 141215 0.7089 0.7227 0.0698 0.6916 0.0303 0.6843 0.035 142113 0.6585 0.6911 0.0543 0.7071 0.0277 0.6917 0.0294 142154 0.6821 0.6844 0.0373 0.6494 0.0281 0.6444 0.0274 142335 0.6654 0.6536 0.0529 0.6164 0.0294 0.6 0.0332 143641 0.5733 0.6151 0.0506 0.5495 0.0329 0.5461 0.0349 143654 0.5028 0.5487 0.0585 0.5145 0.0306 0.5018 0.0341 144341 0.5565 0.72 0.0279 0.5856 0.0275 0.6026 0.0243 Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 7 of 13 Table 1 Posterior inferences for utilities of the 197 health states valued in the empirical survey along with the perfect health (Continued) State X Observed mean UK results HK Model HK/UK Model Posterior mean Posterior SD Posterior mean Posterior SD Posterior mean Posterior SD 144455 0.5676 0.5356 0.0643 0.5839 0.0299 0.5768 0.0352 144613 0.6916 0.6501 0.0583 0.6136 0.0334 0.6147 0.0385 145515 0.5903 0.617 0.0735 0.5834 0.0322 0.5786 0.0371 145621 0.6093 0.6233 0.0645 0.6026 0.0315 0.5952 0.0361 145645 0.5814 0.5077 0.0715 0.5391 0.0316 0.5427 0.0347 145652 0.5291 0.5334 0.0678 0.4771 0.0328 0.4634 0.0385 211111 0.8584 0.9197 0.0215 0.9219 0.0181 0.836 0.0205 211251 0.6738 0.7049 0.0631 0.6901 0.0278 0.6763 0.0299 211615 0.6206 0.6781 0.0713 0.6458 0.0307 0.6372 0.0357 211633 0.7051 0.6622 0.0527 0.62 0.0319 0.6129 0.0354 212145 0.6188 0.6927 0.0446 0.5961 0.0277 0.5851 0.0279 213323 0.6571 0.7761 0.0296 0.6767 0.0228 0.6946 0.0226 214435 0.5943 0.6291 0.0401 0.6097 0.0272 0.5997 0.0293 221452 0.6627 0.6237 0.0459 0.6727 0.0261 0.6585 0.0279 224612 0.6385 0.6256 0.0392 0.6217 0.0288 0.5986 0.0298 232111 0.7796 0.6987 0.0377 0.7564 0.0273 0.7304 0.0264 235224 0.6506 0.6486 0.0335 0.632 0.0271 0.6042 0.0274 241135 0.5824 0.702 0.0601 0.5989 0.0297 0.5758 0.0327 241531 0.6643 0.702 0.0352 0.6189 0.0275 0.625 0.027 243433 0.5053 0.702 0.0351 0.5941 0.0259 0.6017 0.026 243615 0.5913 0.6257 0.0643 0.5651 0.0301 0.5659 0.0332 244353 0.6976 0.61 0.0413 0.5863 0.0307 0.6613 0.034 311654 0.6581 0.5391 0.0452 0.5414 0.0336 0.6066 0.0365 312332 0.701 0.7472 0.0285 0.7068 0.0241 0.7146 0.0229 315123 0.5582 0.8043 0.0542 0.5361 0.0312 0.531 0.0325 315235 0.6161 0.7018 0.0542 0.5866 0.0291 0.585 0.0329 315341 0.6486 0.7105 0.0618 0.592 0.0307 0.5796 0.0359 315515 0.6064 0.6642 0.0363 0.5686 0.0295 0.5675 0.029 321122 0.7987 0.7638 0.0266 0.7525 0.0256 0.7451 0.0239 323644 0.4377 0.5362 0.0287 0.4567 0.0298 0.4148 0.0269 324155 0.6248 0.6015 0.0479 0.5536 0.0334 0.6095 0.0374 325433 0.5685 0.6875 0.0451 0.5845 0.0262 0.5754 0.0294 331115 0.6584 0.7288 0.0598 0.6649 0.0275 0.6621 0.0297 332411 0.6152 0.7217 0.0376 0.6523 0.0246 0.6607 0.0246 333135 0.631 0.6657 0.0349 0.6219 0.0284 0.6249 0.0278 333455 0.6131 0.5504 0.0448 0.5588 0.0315 0.5438 0.0352 334251 0.5031 0.6761 0.0532 0.5621 0.0266 0.5547 0.0289 341123 0.7389 0.7009 0.0393 0.6653 0.0296 0.6685 0.0289 341251 0.6023 0.679 0.067 0.6064 0.0307 0.59 0.0339 341414 0.7513 0.6751 0.0574 0.6503 0.0317 0.6535 0.0363 341634 0.5209 0.6174 0.0409 0.5463 0.0297 0.5454 0.0295 341651 0.6015 0.5904 0.0633 0.5401 0.0325 0.5338 0.0352 Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 8 of 13 Table 1 Posterior inferences for utilities of the 197 health states valued in the empirical survey along with the perfect health (Continued) State X Observed mean UK results HK Model HK/UK Model Posterior mean Posterior SD Posterior mean Posterior SD Posterior mean Posterior SD 342613 0.6672 0.6342 0.0526 0.589 0.0299 0.583 0.0334 343425 0.6307 0.6443 0.0405 0.5981 0.0284 0.5881 0.0303 344633 0.5002 0.6267 0.0395 0.493 0.0299 0.4787 0.0319 345153 0.4966 0.5875 0.0578 0.5378 0.0287 0.5242 0.0311 345355 0.4751 0.5101 0.0557 0.5036 0.0285 0.4895 0.0321 345411 0.6347 0.6506 0.0533 0.6302 0.0303 0.6019 0.0344 345535 0.6564 0.5436 0.0561 0.5377 0.0317 0.6356 0.036 345553 0.4538 0.5276 0.0527 0.4548 0.0307 0.4436 0.0345 411612 0.6595 0.6584 0.0634 0.6355 0.0305 0.6314 0.0332 412152 0.608 0.6558 0.0371 0.5804 0.0254 0.5715 0.0256 413212 0.6879 0.7402 0.0485 0.678 0.028 0.6757 0.0298 414355 0.5976 0.6335 0.0478 0.5634 0.0294 0.5588 0.0317 414522 0.7007 0.6612 0.0301 0.626 0.0303 0.6929 0.0299 415115 0.6264 0.7271 0.0617 0.5911 0.0321 0.592 0.0359 415313 0.5055 0.7889 0.0501 0.5672 0.0263 0.5795 0.0289 415453 0.5826 0.6483 0.0557 0.5458 0.0301 0.5477 0.0328 415651 0.5347 0.5696 0.069 0.4882 0.0334 0.474 0.0377 415655 0.4739 0.5087 0.0623 0.4259 0.0347 0.4026 0.0396 421314 0.6607 0.6689 0.0368 0.658 0.0253 0.6495 0.0261 421455 0.4016 0.6127 0.0383 0.5198 0.0275 0.4093 0.0286 421641 0.6118 0.635 0.0577 0.5533 0.0316 0.5464 0.0354 423435 0.6172 0.5985 0.0435 0.5564 0.0297 0.5321 0.0338 423615 0.6373 0.5506 0.0581 0.5312 0.0323 0.6111 0.038 425131 0.5312 0.6771 0.0551 0.5876 0.0253 0.5817 0.0273 431443 0.5838 0.638 0.0339 0.5927 0.0261 0.5889 0.0261 432621 0.6423 0.6468 0.0487 0.5754 0.0292 0.5735 0.0337 434211 0.6601 0.7068 0.0466 0.6409 0.0302 0.6375 0.0327 435335 0.6579 0.57 0.0499 0.5929 0.0295 0.5788 0.0337 441255 0.5133 0.5918 0.0522 0.5271 0.0324 0.5042 0.0346 441331 0.557 0.7049 0.0434 0.5765 0.0277 0.5772 0.0282 441615 0.4883 0.5871 0.0633 0.5209 0.0303 0.5033 0.0334 442655 0.353 0.5227 0.0536 0.4346 0.0301 0.4359 0.0327 443215 0.5719 0.6548 0.0352 0.5981 0.0272 0.5845 0.0267 443652 0.4431 0.5548 0.0564 0.4242 0.0312 0.4127 0.0353 444611 0.6854 0.6028 0.0592 0.5974 0.0312 0.5983 0.0345 445145 0.3405 0.552 0.0525 0.4903 0.0273 0.3726 0.0307 445233 0.4914 0.6384 0.0434 0.5801 0.0267 0.5741 0.0282 445615 0.4775 0.5487 0.0653 0.4665 0.0327 0.4409 0.0363 445641 0.5364 0.5241 0.0641 0.4739 0.033 0.4687 0.0378 511114 0.6239 0.6993 0.0379 0.64 0.0281 0.6376 0.0276 511435 0.6804 0.654 0.0546 0.6422 0.0298 0.6613 0.0306 511615 0.5991 0.5818 0.0725 0.5918 0.0313 0.5879 0.0372 Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 9 of 13 Table 1 Posterior inferences for utilities of the 197 health states valued in the empirical survey along with the perfect health (Continued) State X Observed mean UK results HK Model HK/UK Model Posterior mean Posterior SD Posterior mean Posterior SD Posterior mean Posterior SD 511633 0.5805 0.5918 0.0611 0.5599 0.0298 0.5497 0.0349 512242 0.6013 0.6906 0.0324 0.5932 0.0255 0.5972 0.0261 513654 0.4584 0.5474 0.0525 0.4182 0.0328 0.4126 0.0361 515155 0.6677 0.5927 0.0618 0.5675 0.0348 0.6586 0.0395 522321 0.7164 0.6846 0.0324 0.6844 0.0264 0.6776 0.026 523551 0.6141 0.6201 0.0471 0.5167 0.0314 0.5206 0.0334 531635 0.5015 0.5323 0.0345 0.5003 0.0292 0.4633 0.0299 533415 0.5342 0.5848 0.0533 0.5228 0.0288 0.5086 0.0329 534113 0.5076 0.7106 0.0437 0.5266 0.0283 0.528 0.0293 541451 0.5194 0.6153 0.0626 0.5266 0.0286 0.5256 0.0325 543533 0.4771 0.674 0.0365 0.4745 0.0293 0.4834 0.0303 545115 0.5171 0.6074 0.0662 0.5582 0.0295 0.5545 0.0325 545151 0.5136 0.5474 0.0686 0.5256 0.0291 0.5225 0.0329 545353 0.5103 0.5243 0.0492 0.4303 0.0326 0.4147 0.0358 545422 0.6088 0.6351 0.0322 0.5954 0.0253 0.5688 0.0276 611154 0.5961 0.658 0.0636 0.5557 0.0329 0.5629 0.0354 611221 0.681 0.6667 0.0521 0.654 0.0319 0.6183 0.0344 611432 0.4712 0.6454 0.05 0.5706 0.0267 0.5654 0.0281 611454 0.3346 0.6146 0.0608 0.4466 0.0286 0.3353 0.0316 611621 0.5816 0.6112 0.0699 0.5529 0.0319 0.5447 0.0349 611645 0.4649 0.5249 0.0688 0.4731 0.031 0.4577 0.0354 611652 0.5207 0.5638 0.0616 0.437 0.034 0.4247 0.0383 612415 0.4566 0.5872 0.0632 0.5267 0.0292 0.5128 0.0327 613625 0.3453 0.5321 0.0646 0.4299 0.0298 0.4105 0.0345 614135 0.5587 0.6619 0.057 0.5224 0.0331 0.5247 0.0368 614434 0.4449 0.6497 0.0383 0.4615 0.0281 0.4682 0.0286 615253 0.6248 0.5737 0.0566 0.5308 0.0342 0.5269 0.0391 615315 0.5634 0.642 0.0628 0.5097 0.0334 0.5097 0.0369 615412 0.4129 0.6469 0.0544 0.5182 0.0282 0.5084 0.031 615451 0.4431 0.5666 0.0689 0.4499 0.0324 0.4353 0.0362 615455 0.4993 0.5404 0.0645 0.4753 0.0327 0.4723 0.0373 615614 0.4344 0.5683 0.0701 0.4885 0.0317 0.4952 0.0343 615631 0.5056 0.5247 0.0664 0.4574 0.0347 0.4338 0.0397 615653 0.381 0.5127 0.0681 0.356 0.0349 0.3388 0.039 621135 0.4934 0.6645 0.0605 0.5417 0.0291 0.535 0.032 622513 0.5108 0.5809 0.0392 0.529 0.0265 0.5069 0.0276 623155 0.4501 0.5938 0.0598 0.4784 0.0315 0.4631 0.0356 623353 0.4256 0.5718 0.043 0.4528 0.0318 0.4181 0.0346 624431 0.5694 0.5912 0.0379 0.53 0.0319 0.4933 0.033 624633 0.3082 0.551 0.0475 0.4345 0.0291 0.3316 0.0317 625141 0.5605 0.5561 0.0466 0.5398 0.0287 0.5047 0.0316 631315 0.5806 0.6157 0.0577 0.5403 0.0326 0.5223 0.0353 Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 10 of 13 Table 1 Posterior inferences for utilities of the 197 health states valued in the empirical survey along with the perfect health (Continued) State X Observed mean UK results HK Model HK/UK Model Posterior mean Posterior SD Posterior mean Posterior SD Posterior mean Posterior SD 631333 0.6175 0.6386 0.0462 0.5443 0.0315 0.5336 0.0354 631355 0.4479 0.5823 0.0354 0.4765 0.0287 0.4666 0.0285 631632 0.4974 0.5525 0.0519 0.5252 0.0307 0.5102 0.0345 632615 0.5484 0.5202 0.0608 0.4831 0.0307 0.4872 0.0349 633122 0.4986 0.6515 0.0338 0.5131 0.0278 0.5084 0.0266 633535 0.3343 0.5378 0.0419 0.3942 0.0303 0.3791 0.0336 633653 0.4335 0.5395 0.0522 0.3644 0.0335 0.3776 0.0378 635611 0.4001 0.5522 0.0674 0.4736 0.0314 0.4538 0.0347 635651 0.4884 0.4829 0.0732 0.3799 0.0378 0.4841 0.044 641114 0.6165 0.6874 0.0653 0.6008 0.0313 0.6049 0.0335 641132 0.4794 0.6094 0.0542 0.5182 0.0312 0.4904 0.034 641154 0.545 0.5742 0.064 0.5188 0.0339 0.5143 0.0374 641211 0.6294 0.6567 0.0652 0.5718 0.0348 0.5505 0.0385 641654 0.4842 0.5225 0.0658 0.4347 0.0348 0.4418 0.0392 642151 0.5356 0.5776 0.0712 0.5119 0.0318 0.5009 0.0351 642313 0.5499 0.6834 0.0541 0.5278 0.0311 0.5332 0.0334 642453 0.5104 0.5844 0.054 0.4419 0.0326 0.4334 0.0366 642612 0.4496 0.5594 0.0336 0.4965 0.0282 0.4698 0.0289 642651 0.3731 0.5104 0.0707 0.4346 0.0308 0.4282 0.035 643,125 0.5007 0.6217 0.0556 0.4801 0.033 0.4661 0.0371 643143 0.463 0.6039 0.0531 0.4581 0.0321 0.4588 0.0333 644614 0.4387 0.5614 0.0573 0.4161 0.0321 0.4004 0.0376 644631 0.416 0.533 0.0623 0.4415 0.0313 0.4276 0.0352 645132 0.601 0.577 0.0517 0.5009 0.0352 0.5749 0.0384 645154 0.4948 0.5184 0.0614 0.396 0.0334 0.4765 0.0379 645235 0.3724 0.551 0.0592 0.4562 0.0299 0.4649 0.0339 645415 0.6023 0.5517 0.069 0.4761 0.0354 0.5666 0.0407 645441 0.4085 0.5106 0.0632 0.4309 0.0314 0.4094 0.0351 645655 0.067 0.3575 0.0186 0.0983 0.0226 0.0708 0.0251 SD Standard Deviation Additionally, Table 1 indicates other noteworthy dif- a result of selecting one health state at random from ferences between the HK and HK/UK models. For the these 6-12 states, 10,000 adjacent pairs were obtained. pits state, for instance, the HK model predicts a value Out of these 10,000 adjacent pairs, 20% display of 0.0983 albeit the actual average for this state is non-monotonicity in the HK model compared to 10% 0.067, whereas the HK/UK model attains a value of for the HK/UK model. 0.0708. Furthermore, the standard deviations corre- A more apparent presentation of the differences be- sponding to the HK/UK model are smaller as a result tween the HK and HK/UK models is shown in Fig. 3, of using the UK results as priors thereby providing a which depicts the fitted values corresponding to the HK better estimate. Differences in performance based on model (Fig. 3a) and the HK/UK model (Fig. 3b) against monotonicity are also apparent. Of the total 18,000 the observed of the 198 health states, as well as the per- health states defined by the SF-6D descriptive system, fect predictions given by a 45° unity line (solid line). 10,000 health states were sampled at random without Theoretically, the fitted values from the two models are replacement. In theory, there are 6–12 health states expected to lie roughly on the unity line. When compar- adjacent to each state of the 10,000 health. Then, as ing these two plots, it is clear from Fig. 3b that estimates Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 11 of 13 Fig. 3 Sample mean and predicted health states valuations for a the HK model and b the HK/UK model from the HK/UK model tend to be more proximate to evaluate the new HK study. The method given here is a the perfect predictions line, in contrast to Fig. 3a, which replication of that used in modelling the US/UK data depicts a larger scatter and the valuations deviate largely (the Kharroubi et al. [14, 15] articles describe this fully). from the 45°theoretical line. As a result, we emphasize Hence, though it does not present new methodological the fact that the HK/UK model provides predictions developments, it further accentuates the key point made much more precisely than the HK model. in the Kharroubi et al. [14, 15] articles, i.e. the good per- formance of the new modelling approach. Discussion Crucial assumption underlying the US/UK analyses In this paper, we have applied a nonparametric Bayesian (Kharroubi et al. [14, 15]) was that preferences of the model to estimate the utility values of health states UK population are in essence the same as those of the based on the SF-6D descriptive system. This model was US; in addition to that both countries have plenty of undertaken in an effort to use the already existing infor- data. The novelty of the analysis presented here was to mation from one country to serve as an informative explore the use of new modelling in the context of prior for a study in another. The methodology was ap- smaller countries with different population composi- plied to the HK SF-6D data set using the already avail- tions, work, cultures, language, all of which can impact able UK valuation, whereby the posterior of the UK on the relative values given to different dimensions of utility function was used as a substantial prior to health (for example, self-care and anxiety/depression) as Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 12 of 13 well as where on the 1-0 full health-dead scale each would be possible to generalize Eqs. 2 and 3 to handle health state lies. This is explored using a case study for more than two countries. Indeed, we can generalize fur- SF-6D HK and UK data, where the HK valuations are ther to a generic form modelled using the already existing UK dataset and the X n 0 EuðÞ ðÞ x ¼ EuðÞ ðÞ x þ γ þ β x estimates are compared to the estimates generated mod- k¼1 elling HK data alone. It is shown that the new modelling and variance-covariance matrix of the utility function permitted the already existing UK dataset to contribute significant prior belief to the HK n 0 2 0 covðÞ u ðÞ x ; u ðÞ xþ σ cðÞ x; x k k k¼1 analysis, and for this to enable the generalisability of this approach by making use of experience in a European where Eðu ðxÞÞ is the total mean utility of health k¼1 country to aid the analysis of a study in another Asian state x and covðu ðxÞ; u ðx ÞÞ is the total variance- k k k¼1 country. Consequently, much more precise estimates of covariance matrix between u (x)and u (x′)fortwodiffer- k k the HK utilities corresponding to the various SF-6D ent states x and x′, all of which are readily available from health states were obtained using the HK/UK model the analysis of the n available countries data. than would have been the case if the data from HK study A final note regarding the potential impact of our was used on its own, yet respect the inherent monoton- study in terms of health and quality of life gains: Note icity of the underlying utility measure even further. from Table 1 that health state 635,651, for instance, has Cautious model diagnostics affirm that the HK/UK an estimated health state utility value of 0.3799 from the model performs well and better than the HK model. HK model and 0.4841 from the HK/UK model. Thus, The nonparametric Bayesian model offers a major the difference in utility estimates is nearly 0.11. This added advantage: in the existence of lots of data on one could bring about an shift in QALYs from a treatment country and limited on another, it permits the utilization that prolongs life by 1 yr from 0.5 to 0.61. This implies of results of country 1 to improve those of country 2, that if a treatment costs 12,000, for example, the cost and as such generated utility estimates of the second per QALY would decrease from £24,000 to £19,672, country will be much more precise than would have thereby it below the cost effectiveness threshold used by been the case if that country’s data was collected and an- National Institute for Health and Clinical Excellence. In alyzed on its own. This in turn reduces the need for other words, it could influence whether or not a treat- undertaking large surveys in every country using costly ment is funded. Heijink et al. [22] found analogous im- and more often time-consuming face to face interviews pact of different valuation functions on QALYs. with techniques such as SG and TTO. To our know- ledge, this concept hasn’t been investigated properly yet, Conclusion but clearly it has a lot of potential value. Further re- In conclusion, this novel method of modelling utility func- search is underway to assess this. tions permitted the UK data to contribute considerable Experimental studies to develop valuations of health prior to the HK analysis. Consequently, estimates of the state descriptive systems like EQ-5D, HUI or SF-6D HK utilities for the various SF-6D health states could be need to be conducted in different countries and such generated much more precisely than would have been the work is costly and is potentially wasteful. The work pre- case if the data from HK study was used alone. It is likely sented here suggests how making use of the already that this will prove to allow the need for much smaller existing data as substantial prior information improve studies compared to what has been employed when devel- the accuracy of prediction, thereby reducing the number oping valuations for new countries. The promising results of states to be valued which in turn reduces the cost of suggest that existing preference data could be combined cross-country valuation. Work on the demonstration of with valuation study in a new country to generate prefer- this idea in a smaller country setting is still in progress. ence weights, making own country value sets more One limitation of this study is that, as many inter- achievable for low and middle income countries. national agencies recommend the use of country own Abbreviations value sets to generate QALYs, it is unclear whether a AQoL: Assessment of Quality of Life; EQ-5D: The EuroQol; HK: Hong Kong; value set generated using own country data modelled HRQoL: Health-related quality of life; HUI: Health Utilities Index; LN(.,.): Log- alongside another country’s dataset would be acceptable. Normal distribution; MLE: maximum likelihood estimator; MVH: Measurement and Valuation of Health; N(.,.): Normal distribution; QALYs: Quality adjusted life However, this may not be a concern if the estimates are years; QWB: Quality of well-being; RMSE: Root mean square error; SD: Standard accurate and the ordering of health states and location deviation; SF-6D: Short form 6 dimensions health survey; SG: Standard gamble; on the 1-0 full health-dead scale is similar to those TTO: Time trade-off; UK: United Kingdom; VAS: visual analogue scale achieved using a large scale valuation study. Acknowledgements Our basic model Eq. 1 has the potential to allow for SAK would like to thank the University Research Bureau at the American more than two countries to be analysed. Additionally, it University of Beirut, Lebanon for funding this study. Kharroubi Health and Quality of Life Outcomes (2018) 16:116 Page 13 of 13 Funding 15. Kharroubi SA. Bayesian nonparametric estimation of EQ-5D utilities for This study was funded by the University Research Bureau at the American United States using the existing United Kingdom data. Health Qual Life University of Beirut, Lebanon. Outcomes. 2017;15:195. https://doi.org/10.1186/s12955-017-0770-1. 16. Brazier JE, Kolotkin RL, Crosby RD, Williams GR. Estimating a preference- Availability of data and materials based single index for the impact of weight on quality of life-lite (IWQOL- Publicly available datasets have been used for this study. lite) instrument from the SF-6D. Value Health. 2004;7(4):490–8. 17. Patrick DL, Starks HE, Cain KC, Uhlmann RF, Pearlman RA. Measuring Author’s contributions preferences for health states worse than death. Med Decis Mak. 1994;14:9–18. SAK has solely carried out the data analysis, wrote and approved the manuscript. 18. McGhee SM, Brazier J, CLK L, et al. Quality adjusted life years: population specific measurement of the quality component. Hong Kong Med. 2011; Authors’ information 17(Suppl.6):S17–21. SAK is an associate professor in Biostatistics based in the Department of 19. Kennedy MC, O’Hagan A. Bayesian calibration of computer models (with Nutrition and Food Sciences at the American University of Beirut. SAK’s discussion). J R Statist Soc B. 2001;63:425–64. research is in the theory and applications of Bayesian statistics. His main area 20. Schmidt AM, O’Hagan A. Bayesian inference for non-stationary spatial of research and consulting activity is in the theory of inference, covariance structure via spatial deformations. J R Stat Soc B. 2003;65:743–58. computational aspects of Bayesian statistics and in Bayesian modelling 21. Bland JM, Altman D. Statistical methods for assessing agreement between generally. He has been involved in many application areas, particularly in two methods of clinical measurement. Lancet. 1986;327(8476):307–10. medicine and Health Economics. 22. Heijink R, van Baal P, Opp M, Koolman X, Westert G. Decomposing cross- country differences in quality adjusted life expectancy: the impact of value Ethics approval and consent to participate sets. Popul Health Metrics. 2011;9:17. Secondary publicly available data were used in this study. Competing interests The author declares that he has no competing interests. Publisher’sNote Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Received: 3 January 2018 Accepted: 23 May 2018 References 1. Drummond MF, Sculpher M, O’Brien B, Stoddart GL, Torrance GW. Methods for the economic evaluation of health care programs. Oxford: Oxford medical publications; 2005. 2. Brooks R. EuroQol: the current state of play. Health Policy. 1996;37:53–72. 3. Torrance GW, Feeny DH, Furlong WJ, Barr RD, Zhang Y, Wang QA. Multi- attribute utility function for a comprehensive health status classification system: health utilities index mark 2. Med Care. 1996;34:702–22. 4. Feeny DH, Furlong WJ, Torrance GW, et al. Multi-attribute and single- attribute utility function for the health utility index mark 3 system. Med Care. 2002;40:113–28. 5. Hawthorne G, Richardson G, Atherton-Day N. A comparison of the assessment of quality of life (AQoL) with four other generic utility instruments. Ann Med. 2001;33:358–70. 6. Kaplan RM, Anderson JP. A general health policy model: update and application. Health Serv Res. 1988;23:203–35. 7. Brazier JE, Roberts J, Deverill M. The estimation of a preference-based measure of health from the SF-36. J Health Econ. 2002;21:271–92. 8. Rowen DL, Brazier J, Ara R, Azzabi Zouraq I. The role of condition-specific preference-based measures in health technology assessment. PharmacoEconomics. 2017;35(Suppl 1):33–41. 9. Kharroubi SA, O’Hagan A, Brazier J. A comparison of United States and United Kingdom EQ-5D health states valuations using a nonparametric Bayesian method. Stat Med. 2010;29(15):1622–34. 10. Johnson JA, Luo N, Shaw JW, Kind P, Coons SJ. Valuations of EQ-5D health states: are the United States and United Kingdom different? Med Care. 2005; 43:221–8. 11. Kharroubi SA, Brazier J, McGhee S. A comparison of Hong Kong and United Kingdom SF-6D health states valuations using a nonparametric Bayesian method. Value Health. 2014;17(4):397–405. 12. Kharroubi SA. A comparison of Japan and United Kingdom SF-6D health states valuations using a nonparametric Bayesian method. Applied Health Economics and Health Policy. 2015;13(4):409–20. 13. Kharroubi SA, O’Hagan A, Brazier JE. Estimating utilities from individual health state preference data: a nonparametric Bayesian approach. Appl Stat. 2005;54:879–95. 14. Kharroubi SA. Valuations of EQ-5D health states: could United Kingdom results be used as informative priors for United States. J Appl Stat. 2017; https://doi.org/10.1080/02664763.2017.1386770.

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Health and Quality of Life OutcomesSpringer Journals

Published: Jun 5, 2018

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