Antiretroviral Therapy and Mortality in Rural South Africa: A Comparison of Causal Modeling Approaches

Catherine E Oldenburg; George R Seage; Frank Tanser; Victor De Gruttola; Kenneth H Mayer; Matthew J Mimiaga; Jacob Bor; Till Bärnighausen

doi:10.1093/aje/kwy065

Antiretroviral Therapy and Mortality in Rural South Africa: A Comparison of Causal Modeling Approaches

Oldenburg, Catherine E; Seage, George R; Tanser, Frank; De Gruttola, Victor; Mayer, Kenneth H; Mimiaga, Matthew J; Bor, Jacob; Bärnighausen, Till 2018-08-01 00:00:00 Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 American Journal of Epidemiology Vol. 187, No. 8 © The Author(s) 2018. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. DOI: 10.1093/aje/kwy065 This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons. Advance Access publication: org/licenses/by/4.0), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. March 23, 2018 Practice of Epidemiology Antiretroviral Therapy and Mortality in Rural South Africa: A Comparison of Causal Modeling Approaches Catherine E. Oldenburg*, George R. Seage, Frank Tanser, Victor De Gruttola, Kenneth H. Mayer, Matthew J. Mimiaga, Jacob Bor, and Till Bärnighausen * Correspondence to Dr. Catherine E. Oldenburg, Francis I. Proctor Foundation, University of California, San Francisco, 513 Parnassus Avenue, San Francisco, CA 94143 (e-mail: catherine.oldenburg@ucsf.edu). Initially submitted June 26, 2017; accepted for publication March 15, 2018. Estimation of causal effects from observational data is a primary goal of epidemiology. The use of multiple meth- ods with different assumptions relating to exchangeability improves causal inference by demonstrating robustness across assumptions. We estimated the effect of antiretroviral therapy (ART) on mortality in rural KwaZulu-Natal, South Africa, from 2007 to 2011, using 2 methods with substantially different assumptions: the regression disconti- nuity design (RDD) and inverse-probability–weighted (IPW) marginal structural models (MSMs). The RDD analysis took advantage of a CD4-cell-count–based threshold for ART initiation (200 cells/μL). The 2 methods yielded con- sistent but nonidentical results for the effect of immediate initiation of ART (RDD intention-to-treat hazard ratio (HR) = 0.66, 95% conﬁdence interval (CI): 0.35, 1.26; RDD complier average causal effect HR = 0.56, 95% CI: 0.41, 0.77; IPW MSM HR = 0.49, 95% CI: 0.42, 0.58). Although RDD and IPW MSM estimates have distinct identi- fying assumptions, strengths, and limitations in terms of internal and external validity, results in this application were similar. The differences in modeling approaches and the external validity of each method may explain the minor differences in effect estimates. The overall consistency of the results lends support for causal inference about the effect of ART on mortality from these data. antiretroviral therapy; causal inference; HIV; marginal structural models; mortality; regression discontinuity; South Africa Abbreviations: ART, antiretroviral therapy; CACE, complier average causal effect; CD4, cluster of differentiation 4; CI, conﬁdence interval; HIV, human immunodeﬁciency virus; HR, hazard ratio; IPW, inverse-probability–weighted; ITT, intention to treat; MSM, marginal structural model; RDD, regression discontinuity design. The most commonly used epidemiologic methods for identi- exchangeability, and they do not require explicit modeling of ﬁcation of causal effects rely on the untestable assumption of or adjustment for covariates (4). However, in order for valid no unmeasured confounding to achieve exchangeability (i.e., causal inferences to be drawn, these designs each require their that the counterfactual risk of outcome for each exposure status own set of assumptions to be met, some of which are not empir- is the same in the exposed and the unexposed) (1, 2). Recently, ically veriﬁable (5). nonrandomized study designs have been classiﬁed into 2 broad The second category, “nonexperimental” studies, encompasses categories based primarily on the underlying assumptions for study designs in which exposure allocation is modeled as a pro- internal validity (3). “Quasi-experimental” study designs have cess that is endogenous to the causal structure under study (3). been deﬁned as those that utilize an exogenous source in varia- Because exposure is allocated nonrandomly, these study designs tion in exposure assignment (e.g., an instrumental variable). require measurement of and adjustment for all potential confound- Because the source of variation in treatment assignment is not ers. The models used under this umbrella must explicitly model related to the causal structure, these designs do not require the all potential confounders to identify causal effects, and thus they typical assumption of no unmeasured confounding to achieve require the assumption of no unmeasured or residual confounding. 1772 Am J Epidemiol. 2018;187(8):1772–1779 Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 ART and Mortality in Rural South Africa 1773 METHODS In addition to differences in assumptions for exchangeabil- ity, the external validity of results differs by causal inference Regression discontinuity design method. To achieve exchangeability, restricting the analyti- cal population of a quasi-experimental study to persons with The RDD can be used in settings where an exposure is as- values that are close to the exogenous source of exposure signed by a threshold rule based on a continuously measured allocation is often necessary. Without untestable assump- variable (the assignment variable) (10, 15–19). Persons who tions, these results will only be generalizable to target pop- present for care close to the threshold value who are measured ulations with a similar distribution of values. Conversely, just above and just below the threshold are expected to be simi- nonexperiments may be generalizable to a larger population, lar with respect to the distributions of measured and unmea- as they estimate the association in the entire study population. sured covariates. Patients immediately above and below the The answer to the same research question can thus differ de- threshold value are expected to be exchangeable (see Web pending on whether it has been derived from a quasi-experiment Appendix 1, available at https://academic.oup.com/aje). or a nonexperiment. A discontinuity in treatment assignment occurs when the In controlled trials of antiretroviral therapy (ART) among probability of receiving treatment given that a patient is above persons with human immunodeﬁciency virus (HIV) infection, the threshold does not equal the probability of receiving treat- immediate initiation of ART has been shown to reduce mortal- ment given that the patient is below the threshold. Causal ef- ity in comparison with delayed initiation (6–8). Real-world fects can then be estimated in a small neighborhood around the causal effects outside of tightly controlled randomized trials threshold. This process has been formally described elsewhere may differ because of differences in adherence (e.g., without (10). When the assignment procedure is deterministic (when the counseling provided in a trial) or drug stock-outs. However, the threshold rule perfectly determines treatment), the proce- identiﬁcation of the effect of ART on mortality in observational dure is known as “sharp regression discontinuity.” In the prob- data using traditional covariate-adjustment regression methods abilistic case, where not all patients receive the treatment they is limited by confounding by indication. ART initiation is a are assigned by the threshold, the procedure is known as “fuzzy function of cluster of differentiation 4 (CD4)-positive T-cell regression discontinuity.” With sharpregressiondiscontinuity, count, which is also an indicator of disease progression and the association estimated is equal to the average causal effect in thus is associated with mortality. Failing to account for CD4 the population around the threshold. With fuzzy regression dis- cell count will therefore lead to incorrect inferences (9). How- continuity, where treatment is assigned probabilistically, this ever, standard covariate adjustment cannot be used if the expo- measure becomes the intention to treat (ITT), or the effect of eli- sure is time-varying, because time-varying confounders are gibility for treatment as determined by the threshold. This is affected by previous treatment. For time-ﬁxed exposures, analogous to the ITT commonly estimated in a randomized standard regression could be used, although it is not ideal controlled trial (20–22). because the hazard ratio is noncollapsible. Here we compare the In practice, a bias-variance tradeoff exists in the estimation of assumptions and external validity of the regression discontinuity these models. While theoretically resulting in the least biased design (RDD) (10–14), classiﬁed as a quasi-experimental ap- estimate of the causal effect, an analysis restricted only to per- proach, with that of inverse- probability–weighted (IPW) marginal sons immediately above and below the threshold may have structural models (MSMs) (9), classiﬁed as a nonexperimental insufﬁcient statistical power. To increase power, information approach. We then illustrate the comparison of approaches with can be borrowed from persons further away from the thresh- an application to assessment of the causal effect of ART on sur- old. However, as the bandwidth around the threshold widens, vival in rural KwaZulu-Natal, South Africa (Table 1). correct modeling of the functional form of the expected value Table 1. Comparison of Regression Discontinuity Design and Inverse-Probability–Weighted Marginal Structural Models as Causal Modeling Strategies for Initiation of Antiretroviral Therapy Among Persons With Human Immunodeﬁciency Virus Infection Element of Inverse-Probability–Weighted Regression Discontinuity Design Study Design Marginal Structural Model Causal question The causal effect of immediate ART eligibility on The causal effect of ART initiation at mortality entry to care on mortality Effect estimated Local treatment effect Average causal effect Key assumption Potential outcomes are continuous at the No unmeasured confounding threshold (continuity assumption) Handling of Whether or not a person near the threshold Creating a pseudopopulation where confounding presents to the clinic just above or just below treatment is random conditional the threshold is assumed to be random on measured covariates Statistical power Strongly reduced Reduced relative to standard cohort methods Abbreviation: ART, antiretroviral therapy. Am J Epidemiol. 2018;187(8):1772–1779 Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 1774 Oldenburg et al. of the outcome given the assignment variable becomes increas- association between confounding variables and treatment by esti- ingly important to maintain exchangeability. mating the probability of receiving the treatment that the subject Two assumptions must be evaluated and met for estimating actually received at time k, conditional on past treatment and risk the causal effect in the ITT for RDDs. First, the assignment factor history (9, 27, 28). In the pseudopopulation, under the variable must be continuous at the threshold. Second, the so- assumption of no unmeasured confounding (i.e., conditional called continuity assumption (which is that potential outcomes exchangeability in the original population), the unexposed and are continuous at the threshold) must hold. When it is met, exposed are expected to be unconditionally exchangeable, and it implies exchangeability. There can be no other factors at the causal effects can be estimated (2). threshold that would cause a discontinuity in the potential out- The key assumption for identiﬁcation of causal effects in comes. If there exist other variables that are discontinuous at the IPW MSMs is conditional exchangeability. Any unmeasured threshold and also affect outcomes, the continuity assumption variables that are associated with both the exposure of would be violated and causal inference jeopardized. In prac- interest and the outcome would jeopardize causal infer- tice, when an assignment variable is measured with random ence in this framework. If the exposed and unexposed are noise, we expect this key assumption to be met for persons conditionally exchangeable in the original population, they close to the threshold. Another assumption of RDD, consis- will be unconditionally exchangeable in the pseudopopula- tency (23) (e.g., that interventions are well-deﬁned) and positiv- tion, allowing for identiﬁcation of marginal causal effects. ity (24) (e.g., that there are observations in each stratum), is The exposed and unexposed may be conditionally exchangeable generally expected to be met, since interventions assigned by a if time-varying stabilized inverse probability weights include threshold rule are generally well-deﬁned, and we expect there baseline covariates in the numerator. However, if the assump- to be persons both above and below the threshold (13). One tion of conditional exchangeability (i.e., no unmeasured or precondition for regression discontinuity is that the thresh- residual confounding) does not hold in the original population, old rule is known (10). When this precondition is met, the con- the exchangeability assumption will not hold in the pseudo- sistency assumption will also hold. population. This assumption is empirically unveriﬁable. Re- In fuzzy regression discontinuity, an alternative to the ITT searchers must rely on subject-matter knowledge to assess the estimate is the effect of the exposure itself on outcomes. This degree to which this assumption is reasonable. The additional measure, called the complier average causal effect (CACE) or identifying assumptions of consistency and positivity must local average treatment effect (LATE), can be estimated using also hold for valid causal inference (23). instrumental variable approaches (4, 10, 25), where the instru- ment is treatment assignment by the threshold rule and is used Application to ART initiation and mortality to identify the exogenous variation in actual treatment. The CACE is what would have occurred had everyone in the sam- We applied both the RDD and IPW MSMs to estimate the ple complied with the treatment assignment by the threshold effect of immediate ART initiation on all-cause mortality in rural rule. This estimate can be viewed as the “undiluted” effect South Africa. The ITT for the RDD estimates the effect of imme- of treatment, which will only coincide with the ITT under the diate ART eligibility on all-cause mortality. The CACE for the ideal conditions of perfect compliance (26). RDD estimates the effect of immediate ART initiation in the Estimation of the CACE using treatment assignment by the population of persons who initiated ART because of the thresh- threshold rule as the instrument requires monotonicity—that is, old rule (e.g., the compliers). The time-invariant MSM estimates all people who are affected by the instrument are affected by it the effect of immediate initiation of ART, remaining in care and in the same way. Monotonicity rules out the possibility that for on ART throughout follow-up. The time-varying MSM estimates a given change in the instrument, there are both some indivi- the effect of initiating ART during follow-up and remaining on duals whose treatment status changes in one direction and ART and remaining in care such that laboratory values are re- other individuals whose treatment status changes in the opposite corded as compared with never initiating ART during follow-up. direction (i.e., there are no so-called deﬁers). Unfortunately, de- We used data from a large population-based cohort in rural ﬁers are not an empirically identiﬁable population. In general, South Africa (29, 30), whichismaintainedbythe Africa Health instrumental variable analyses require the exclusion restriction Research Institute, one of the Wellcome Trust’s 5 Africa and Asia (4). The exclusion restriction states that the instrument only af- programs. The cohort includes data for all patients initiating care fects the outcome via treatment status itself. In regression dis- at public-sector ART clinics between 2007 and 2011 who pre- continuity, if the continuity assumption has been met, there is sented with a CD4 cell count less than or equal to 350 cells/μL. no confounding of the threshold (e.g., common causes of the We excluded patients initiating care after August 2011, as the threshold and the outcome) and thus the exclusion restriction CD4 cell count threshold changed after this date. Patients with will be met (5). CD4 counts greater than 350 cells/μL at baseline were excluded from all analyses to ensure that the analytical population was the same for all analyses. Data from the public-sector ART clinics Inverse probability weighting were linked to the population-based cohort, in which all mem- Inverse probability weighting of MSMs reduces bias in the bers of households in a 438-km (274-square-mile) area are presence of time-varying confounding (9). Conventional multiple followed longitudinally. Household response rates exceed regression models result in bias in the presence of time-varying 99% (29). Data collected include information on demographic, confounding, as they rely on conditioning on all covariates in the socioeconomic, and health indicators. Mortality is assessed via model. Inverse probability weighting of MSMs overcomes these verbal autopsy (31). For this analysis, all-cause mortality was limitations by creating a pseudopopulation in which there is no the outcome of interest. Am J Epidemiol. 2018;187(8):1772–1779 Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 ART and Mortality in Rural South Africa 1775 0.15 ART initiation in this context is assigned via a CD4-count– based threshold rule: Until August 2011, patients with HIV were eligible for ART once their CD4 counts dropped below 200 0.10 cells/μL. If patients had a CD4 count above 200 cells/μL, they were deferred from ART until their next monitoring visit, in approximately 6 months. For the regression discontinuity 0.05 method, we estimated the ITT using a discrete-time hazards model with terms for the gap in CD4 count above and below the threshold. The ITT was estimated for 3 bandwidths of 0.00 CD4 count around the threshold: ≤350 cells/μL(theentire 50 125 200 275 350 study sample; n = 4,435), 150–250 cells/μL(n = 1,304), and Earliest CD4 Count, cells/µL 175–225 cells/μL(n = 626). We conducted sensitivity analyses to assess whether results were robust to the inclusion of baseline Figure 1. Hazard of mortality among persons with human immunodeﬁ- covariates (Web Appendix 2). To estimate the effect of initia- ciency virus infection according to baseline CD4 cell count, KwaZulu- tion of ART itself in the RDD, we calculated the CACE in each Natal, South Africa, 2007–2011. Black dots ( ) indicate the raw mortality hazard (incidence) for each 10-cell/μL group. The solid lines are ﬁtted of the 3 bandwidths described above (10, 13). To estimate the regression lines showing the incidence of mortality as a function of the CACE, we used a discrete-time hazards model using ivprobit in earliest CD4 cell counts above and below the threshold (dashed line). Stata (StataCorp LLC, College Station, Texas). Patients were The dashed gray line is the projection for the curve below the threshold, followed from the date of their ﬁrst CD4 count in the HIV which is the estimate of what mortality incidence would have been for per- sons who were above the threshold (and thus not eligible for immediate care system (as a proxy for the date of initiation of HIV care) initiation of antiretroviral therapy (ART)) if they had actually been eligible to the date of their last observance in the surveillance system, for ART immediately. The discontinuity at the threshold is the estimate of classiﬁed as either the end of follow-up (censored) or death. the effect of ART eligibility on mortality incidence. Using the IPW MSM, we estimated the effect of initiating treatment at entry into care (within a 3-month grace period) ver- sus not. Participants were followed until the end of follow-up (December 2014) or death, whichever came ﬁrst. We also esti- mated the effect of time-updated ART status. Because not all par- distribution of inverse-probability-of-treatment and inverse- ticipants had laboratory measurements taken every 6 months per probability-of-censoring weights (Web Appendix 4). monitoring guidelines and some were lost to care entirely, in the time-varying analysis we censored persons who had not had a lab- oratory measurement for 12 months or more. An additional model RESULTS included both censoring at 12 months and an interaction term for ART status × time, which allowed for estimation of heterogeneity A total of 4,435 persons initiated care between 2007 and of effects over time. Time-invariant models were not censored. 2011 with a baseline CD4 count less than or equal to 350 cells/μL. For the model estimating the effect of ART initiation at entry into care, we ﬁrst estimated inverse probability weights with the following baseline covariates: age, sex, CD4 count, educational status, household wealth (estimated as the ﬁrst principal compo- nent in a principal components analysis of 32 household assets 1.00 and characteristics and discretized into quintiles (29)), distance from the patient’s place of residence to the clinic (in kilometers), and place of residence (whether the patient lived in an urban or 0.75 rural area). Although we permitted a 3-month grace period to allow for minor delays in initiating ART, only baseline CD4 cell 0.50 count was used in the calculation of the inverse probability weights, as CD4 count monitoring is typically done at 6-month intervals. A discrete-time hazards model was then used to ﬁtthe 0.25 MSM, without adjustment for any covariates. The discrete-time hazards model was utilized to accommodate time-varying weights for the time-varying MSM, and an identical approach 0.00 was used for all other models to maintain consistency. 0 50 100 150 200 250 300 350 To compare the regression discontinuity model with models Earliest CD4 Count, cells/µL of the effect of time-varying ART status on mortality, we con- ducted a time-varying analysis with inverse probability weight- Figure 2. Probability of antiretroviral therapy (ART) initiation within 6 months of entering care among persons with human immunodeﬁciency ing. Methods used for these models are included in Web virus infection, according to baseline CD4 cell count, KwaZulu-Natal, Appendix 3. Due to the noncollapsibility of the hazard ratio, South Africa, 2007–2011. The probability of ART initiation within 6 months results of the time-varying analysis with stabilized weights are of the earliest CD4 cell count was calculated by baseline CD4 cell count as not directly comparable to results derived from the time-invariant the number of persons in a given 10-cell/μL group over the total number of MSM. An additional analysis included accounting for time- persons in that group. A discontinuity in the probability of ART initiation is evident at the 200-cells/μL threshold. varying confounding and informative censoring using the joint Am J Epidemiol. 2018;187(8):1772–1779 Probability of ART Initiation in 3 Months Mortality Hazard Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 1776 Oldenburg et al. Of these, 935 participants died over the course of 19,269 person- cells/μL below the threshold); 3) the addition of age at base- years of follow-up (mortality incidence rate = 4.9 per 100 person- line and sex as covariates in the model (Web Table 2). years). Table 2 and Web Table 1 show the distribution of baseline Figure 3 graphically displays the results of each analysis. covariates for persons above and below the threshold. Of the 935 In the regression discontinuity model at a bandwidth of deaths, 734 were among persons who were eligible for ART ≤350 cells/μL, there was a 41% reduction in mortality with at baseline (incidence rate = 6.6 per 100 person-years) and 201 immediate eligibility for ART (hazard ratio (HR) = 0.59, 95% occurred among those who were not eligible (2.5 per 100 person- conﬁdence interval (CI): 0.42, 0.81) (Figure 2,Table 3), which years). Mortality decreased as baseline CD4 count increased, and was lowered to a 30% reduction in a model with a restricted there was evidence of a discontinuity at the 200-cells/μL thresh- cubic spline (HR = 0.70, 95% CI: 0.46, 1.05) and in a model old (Figure 1). with a squared functional form for CD4 count (HR = 0.70, Figure 2 demonstrates evidence of discontinuity in the proba- 95% CI: 0.43, 1.13). These results were similar in magni- bility of initiating ART within 6 months by baseline CD4 count. tude to the effect estimates at a narrower bandwidth of 150–250 Baseline characteristics for the overall sample were roughly bal- cells/μL(HR = 0.66, 95% CI: 0.35, 1.26). The CACE demon- anced between persons who were eligible for treatment at base- strated a 44% reduction in mortality with immediate initiation line and those who were not eligible (Table 2) but were more of ART among the compliers at the widest bandwidth (HR = closely balanced for persons closer to the threshold (Web 0.56, 95% CI: 0.41, 0.77). These estimates were robust to the Table 1). Sensitivity analyses were conducted with additional inclusion of baseline covariates in the model (Web Table 2). functional forms for CD4 counts above and below the threshold, In the IPW MSM, initiating ART within a 3-month grace including 1) a squared functional form for CD4 counts below period from study entry was associated with a 51% reduction the threshold; 2) a restricted cubic spline at 125 cells/μL(75 in all-cause mortality (HR = 0.49, 95% CI: 0.42, 0.58) and a Table 2. Baseline Characteristics of Participants in a Study of Immediate Initiation of Antiretroviral Therapy Among Persons With Human Immunodeﬁciency Virus Infection (n = 4,435), KwaZulu-Natal, South Africa, 2007–2011 Eligibility for ART Initiation at Baseline Characteristic Below Threshold (Eligible) (n = 2,751) Above Threshold (Ineligible) (n = 1,684) No. of Persons % Median (IQR) No. of Persons % Median (IQR) Age, years 33.1 (27.5–41.4) 31.3 (24.8–40.3) Female sex 1,790 65.1 1,278 75.9 Baseline CD4 cell count, cells/μL 101 (49–140) 268 (233–306) Asset index quintile Lowest 594 21.6 402 23.9 Second lowest 571 20.8 357 21.2 Middle 488 17.7 315 18.7 Second highest 404 14.7 239 14.2 Highest 347 12.6 241 14.3 Missing data 347 12.6 130 7.7 Distance to nearest clinic, km 2.6 (1.5–3.4) 2.4 (1.5–3.5) Place of residence Rural 1,249 45.4 813 48.3 Periurban 918 33.4 553 32.8 Urban 252 9.2 189 11.2 Missing data 332 12.1 129 7.7 Educational attainment, years ≤7 (none or primary) 920 33.4 564 33.5 8–12 (secondary) 1,523 55.4 951 56.5 >12 (tertiary) 246 8.9 133 7.9 Missing data 62 2.3 36 2.1 Abbreviations: ART, antiretroviral therapy; IQR, interquartile range. Household wealth was estimated as quintiles of the ﬁrst components identiﬁed by principal components analysis of 32 household assets and characteristics. Am J Epidemiol. 2018;187(8):1772–1779 Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 ART and Mortality in Rural South Africa 1777 1.0 Table 3. Primary Analysis Results for Regression Discontinuity and Inverse-Probability–Weighted Analyses of Immediate Initiation of 0.5 Antiretroviral Therapy Among Persons With Human Immunodeﬁciency Virus Infection, KwaZulu-Natal, South Africa, 0.0 2007–2011 –0.5 Model and CD4 Cell Count HR 95% CI –1.0 Unadjusted 1.28 1.08, 1.51 –1.5 Regression discontinuity—ITT –2.0 ≤350 cells/μL 0.59 0.42, 0.81 150–250 cells/μL 0.66 0.35, 1.26 –2.5 175–225 cells/μL 0.50 0.23, 1.55 Regression discontinuity—CACE ≤350 cells/μL 0.56 0.41, 0.77 150–250 cells/μL 0.58 0.25, 1.31 Modeling Method 175–225 cells/μL 0.43 0.10, 1.81 Figure 3. Primary analysis results for the relationship between antiret- Inverse probability weighting roviral therapy (ART) and mortality among persons with human immu- nodeﬁciency virus infection, KwaZulu-Natal, South Africa, 2007–2011. Time-invariant ART status 0.49 0.42, 0.58 Results were derived using the regression discontinuity design (RDD) a Time-varying ART status 0.54 0.41, 0.70 for both the intention-to-treat (ITT) effect ( ) and the complier average □ Time-varying ART status with 0.50 0.37, 0.66 causal effect (CACE; )atthe ≤350-cells/μL, 50- to 350-cells/μL, and censoring weights 150- to 250-cells/μL bandwidths (left to right); inverse-probability– weighted (IPW) marginal structural models (MSMs) (from left to right, Abbreviations: ART, antiretroviral therapy; CACE, complier average baseline time-invariant ART initiation, time-updated ART status censor- causal effect; CI, conﬁdence interval; HR, hazard ratio; ITT, intention to ing persons without laboratory tests at 12 months, and time-updated treat. ART status censoring persons without laboratory tests at 12 months with inverse-probability-of-censoring weights applied) ( ); the unad- Censored at a 12-month gap in laboratory values. justed effect of ART on mortality (♦); and the effect adjusted for baseline Censored at a 12-month gap in laboratory values and accounting covariates ( ). Bars, 95% conﬁdence intervals. for censoring with inverse-probability-of-censoring weights applied. future applications, triangulation of causal inference across mul- 46% reduction in a time-varying model censoring persons tiple methods may be most valuable when the preexisting evi- without a laboratory test in the previous 12 months (HR = 0.54, dence is weak or inconsistent. In these cases, inconsistent 95% CI: 0.41, 0.70). In the censored model with an ART status × ﬁndings across different causal methods will be more likely time-since-initiation interaction term, there was signiﬁcant evi- than in our application, and consistent ﬁndings thus have dence of an increase in the protective effect of ART over time greater potential to substantially strengthen the evidence on (per year, HR = 0.84, 95% CI: 0.76, 0.94). causality. While the broad causal question of interest in the present application was the relationship between ART and mortality, DISCUSSION each study design presented herein answered a subtly different The RDD and the IPW MSM yielded consistent results, in- speciﬁc causal question. Each of these results has a slightly dif- dicating an approximately 40%–50% reduction in mortality due ferent interpretation. The unadjusted association showed an to immediate initiation of ART. These results provide both con- increased risk of mortality with ART use, which is expected given sistent and complementary information. The CACE and the time- the strong confounding by CD4 count. Each method of causal invariant MSM estimate the effect of immediate ART initiation inference evaluated here showed that, as expected, ART use (within 3 months of entry into care) on all-cause mortality. The was protective against mortality. Taken together, these results CACE found a 44% reduction in all-cause mortality, as com- demonstrate the robustness of the causal effect of ART on pared with 51% with the time-invariant MSM, with completely mortality in “real life.” Using a large population-based cohort overlapping conﬁdence intervals. The time-varying MSM, without the resources of a carefully conducted randomized con- a commonly used method for modeling ART status as an expo- trolled trial, we demonstrated a large decrease in mortality with sure due to the potential for time-varying confounding, was simi- the use of ART. The use of multiple approaches for causal infer- larly consistent with the previous 2 approaches. Prior studies have ence also strengthens the evidence arising from this study in established the efﬁcacy of ART for prevention of mortality, and comparison with most cohort studies, which do not use such CD4 count is a well-known confounder of this relationship. We approaches. chose the causal effect of ART on mortality for our study using The different methods we used generate different types of multiple causal inference methods, because this relationship is causal effect size estimates. Time-invariant inverse probability well-understood and thus provides a good example with which to weighting of MSMs determines the estimate in the entire study demonstrate the usefulness of a methodological approach. In population and thus can be generalized across the entire Am J Epidemiol. 2018;187(8):1772–1779 Unadjusted RDD ITT RDD CACE IPW MSM Baseline-Adjusted Log Hazard Ratio Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 1778 Oldenburg et al. distribution of CD4 cell counts. Notably, in the time-varying same overarching question adds additional robustness to the model, the estimate is conditional on baseline covariates. In interpretation of results. When the data allow, approaches that the RDD, generalizability will depend on additional assump- have different assumptions for validity should be used rou- tions. In the presence of heterogeneity of treatment effects ac- tinely to strengthen conﬁdence in causal effect estimates. cording to the assignment variable (in this application, CD4 count), the RDD effect may have limited generalizability. In the RDD literature, 3 perspectives on the generalizability of effects have been posited (5, 12). First is that the effect size is ACKNOWLEDGMENTS generalizable to the entire study population and is an average Author afﬁliations: Department of Epidemiology, treatment effect (32). The assumption required for this interpreta- Harvard T.H. Chan School of Public Health, Boston, tion is that the functional form of the potential outcomes (e.g., had Massachusetts (Catherine E. Oldenburg, George R. Seage); everyone been treated versus had no one been treated) are known. Francis I. Proctor Foundation, University of California, San However, this is a strong and untestable assumption. The second Francisco, San Francisco, California (Catherine E. perspective is that the effect estimated under the RDD is only gen- Oldenburg); Africa Health Research Institute, Durban and eralizable locally, within an arbitrary region around the threshold. Somkhele, South Africa (Frank Tanser, Till Bärnighausen); The third perspective is that the effect size estimated under the Department of Epidemiology, Faculty of Health Sciences, RDD represents a weighted average of the treatment effect in the University of KwaZulu-Natal, Durban, South Africa (Frank entire study population, with weights that are proportional to the Tanser); Department of Biostatistics, Harvard T.H. Chan probability of an individual’s value of the assignment variable School of Public Health, Boston, Massachusetts (Victor De (CD4 count) being in the neighborhood of the threshold (33). Gruttola); The Fenway Institute, Fenway Community Given the strong assumptions required for the ﬁrst perspective, Health, Boston, Massachusetts (Kenneth H. Mayer); the IPW estimate, which is an average treatment effect, could Department of Global Health and Population, Harvard T.H. differ from the regression discontinuity estimate if the rela- Chan School of Public Health, Boston, Massachusetts tionship between ART and mortality is stronger at lower CD4 (Kenneth H. Mayer, Till Bärnighausen); Department of counts (i.e., in persons who are sicker at baseline), compared Medicine, Beth Israel Deaconess Medical Center, Boston, with those whose baseline CD4 count is 200 cells/μL. Massachusetts (Kenneth H. Mayer); Department of For both methodological approaches, the data we used for these Behavioral and Social Sciences and Department of analyses had signiﬁcant strengths. The public-sector ART clinic Epidemiology, Institute for Community Health Promotion, in this region (the Hlabisa HIV Treatment and Care Programme) School of Public Health, Brown University, Providence, provides the vast majority of HIV care in the area, and thus mis- Rhode Island (Matthew J. Mimiaga); Department of Global classiﬁcation of exposure is likely to have been minimal. Follow- Health, School of Public Health, Boston University, Boston, up information was very complete in our study, because it was Massachusetts (Jacob Bor); Research Department of collected through one of Africa’s largest and most rigorous Infection and Population Health, Centre for Sexual Health, population-based cohorts. The cohort covers the entire popu- University College London, London, United Kingdom (Till lation in the catchment areas of the clinics through which pa- Bärnighausen); and Heidelberg Institute of Public Health, tients were recruited for our study, and data on mortality have University of Heidelberg, Heidelberg, Germany (Till been collectedonanongoing basis for over 15 years. Death Bärnighausen). registration in the cohort is near-complete (34). As a result, we The Hlabisa HIV Treatment and Care Programme is funded still observed our outcome of interest in nearly all of the patients by the US Agency for International Development and the who were lost to follow-up from clinical HIV care. Use of com- President’s Emergency Plan for AIDS Relief (grant 674-A- plete, high-quality data allows for direct comparison of esti- 00-08-001-00). This work was partially supported by the US mates generated by the two approaches, speciﬁcally in how National Institutes of Health (grants T32-DA013911 and they each meet the exchangeability requirement for causal R25-MH083620 to C.E.O., grant R37-AI51164 to V.D.G., inference from observational data, as well as the generalizabil- grant R01-HD084233 to T.B., and grants R01-AI124389 and ity of each estimate. R01-HD084233 to T.B. and F.T.). The Africa Health The effect estimates from the RDD and MSM were not iden- Research Institute, University of KwaZulu-Natal (Durban, tical, but they were similar in magnitude, providing strong evi- South Africa), receives core funding from the Wellcome Trust dence of a protective effect of ART against all-cause mortality (grant 082384/Z/07/Z). among HIV-infected persons receiving care in rural South Africa. Conﬂict of interest: none declared. The fact that the IPW MSM estimate was similar to the RDD estimate suggests that the regression discontinuity effect may be generalizable to a wider range of CD4 counts from the 200- cells/μL threshold. When covariate data are available and well- REFERENCES measured, inclusion of an IPW MSM as a sensitivity analysis may yield greater information than the regression disconti- 1. Hernán MA, Robins JM. Estimating causal effects from nuity effect alone. The use of both models provides estima- epidemiological data. J Epidemiol Community Health. 2006; tion of effects with alternative exchangeability assumptions 60(7):578–586. and yields complementary information regarding external 2. Hernan MA, Robbins JM. Causal inference book. 2015. https:// validity. Although the exact speciﬁcation of the causal ques- www.hsph.harvard.edu/miguel-hernan/causal-inference-book/. tion may differ slightly, using multiple methods to address the Accessed September 18, 2015. 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Publisher: Oxford University Press
Copyright: Copyright © 2022 Johns Hopkins Bloomberg School of Public Health
ISSN: 0002-9262
eISSN: 1476-6256
DOI: 10.1093/aje/kwy065
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Abstract

Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 American Journal of Epidemiology Vol. 187, No. 8 © The Author(s) 2018. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. DOI: 10.1093/aje/kwy065 This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons. Advance Access publication: org/licenses/by/4.0), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited. March 23, 2018 Practice of Epidemiology Antiretroviral Therapy and Mortality in Rural South Africa: A Comparison of Causal Modeling Approaches Catherine E. Oldenburg*, George R. Seage, Frank Tanser, Victor De Gruttola, Kenneth H. Mayer, Matthew J. Mimiaga, Jacob Bor, and Till Bärnighausen * Correspondence to Dr. Catherine E. Oldenburg, Francis I. Proctor Foundation, University of California, San Francisco, 513 Parnassus Avenue, San Francisco, CA 94143 (e-mail: catherine.oldenburg@ucsf.edu). Initially submitted June 26, 2017; accepted for publication March 15, 2018. Estimation of causal effects from observational data is a primary goal of epidemiology. The use of multiple meth- ods with different assumptions relating to exchangeability improves causal inference by demonstrating robustness across assumptions. We estimated the effect of antiretroviral therapy (ART) on mortality in rural KwaZulu-Natal, South Africa, from 2007 to 2011, using 2 methods with substantially different assumptions: the regression disconti- nuity design (RDD) and inverse-probability–weighted (IPW) marginal structural models (MSMs). The RDD analysis took advantage of a CD4-cell-count–based threshold for ART initiation (200 cells/μL). The 2 methods yielded con- sistent but nonidentical results for the effect of immediate initiation of ART (RDD intention-to-treat hazard ratio (HR) = 0.66, 95% conﬁdence interval (CI): 0.35, 1.26; RDD complier average causal effect HR = 0.56, 95% CI: 0.41, 0.77; IPW MSM HR = 0.49, 95% CI: 0.42, 0.58). Although RDD and IPW MSM estimates have distinct identi- fying assumptions, strengths, and limitations in terms of internal and external validity, results in this application were similar. The differences in modeling approaches and the external validity of each method may explain the minor differences in effect estimates. The overall consistency of the results lends support for causal inference about the effect of ART on mortality from these data. antiretroviral therapy; causal inference; HIV; marginal structural models; mortality; regression discontinuity; South Africa Abbreviations: ART, antiretroviral therapy; CACE, complier average causal effect; CD4, cluster of differentiation 4; CI, conﬁdence interval; HIV, human immunodeﬁciency virus; HR, hazard ratio; IPW, inverse-probability–weighted; ITT, intention to treat; MSM, marginal structural model; RDD, regression discontinuity design. The most commonly used epidemiologic methods for identi- exchangeability, and they do not require explicit modeling of ﬁcation of causal effects rely on the untestable assumption of or adjustment for covariates (4). However, in order for valid no unmeasured confounding to achieve exchangeability (i.e., causal inferences to be drawn, these designs each require their that the counterfactual risk of outcome for each exposure status own set of assumptions to be met, some of which are not empir- is the same in the exposed and the unexposed) (1, 2). Recently, ically veriﬁable (5). nonrandomized study designs have been classiﬁed into 2 broad The second category, “nonexperimental” studies, encompasses categories based primarily on the underlying assumptions for study designs in which exposure allocation is modeled as a pro- internal validity (3). “Quasi-experimental” study designs have cess that is endogenous to the causal structure under study (3). been deﬁned as those that utilize an exogenous source in varia- Because exposure is allocated nonrandomly, these study designs tion in exposure assignment (e.g., an instrumental variable). require measurement of and adjustment for all potential confound- Because the source of variation in treatment assignment is not ers. The models used under this umbrella must explicitly model related to the causal structure, these designs do not require the all potential confounders to identify causal effects, and thus they typical assumption of no unmeasured confounding to achieve require the assumption of no unmeasured or residual confounding. 1772 Am J Epidemiol. 2018;187(8):1772–1779 Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 ART and Mortality in Rural South Africa 1773 METHODS In addition to differences in assumptions for exchangeabil- ity, the external validity of results differs by causal inference Regression discontinuity design method. To achieve exchangeability, restricting the analyti- cal population of a quasi-experimental study to persons with The RDD can be used in settings where an exposure is as- values that are close to the exogenous source of exposure signed by a threshold rule based on a continuously measured allocation is often necessary. Without untestable assump- variable (the assignment variable) (10, 15–19). Persons who tions, these results will only be generalizable to target pop- present for care close to the threshold value who are measured ulations with a similar distribution of values. Conversely, just above and just below the threshold are expected to be simi- nonexperiments may be generalizable to a larger population, lar with respect to the distributions of measured and unmea- as they estimate the association in the entire study population. sured covariates. Patients immediately above and below the The answer to the same research question can thus differ de- threshold value are expected to be exchangeable (see Web pending on whether it has been derived from a quasi-experiment Appendix 1, available at https://academic.oup.com/aje). or a nonexperiment. A discontinuity in treatment assignment occurs when the In controlled trials of antiretroviral therapy (ART) among probability of receiving treatment given that a patient is above persons with human immunodeﬁciency virus (HIV) infection, the threshold does not equal the probability of receiving treat- immediate initiation of ART has been shown to reduce mortal- ment given that the patient is below the threshold. Causal ef- ity in comparison with delayed initiation (6–8). Real-world fects can then be estimated in a small neighborhood around the causal effects outside of tightly controlled randomized trials threshold. This process has been formally described elsewhere may differ because of differences in adherence (e.g., without (10). When the assignment procedure is deterministic (when the counseling provided in a trial) or drug stock-outs. However, the threshold rule perfectly determines treatment), the proce- identiﬁcation of the effect of ART on mortality in observational dure is known as “sharp regression discontinuity.” In the prob- data using traditional covariate-adjustment regression methods abilistic case, where not all patients receive the treatment they is limited by confounding by indication. ART initiation is a are assigned by the threshold, the procedure is known as “fuzzy function of cluster of differentiation 4 (CD4)-positive T-cell regression discontinuity.” With sharpregressiondiscontinuity, count, which is also an indicator of disease progression and the association estimated is equal to the average causal effect in thus is associated with mortality. Failing to account for CD4 the population around the threshold. With fuzzy regression dis- cell count will therefore lead to incorrect inferences (9). How- continuity, where treatment is assigned probabilistically, this ever, standard covariate adjustment cannot be used if the expo- measure becomes the intention to treat (ITT), or the effect of eli- sure is time-varying, because time-varying confounders are gibility for treatment as determined by the threshold. This is affected by previous treatment. For time-ﬁxed exposures, analogous to the ITT commonly estimated in a randomized standard regression could be used, although it is not ideal controlled trial (20–22). because the hazard ratio is noncollapsible. Here we compare the In practice, a bias-variance tradeoff exists in the estimation of assumptions and external validity of the regression discontinuity these models. While theoretically resulting in the least biased design (RDD) (10–14), classiﬁed as a quasi-experimental ap- estimate of the causal effect, an analysis restricted only to per- proach, with that of inverse- probability–weighted (IPW) marginal sons immediately above and below the threshold may have structural models (MSMs) (9), classiﬁed as a nonexperimental insufﬁcient statistical power. To increase power, information approach. We then illustrate the comparison of approaches with can be borrowed from persons further away from the thresh- an application to assessment of the causal effect of ART on sur- old. However, as the bandwidth around the threshold widens, vival in rural KwaZulu-Natal, South Africa (Table 1). correct modeling of the functional form of the expected value Table 1. Comparison of Regression Discontinuity Design and Inverse-Probability–Weighted Marginal Structural Models as Causal Modeling Strategies for Initiation of Antiretroviral Therapy Among Persons With Human Immunodeﬁciency Virus Infection Element of Inverse-Probability–Weighted Regression Discontinuity Design Study Design Marginal Structural Model Causal question The causal effect of immediate ART eligibility on The causal effect of ART initiation at mortality entry to care on mortality Effect estimated Local treatment effect Average causal effect Key assumption Potential outcomes are continuous at the No unmeasured confounding threshold (continuity assumption) Handling of Whether or not a person near the threshold Creating a pseudopopulation where confounding presents to the clinic just above or just below treatment is random conditional the threshold is assumed to be random on measured covariates Statistical power Strongly reduced Reduced relative to standard cohort methods Abbreviation: ART, antiretroviral therapy. Am J Epidemiol. 2018;187(8):1772–1779 Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 1774 Oldenburg et al. of the outcome given the assignment variable becomes increas- association between confounding variables and treatment by esti- ingly important to maintain exchangeability. mating the probability of receiving the treatment that the subject Two assumptions must be evaluated and met for estimating actually received at time k, conditional on past treatment and risk the causal effect in the ITT for RDDs. First, the assignment factor history (9, 27, 28). In the pseudopopulation, under the variable must be continuous at the threshold. Second, the so- assumption of no unmeasured confounding (i.e., conditional called continuity assumption (which is that potential outcomes exchangeability in the original population), the unexposed and are continuous at the threshold) must hold. When it is met, exposed are expected to be unconditionally exchangeable, and it implies exchangeability. There can be no other factors at the causal effects can be estimated (2). threshold that would cause a discontinuity in the potential out- The key assumption for identiﬁcation of causal effects in comes. If there exist other variables that are discontinuous at the IPW MSMs is conditional exchangeability. Any unmeasured threshold and also affect outcomes, the continuity assumption variables that are associated with both the exposure of would be violated and causal inference jeopardized. In prac- interest and the outcome would jeopardize causal infer- tice, when an assignment variable is measured with random ence in this framework. If the exposed and unexposed are noise, we expect this key assumption to be met for persons conditionally exchangeable in the original population, they close to the threshold. Another assumption of RDD, consis- will be unconditionally exchangeable in the pseudopopula- tency (23) (e.g., that interventions are well-deﬁned) and positiv- tion, allowing for identiﬁcation of marginal causal effects. ity (24) (e.g., that there are observations in each stratum), is The exposed and unexposed may be conditionally exchangeable generally expected to be met, since interventions assigned by a if time-varying stabilized inverse probability weights include threshold rule are generally well-deﬁned, and we expect there baseline covariates in the numerator. However, if the assump- to be persons both above and below the threshold (13). One tion of conditional exchangeability (i.e., no unmeasured or precondition for regression discontinuity is that the thresh- residual confounding) does not hold in the original population, old rule is known (10). When this precondition is met, the con- the exchangeability assumption will not hold in the pseudo- sistency assumption will also hold. population. This assumption is empirically unveriﬁable. Re- In fuzzy regression discontinuity, an alternative to the ITT searchers must rely on subject-matter knowledge to assess the estimate is the effect of the exposure itself on outcomes. This degree to which this assumption is reasonable. The additional measure, called the complier average causal effect (CACE) or identifying assumptions of consistency and positivity must local average treatment effect (LATE), can be estimated using also hold for valid causal inference (23). instrumental variable approaches (4, 10, 25), where the instru- ment is treatment assignment by the threshold rule and is used Application to ART initiation and mortality to identify the exogenous variation in actual treatment. The CACE is what would have occurred had everyone in the sam- We applied both the RDD and IPW MSMs to estimate the ple complied with the treatment assignment by the threshold effect of immediate ART initiation on all-cause mortality in rural rule. This estimate can be viewed as the “undiluted” effect South Africa. The ITT for the RDD estimates the effect of imme- of treatment, which will only coincide with the ITT under the diate ART eligibility on all-cause mortality. The CACE for the ideal conditions of perfect compliance (26). RDD estimates the effect of immediate ART initiation in the Estimation of the CACE using treatment assignment by the population of persons who initiated ART because of the thresh- threshold rule as the instrument requires monotonicity—that is, old rule (e.g., the compliers). The time-invariant MSM estimates all people who are affected by the instrument are affected by it the effect of immediate initiation of ART, remaining in care and in the same way. Monotonicity rules out the possibility that for on ART throughout follow-up. The time-varying MSM estimates a given change in the instrument, there are both some indivi- the effect of initiating ART during follow-up and remaining on duals whose treatment status changes in one direction and ART and remaining in care such that laboratory values are re- other individuals whose treatment status changes in the opposite corded as compared with never initiating ART during follow-up. direction (i.e., there are no so-called deﬁers). Unfortunately, de- We used data from a large population-based cohort in rural ﬁers are not an empirically identiﬁable population. In general, South Africa (29, 30), whichismaintainedbythe Africa Health instrumental variable analyses require the exclusion restriction Research Institute, one of the Wellcome Trust’s 5 Africa and Asia (4). The exclusion restriction states that the instrument only af- programs. The cohort includes data for all patients initiating care fects the outcome via treatment status itself. In regression dis- at public-sector ART clinics between 2007 and 2011 who pre- continuity, if the continuity assumption has been met, there is sented with a CD4 cell count less than or equal to 350 cells/μL. no confounding of the threshold (e.g., common causes of the We excluded patients initiating care after August 2011, as the threshold and the outcome) and thus the exclusion restriction CD4 cell count threshold changed after this date. Patients with will be met (5). CD4 counts greater than 350 cells/μL at baseline were excluded from all analyses to ensure that the analytical population was the same for all analyses. Data from the public-sector ART clinics Inverse probability weighting were linked to the population-based cohort, in which all mem- Inverse probability weighting of MSMs reduces bias in the bers of households in a 438-km (274-square-mile) area are presence of time-varying confounding (9). Conventional multiple followed longitudinally. Household response rates exceed regression models result in bias in the presence of time-varying 99% (29). Data collected include information on demographic, confounding, as they rely on conditioning on all covariates in the socioeconomic, and health indicators. Mortality is assessed via model. Inverse probability weighting of MSMs overcomes these verbal autopsy (31). For this analysis, all-cause mortality was limitations by creating a pseudopopulation in which there is no the outcome of interest. Am J Epidemiol. 2018;187(8):1772–1779 Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 ART and Mortality in Rural South Africa 1775 0.15 ART initiation in this context is assigned via a CD4-count– based threshold rule: Until August 2011, patients with HIV were eligible for ART once their CD4 counts dropped below 200 0.10 cells/μL. If patients had a CD4 count above 200 cells/μL, they were deferred from ART until their next monitoring visit, in approximately 6 months. For the regression discontinuity 0.05 method, we estimated the ITT using a discrete-time hazards model with terms for the gap in CD4 count above and below the threshold. The ITT was estimated for 3 bandwidths of 0.00 CD4 count around the threshold: ≤350 cells/μL(theentire 50 125 200 275 350 study sample; n = 4,435), 150–250 cells/μL(n = 1,304), and Earliest CD4 Count, cells/µL 175–225 cells/μL(n = 626). We conducted sensitivity analyses to assess whether results were robust to the inclusion of baseline Figure 1. Hazard of mortality among persons with human immunodeﬁ- covariates (Web Appendix 2). To estimate the effect of initia- ciency virus infection according to baseline CD4 cell count, KwaZulu- tion of ART itself in the RDD, we calculated the CACE in each Natal, South Africa, 2007–2011. Black dots ( ) indicate the raw mortality hazard (incidence) for each 10-cell/μL group. The solid lines are ﬁtted of the 3 bandwidths described above (10, 13). To estimate the regression lines showing the incidence of mortality as a function of the CACE, we used a discrete-time hazards model using ivprobit in earliest CD4 cell counts above and below the threshold (dashed line). Stata (StataCorp LLC, College Station, Texas). Patients were The dashed gray line is the projection for the curve below the threshold, followed from the date of their ﬁrst CD4 count in the HIV which is the estimate of what mortality incidence would have been for per- sons who were above the threshold (and thus not eligible for immediate care system (as a proxy for the date of initiation of HIV care) initiation of antiretroviral therapy (ART)) if they had actually been eligible to the date of their last observance in the surveillance system, for ART immediately. The discontinuity at the threshold is the estimate of classiﬁed as either the end of follow-up (censored) or death. the effect of ART eligibility on mortality incidence. Using the IPW MSM, we estimated the effect of initiating treatment at entry into care (within a 3-month grace period) ver- sus not. Participants were followed until the end of follow-up (December 2014) or death, whichever came ﬁrst. We also esti- mated the effect of time-updated ART status. Because not all par- distribution of inverse-probability-of-treatment and inverse- ticipants had laboratory measurements taken every 6 months per probability-of-censoring weights (Web Appendix 4). monitoring guidelines and some were lost to care entirely, in the time-varying analysis we censored persons who had not had a lab- oratory measurement for 12 months or more. An additional model RESULTS included both censoring at 12 months and an interaction term for ART status × time, which allowed for estimation of heterogeneity A total of 4,435 persons initiated care between 2007 and of effects over time. Time-invariant models were not censored. 2011 with a baseline CD4 count less than or equal to 350 cells/μL. For the model estimating the effect of ART initiation at entry into care, we ﬁrst estimated inverse probability weights with the following baseline covariates: age, sex, CD4 count, educational status, household wealth (estimated as the ﬁrst principal compo- nent in a principal components analysis of 32 household assets 1.00 and characteristics and discretized into quintiles (29)), distance from the patient’s place of residence to the clinic (in kilometers), and place of residence (whether the patient lived in an urban or 0.75 rural area). Although we permitted a 3-month grace period to allow for minor delays in initiating ART, only baseline CD4 cell 0.50 count was used in the calculation of the inverse probability weights, as CD4 count monitoring is typically done at 6-month intervals. A discrete-time hazards model was then used to ﬁtthe 0.25 MSM, without adjustment for any covariates. The discrete-time hazards model was utilized to accommodate time-varying weights for the time-varying MSM, and an identical approach 0.00 was used for all other models to maintain consistency. 0 50 100 150 200 250 300 350 To compare the regression discontinuity model with models Earliest CD4 Count, cells/µL of the effect of time-varying ART status on mortality, we con- ducted a time-varying analysis with inverse probability weight- Figure 2. Probability of antiretroviral therapy (ART) initiation within 6 months of entering care among persons with human immunodeﬁciency ing. Methods used for these models are included in Web virus infection, according to baseline CD4 cell count, KwaZulu-Natal, Appendix 3. Due to the noncollapsibility of the hazard ratio, South Africa, 2007–2011. The probability of ART initiation within 6 months results of the time-varying analysis with stabilized weights are of the earliest CD4 cell count was calculated by baseline CD4 cell count as not directly comparable to results derived from the time-invariant the number of persons in a given 10-cell/μL group over the total number of MSM. An additional analysis included accounting for time- persons in that group. A discontinuity in the probability of ART initiation is evident at the 200-cells/μL threshold. varying confounding and informative censoring using the joint Am J Epidemiol. 2018;187(8):1772–1779 Probability of ART Initiation in 3 Months Mortality Hazard Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 1776 Oldenburg et al. Of these, 935 participants died over the course of 19,269 person- cells/μL below the threshold); 3) the addition of age at base- years of follow-up (mortality incidence rate = 4.9 per 100 person- line and sex as covariates in the model (Web Table 2). years). Table 2 and Web Table 1 show the distribution of baseline Figure 3 graphically displays the results of each analysis. covariates for persons above and below the threshold. Of the 935 In the regression discontinuity model at a bandwidth of deaths, 734 were among persons who were eligible for ART ≤350 cells/μL, there was a 41% reduction in mortality with at baseline (incidence rate = 6.6 per 100 person-years) and 201 immediate eligibility for ART (hazard ratio (HR) = 0.59, 95% occurred among those who were not eligible (2.5 per 100 person- conﬁdence interval (CI): 0.42, 0.81) (Figure 2,Table 3), which years). Mortality decreased as baseline CD4 count increased, and was lowered to a 30% reduction in a model with a restricted there was evidence of a discontinuity at the 200-cells/μL thresh- cubic spline (HR = 0.70, 95% CI: 0.46, 1.05) and in a model old (Figure 1). with a squared functional form for CD4 count (HR = 0.70, Figure 2 demonstrates evidence of discontinuity in the proba- 95% CI: 0.43, 1.13). These results were similar in magni- bility of initiating ART within 6 months by baseline CD4 count. tude to the effect estimates at a narrower bandwidth of 150–250 Baseline characteristics for the overall sample were roughly bal- cells/μL(HR = 0.66, 95% CI: 0.35, 1.26). The CACE demon- anced between persons who were eligible for treatment at base- strated a 44% reduction in mortality with immediate initiation line and those who were not eligible (Table 2) but were more of ART among the compliers at the widest bandwidth (HR = closely balanced for persons closer to the threshold (Web 0.56, 95% CI: 0.41, 0.77). These estimates were robust to the Table 1). Sensitivity analyses were conducted with additional inclusion of baseline covariates in the model (Web Table 2). functional forms for CD4 counts above and below the threshold, In the IPW MSM, initiating ART within a 3-month grace including 1) a squared functional form for CD4 counts below period from study entry was associated with a 51% reduction the threshold; 2) a restricted cubic spline at 125 cells/μL(75 in all-cause mortality (HR = 0.49, 95% CI: 0.42, 0.58) and a Table 2. Baseline Characteristics of Participants in a Study of Immediate Initiation of Antiretroviral Therapy Among Persons With Human Immunodeﬁciency Virus Infection (n = 4,435), KwaZulu-Natal, South Africa, 2007–2011 Eligibility for ART Initiation at Baseline Characteristic Below Threshold (Eligible) (n = 2,751) Above Threshold (Ineligible) (n = 1,684) No. of Persons % Median (IQR) No. of Persons % Median (IQR) Age, years 33.1 (27.5–41.4) 31.3 (24.8–40.3) Female sex 1,790 65.1 1,278 75.9 Baseline CD4 cell count, cells/μL 101 (49–140) 268 (233–306) Asset index quintile Lowest 594 21.6 402 23.9 Second lowest 571 20.8 357 21.2 Middle 488 17.7 315 18.7 Second highest 404 14.7 239 14.2 Highest 347 12.6 241 14.3 Missing data 347 12.6 130 7.7 Distance to nearest clinic, km 2.6 (1.5–3.4) 2.4 (1.5–3.5) Place of residence Rural 1,249 45.4 813 48.3 Periurban 918 33.4 553 32.8 Urban 252 9.2 189 11.2 Missing data 332 12.1 129 7.7 Educational attainment, years ≤7 (none or primary) 920 33.4 564 33.5 8–12 (secondary) 1,523 55.4 951 56.5 >12 (tertiary) 246 8.9 133 7.9 Missing data 62 2.3 36 2.1 Abbreviations: ART, antiretroviral therapy; IQR, interquartile range. Household wealth was estimated as quintiles of the ﬁrst components identiﬁed by principal components analysis of 32 household assets and characteristics. Am J Epidemiol. 2018;187(8):1772–1779 Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 ART and Mortality in Rural South Africa 1777 1.0 Table 3. Primary Analysis Results for Regression Discontinuity and Inverse-Probability–Weighted Analyses of Immediate Initiation of 0.5 Antiretroviral Therapy Among Persons With Human Immunodeﬁciency Virus Infection, KwaZulu-Natal, South Africa, 0.0 2007–2011 –0.5 Model and CD4 Cell Count HR 95% CI –1.0 Unadjusted 1.28 1.08, 1.51 –1.5 Regression discontinuity—ITT –2.0 ≤350 cells/μL 0.59 0.42, 0.81 150–250 cells/μL 0.66 0.35, 1.26 –2.5 175–225 cells/μL 0.50 0.23, 1.55 Regression discontinuity—CACE ≤350 cells/μL 0.56 0.41, 0.77 150–250 cells/μL 0.58 0.25, 1.31 Modeling Method 175–225 cells/μL 0.43 0.10, 1.81 Figure 3. Primary analysis results for the relationship between antiret- Inverse probability weighting roviral therapy (ART) and mortality among persons with human immu- nodeﬁciency virus infection, KwaZulu-Natal, South Africa, 2007–2011. Time-invariant ART status 0.49 0.42, 0.58 Results were derived using the regression discontinuity design (RDD) a Time-varying ART status 0.54 0.41, 0.70 for both the intention-to-treat (ITT) effect ( ) and the complier average □ Time-varying ART status with 0.50 0.37, 0.66 causal effect (CACE; )atthe ≤350-cells/μL, 50- to 350-cells/μL, and censoring weights 150- to 250-cells/μL bandwidths (left to right); inverse-probability– weighted (IPW) marginal structural models (MSMs) (from left to right, Abbreviations: ART, antiretroviral therapy; CACE, complier average baseline time-invariant ART initiation, time-updated ART status censor- causal effect; CI, conﬁdence interval; HR, hazard ratio; ITT, intention to ing persons without laboratory tests at 12 months, and time-updated treat. ART status censoring persons without laboratory tests at 12 months with inverse-probability-of-censoring weights applied) ( ); the unad- Censored at a 12-month gap in laboratory values. justed effect of ART on mortality (♦); and the effect adjusted for baseline Censored at a 12-month gap in laboratory values and accounting covariates ( ). Bars, 95% conﬁdence intervals. for censoring with inverse-probability-of-censoring weights applied. future applications, triangulation of causal inference across mul- 46% reduction in a time-varying model censoring persons tiple methods may be most valuable when the preexisting evi- without a laboratory test in the previous 12 months (HR = 0.54, dence is weak or inconsistent. In these cases, inconsistent 95% CI: 0.41, 0.70). In the censored model with an ART status × ﬁndings across different causal methods will be more likely time-since-initiation interaction term, there was signiﬁcant evi- than in our application, and consistent ﬁndings thus have dence of an increase in the protective effect of ART over time greater potential to substantially strengthen the evidence on (per year, HR = 0.84, 95% CI: 0.76, 0.94). causality. While the broad causal question of interest in the present application was the relationship between ART and mortality, DISCUSSION each study design presented herein answered a subtly different The RDD and the IPW MSM yielded consistent results, in- speciﬁc causal question. Each of these results has a slightly dif- dicating an approximately 40%–50% reduction in mortality due ferent interpretation. The unadjusted association showed an to immediate initiation of ART. These results provide both con- increased risk of mortality with ART use, which is expected given sistent and complementary information. The CACE and the time- the strong confounding by CD4 count. Each method of causal invariant MSM estimate the effect of immediate ART initiation inference evaluated here showed that, as expected, ART use (within 3 months of entry into care) on all-cause mortality. The was protective against mortality. Taken together, these results CACE found a 44% reduction in all-cause mortality, as com- demonstrate the robustness of the causal effect of ART on pared with 51% with the time-invariant MSM, with completely mortality in “real life.” Using a large population-based cohort overlapping conﬁdence intervals. The time-varying MSM, without the resources of a carefully conducted randomized con- a commonly used method for modeling ART status as an expo- trolled trial, we demonstrated a large decrease in mortality with sure due to the potential for time-varying confounding, was simi- the use of ART. The use of multiple approaches for causal infer- larly consistent with the previous 2 approaches. Prior studies have ence also strengthens the evidence arising from this study in established the efﬁcacy of ART for prevention of mortality, and comparison with most cohort studies, which do not use such CD4 count is a well-known confounder of this relationship. We approaches. chose the causal effect of ART on mortality for our study using The different methods we used generate different types of multiple causal inference methods, because this relationship is causal effect size estimates. Time-invariant inverse probability well-understood and thus provides a good example with which to weighting of MSMs determines the estimate in the entire study demonstrate the usefulness of a methodological approach. In population and thus can be generalized across the entire Am J Epidemiol. 2018;187(8):1772–1779 Unadjusted RDD ITT RDD CACE IPW MSM Baseline-Adjusted Log Hazard Ratio Downloaded from https://academic.oup.com/aje/article/187/8/1772/4952669 by DeepDyve user on 20 July 2022 1778 Oldenburg et al. distribution of CD4 cell counts. Notably, in the time-varying same overarching question adds additional robustness to the model, the estimate is conditional on baseline covariates. In interpretation of results. When the data allow, approaches that the RDD, generalizability will depend on additional assump- have different assumptions for validity should be used rou- tions. In the presence of heterogeneity of treatment effects ac- tinely to strengthen conﬁdence in causal effect estimates. cording to the assignment variable (in this application, CD4 count), the RDD effect may have limited generalizability. In the RDD literature, 3 perspectives on the generalizability of effects have been posited (5, 12). First is that the effect size is ACKNOWLEDGMENTS generalizable to the entire study population and is an average Author afﬁliations: Department of Epidemiology, treatment effect (32). The assumption required for this interpreta- Harvard T.H. Chan School of Public Health, Boston, tion is that the functional form of the potential outcomes (e.g., had Massachusetts (Catherine E. Oldenburg, George R. Seage); everyone been treated versus had no one been treated) are known. Francis I. Proctor Foundation, University of California, San However, this is a strong and untestable assumption. The second Francisco, San Francisco, California (Catherine E. perspective is that the effect estimated under the RDD is only gen- Oldenburg); Africa Health Research Institute, Durban and eralizable locally, within an arbitrary region around the threshold. Somkhele, South Africa (Frank Tanser, Till Bärnighausen); The third perspective is that the effect size estimated under the Department of Epidemiology, Faculty of Health Sciences, RDD represents a weighted average of the treatment effect in the University of KwaZulu-Natal, Durban, South Africa (Frank entire study population, with weights that are proportional to the Tanser); Department of Biostatistics, Harvard T.H. Chan probability of an individual’s value of the assignment variable School of Public Health, Boston, Massachusetts (Victor De (CD4 count) being in the neighborhood of the threshold (33). Gruttola); The Fenway Institute, Fenway Community Given the strong assumptions required for the ﬁrst perspective, Health, Boston, Massachusetts (Kenneth H. Mayer); the IPW estimate, which is an average treatment effect, could Department of Global Health and Population, Harvard T.H. differ from the regression discontinuity estimate if the rela- Chan School of Public Health, Boston, Massachusetts tionship between ART and mortality is stronger at lower CD4 (Kenneth H. Mayer, Till Bärnighausen); Department of counts (i.e., in persons who are sicker at baseline), compared Medicine, Beth Israel Deaconess Medical Center, Boston, with those whose baseline CD4 count is 200 cells/μL. Massachusetts (Kenneth H. Mayer); Department of For both methodological approaches, the data we used for these Behavioral and Social Sciences and Department of analyses had signiﬁcant strengths. The public-sector ART clinic Epidemiology, Institute for Community Health Promotion, in this region (the Hlabisa HIV Treatment and Care Programme) School of Public Health, Brown University, Providence, provides the vast majority of HIV care in the area, and thus mis- Rhode Island (Matthew J. Mimiaga); Department of Global classiﬁcation of exposure is likely to have been minimal. Follow- Health, School of Public Health, Boston University, Boston, up information was very complete in our study, because it was Massachusetts (Jacob Bor); Research Department of collected through one of Africa’s largest and most rigorous Infection and Population Health, Centre for Sexual Health, population-based cohorts. The cohort covers the entire popu- University College London, London, United Kingdom (Till lation in the catchment areas of the clinics through which pa- Bärnighausen); and Heidelberg Institute of Public Health, tients were recruited for our study, and data on mortality have University of Heidelberg, Heidelberg, Germany (Till been collectedonanongoing basis for over 15 years. Death Bärnighausen). registration in the cohort is near-complete (34). As a result, we The Hlabisa HIV Treatment and Care Programme is funded still observed our outcome of interest in nearly all of the patients by the US Agency for International Development and the who were lost to follow-up from clinical HIV care. Use of com- President’s Emergency Plan for AIDS Relief (grant 674-A- plete, high-quality data allows for direct comparison of esti- 00-08-001-00). This work was partially supported by the US mates generated by the two approaches, speciﬁcally in how National Institutes of Health (grants T32-DA013911 and they each meet the exchangeability requirement for causal R25-MH083620 to C.E.O., grant R37-AI51164 to V.D.G., inference from observational data, as well as the generalizabil- grant R01-HD084233 to T.B., and grants R01-AI124389 and ity of each estimate. R01-HD084233 to T.B. and F.T.). The Africa Health The effect estimates from the RDD and MSM were not iden- Research Institute, University of KwaZulu-Natal (Durban, tical, but they were similar in magnitude, providing strong evi- South Africa), receives core funding from the Wellcome Trust dence of a protective effect of ART against all-cause mortality (grant 082384/Z/07/Z). among HIV-infected persons receiving care in rural South Africa. Conﬂict of interest: none declared. 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Journal

American Journal of Epidemiology – Oxford University Press

Published: Aug 1, 2018

Keywords: models, structural; mortality; anti-retroviral agents; dirty bombs

References

Estimating causal effects from epidemiological data

Hernán, MA; Robins, JM
Inclusion of quasi-experimental studies in systematic reviews of health systems research

Rockers, PC; Røttingen, JA; Shemilt, I
Instruments for causal inference: an epidemiologist’s dream?

Hernán, MA; Robins, JM
Quasi-experimental study designs series—paper 7: assessing the assumptions

Bärnighausen, T; Oldenburg, C; Tugwell, P
Early versus standard antiretroviral therapy for HIV-infected adults in Haiti

Severe, P; Juste, MA; Ambroise, A
Effects of early versus delayed initiation of antiretroviral treatment on clinical outcomes of HIV-1 infection: results from the phase 3 HPTN 052 randomised controlled trial

Grinsztejn, B; Hosseinipour, MC; Ribaudo, HJ
Initiation of antiretroviral therapy in early asymptomatic HIV infection

INSIGHT, START Study Group; Lundgren, JD; Babiker, AG
Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men

Hernán, MA; Brumback, B; Robins, JM
Regression discontinuity designs in epidemiology: causal inference without randomized trials

Bor, J; Moscoe, E; Mutevedzi, P
Regression discontinuity designs are underutilized in medicine, epidemiology, and public health: a review of current and best practice

Moscoe, E; Bor, J; Bärnighausen, T
Three approaches to causal inference in regression discontinuity designs

Bor, J; Moscoe, E; Bärnighausen, T
Regression discontinuity for causal effect estimation in epidemiology

Oldenburg, CE; Moscoe, E; Bärnighausen, T
Commentary: regression discontinuity design: let’s give it a try to evaluate medical and public health interventions

Vandenbroucke, JP; le, Cessie S
Regression-discontinuity analysis: an alternative to the ex post factor experiment

Thistlethwaite, DL; Campbell, DT
Estimating marginal returns to medical care: evidence from at-risk newborns

Almond, D; Doyle, JJ; Kowalski, AE
The early benefits of human papillomavirus vaccination on cervical dysplasia and anogenital warts

Smith, LM; Strumpf, EC; Kaufman, JS
Effect of human papillomavirus (HPV) vaccination on clinical indicators of sexual behaviour among adolescent girls: the Ontario Grade 8 HPV Vaccine Cohort Study

Smith, LM; Kaufman, JS; Strumpf, EC
Efficacy of prostate-specific antigen screening: use of the regression discontinuity in the PLCO Cancer Screening Trial

Shoag, J; Halpern, J; Eisner, B
Estimating efficacy in a randomized trial with product nonadherence: application of multiple methods to a trial of preexposure prophylaxis for HIV prevention

Murnane, PM; Brown, ER; Donnell, D
Beyond the intention-to-treat in comparative effectiveness research

Hernán, MA; Hernández-Díaz, S
Beyond intention to treat: what is the right question?

Shrier, I; Steele, RJ; Verhagen, E
Does obesity shorten life? The importance of well-defined interventions to answer causal questions

Hernán, MA; Taubman, SL
Invited commentary: positivity in practice

Westreich, D; Cole, SR
Instrumental variable estimation in a survival context

Tchetgen, Tchetgen EJ; Walter, S; Vansteelandt, S
Identification and estimation of local average treatment effects

Imbens, GW; Angrist, JD
Constructing inverse probability weights for marginal structural models

Cole, SR; Hernán, MA
Marginal structural models for estimating the effect of highly active antiretroviral therapy initiation on CD4 cell count

Cole, SR; Hernán, MA; Margolick, JB
Cohort profile: Africa Centre Demographic Information System (ACDIS) and population-based HIV survey

Tanser, F; Hosegood, V; Bärnighausen, T
Cohort profile: Hlabisa HIV Treatment and Care Programme

Houlihan, CF; Bland, RM; Mutevedzi, PC
Mass HIV treatment and sex disparities in life expectancy: demographic surveillance in rural South Africa

Bor, J; Rosen, S; Chimbindi, N
Assignment to treatment group on the basis of a covariate
Regression discontinuity designs in economics

Lee, DS; Lemieux, T
Increases in adult life expectancy in rural South Africa: valuing the scale-up of HIV treatment

Bor, J; Herbst, AJ; Newell, ML

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Antiretroviral Therapy and Mortality in Rural South Africa: A Comparison of Causal Modeling Approaches

Antiretroviral Therapy and Mortality in Rural South Africa: A Comparison of Causal Modeling Approaches

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Antiretroviral Therapy and Mortality in Rural South Africa: A Comparison of Causal Modeling Approaches

Antiretroviral Therapy and Mortality in Rural South Africa: A Comparison of Causal Modeling Approaches

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