Biometrics

Louis, Thomas A.; Molenberghs, Geert; Verbeke, Geert; Zucker, David; Davidian, Marie

doi: 10.1111/j.1541-0420.2009.01394.xpmid: N/A

Balasubramanian, Raji; Lagakos, Stephen W.

doi: 10.1111/j.1541-0420.2009.01242.xpmid: 19397583

Summary Knowledge of incidence rates of HIV and other infectious diseases is important in evaluating the state of an epidemic as well as for designing interventional studies. Estimation of disease incidence from longitudinal studies can be expensive and time consuming. Alternatively, Janssen et al. (1998, Journal of the American Medical Association 280, 42–48) proposed the estimation of HIV incidence at a single point in time based on the combined use of a standard and “detuned” antibody assay. This article frames the problem from a longitudinal perspective, from which the maximum likelihood estimator of incidence is determined and compared with the Janssen estimator. The formulation also allows estimation for general situations, including different batteries of tests among subjects, inclusion of covariates, and a comparative evaluation of different test batteries to help guide study design. The methods are illustrated with data from an HIV interventional trial and a seroprevalence survey recently conducted in Botswana.

Jacqmin‐Gadda, Hélène; Proust‐Lima, Cécile; Taylor, Jeremy M.G.; Commenges, Daniel

doi: 10.1111/j.1541-0420.2009.01234.xpmid: 19432771

Summary Latent class models have been recently developed for the joint analysis of a longitudinal quantitative outcome and a time to event. These models assume that the population is divided in G latent classes characterized by different risk functions for the event, and different profiles of evolution for the markers that are described by a mixed model for each class. However, the key assumption of conditional independence between the marker and the event given the latent classes is difficult to evaluate because the latent classes are not observed. Using a joint model with latent classes and shared random effects, we propose a score test for the null hypothesis of independence between the marker and the outcome given the latent classes versus the alternative hypothesis that the risk of event depends on one or several random effects from the mixed model in addition to the latent classes. A simulation study was performed to compare the behavior of the score test to other previously proposed tests, including situations where the alternative hypothesis or the baseline risk function are misspecified. In all the investigated situations, the score test was the most powerful. The methodology was applied to develop a prognostic model for recurrence of prostate cancer given the evolution of prostate‐specific antigen in a cohort of patients treated by radiation therapy.

Rizopoulos, Dimitris; Verbeke, Geert; Molenberghs, Geert

doi: 10.1111/j.1541-0420.2009.01273.xpmid: 19459832

Summary The majority of the statistical literature for the joint modeling of longitudinal and time‐to‐event data has focused on the development of models that aim at capturing specific aspects of the motivating case studies. However, little attention has been given to the development of diagnostic and model‐assessment tools. The main difficulty in using standard model diagnostics in joint models is the nonrandom dropout in the longitudinal outcome caused by the occurrence of events. In particular, the reference distribution of statistics, such as the residuals, in missing data settings is not directly available and complex calculations are required to derive it. In this article, we propose a multiple‐imputation‐based approach for creating multiple versions of the completed data set under the assumed joint model. Residuals and diagnostic plots for the complete data model can then be calculated based on these imputed data sets. Our proposals are exemplified using two real data sets.

Yang, Song; Prentice, Ross

doi: 10.1111/j.1541-0420.2009.01243.xpmid: 19397582

Summary For testing for treatment effects with time‐to‐event data, the logrank test is the most popular choice and has some optimality properties under proportional hazards alternatives. It may also be combined with other tests when a range of nonproportional alternatives are entertained. We introduce some versatile tests that use adaptively weighted logrank statistics. The adaptive weights utilize the hazard ratio obtained by fitting the model of Yang and Prentice (2005, Biometrika 92, 1–17). Extensive numerical studies have been performed under proportional and nonproportional alternatives, with a wide range of hazard ratios patterns. These studies show that these new tests typically improve the tests they are designed to modify. In particular, the adaptively weighted logrank test maintains optimality at the proportional alternatives, while improving the power over a wide range of nonproportional alternatives. The new tests are illustrated in several real data examples.

Huang, C.‐Y.; Qin, J.; Wang, M.‐C.

doi: 10.1111/j.1541-0420.2009.01266.xpmid: 19459839

Summary Recurrent event data analyses are usually conducted under the assumption that the censoring time is independent of the recurrent event process. In many applications the censoring time can be informative about the underlying recurrent event process, especially in situations where a correlated failure event could potentially terminate the observation of recurrent events. In this article, we consider a semiparametric model of recurrent event data that allows correlations between censoring times and recurrent event process via frailty. This flexible framework incorporates both time‐dependent and time‐independent covariates in the formulation, while leaving the distributions of frailty and censoring times unspecified. We propose a novel semiparametric inference procedure that depends on neither the frailty nor the censoring time distribution. Large sample properties of the regression parameter estimates and the estimated baseline cumulative intensity functions are studied. Numerical studies demonstrate that the proposed methodology performs well for realistic sample sizes. An analysis of hospitalization data for patients in an AIDS cohort study is presented to illustrate the proposed method.

Zheng, Yingye; Cai, Tianxi; Stanford, Janet L.; Feng, Ziding

doi: 10.1111/j.1541-0420.2009.01246.xpmid: 19397579

Summary Rigorous statistical evaluation of the predictive values of novel biomarkers is critical prior to applying novel biomarkers into routine standard care. It is important to identify factors that influence the performance of a biomarker in order to determine the optimal conditions for test performance. We propose a covariate‐specific time‐dependent positive predictive values curve to quantify the predictive accuracy of a prognostic marker measured on a continuous scale and with censored failure time outcome. The covariate effect is accommodated with a semiparametric regression model framework. In particular, we adopt a smoothed survival time regression technique (Dabrowska, 1997, The Annals of Statistics 25, 1510–1540) to account for the situation where risk for the disease occurrence and progression is likely to change over time. In addition, we provide asymptotic distribution theory and resampling‐based procedures for making statistical inference on the covariate‐specific positive predictive values. We illustrate our approach with numerical studies and a dataset from a prostate cancer study.

Reiss, Philip T.; Ogden, R. Todd

doi: 10.1111/j.1541-0420.2009.01233.xpmid: 19432766

Summary Functional principal component regression (FPCR) is a promising new method for regressing scalar outcomes on functional predictors. In this article, we present a theoretical justification for the use of principal components in functional regression. FPCR is then extended in two directions: from linear to the generalized linear modeling, and from univariate signal predictors to high‐resolution image predictors. We show how to implement the method efficiently by adapting generalized additive model technology to the functional regression context. A technique is proposed for estimating simultaneous confidence bands for the coefficient function; in the neuroimaging setting, this yields a novel means to identify brain regions that are associated with a clinical outcome. A new application of likelihood ratio testing is described for assessing the null hypothesis of a constant coefficient function. The performance of the methodology is illustrated via simulations and real data analyses with positron emission tomography images as predictors.

Li, Yisheng; Lin, Xihong; Müller, Peter

doi: 10.1111/j.1541-0420.2009.01227.xpmid: 19432777

Summary We consider Bayesian inference in semiparametric mixed models (SPMMs) for longitudinal data. SPMMs are a class of models that use a nonparametric function to model a time effect, a parametric function to model other covariate effects, and parametric or nonparametric random effects to account for the within‐subject correlation. We model the nonparametric function using a Bayesian formulation of a cubic smoothing spline, and the random effect distribution using a normal distribution and alternatively a nonparametric Dirichlet process (DP) prior. When the random effect distribution is assumed to be normal, we propose a uniform shrinkage prior (USP) for the variance components and the smoothing parameter. When the random effect distribution is modeled nonparametrically, we use a DP prior with a normal base measure and propose a USP for the hyperparameters of the DP base measure. We argue that the commonly assumed DP prior implies a nonzero mean of the random effect distribution, even when a base measure with mean zero is specified. This implies weak identifiability for the fixed effects, and can therefore lead to biased estimators and poor inference for the regression coefficients and the spline estimator of the nonparametric function. We propose an adjustment using a postprocessing technique. We show that under mild conditions the posterior is proper under the proposed USP, a flat prior for the fixed effect parameters, and an improper prior for the residual variance. We illustrate the proposed approach using a longitudinal hormone dataset, and carry out extensive simulation studies to compare its finite sample performance with existing methods.

Ni, Xiao; Zhang, Daowen; Zhang, Hao Helen

doi: 10.1111/j.1541-0420.2009.01240.xpmid: 19397585

Summary We propose a double‐penalized likelihood approach for simultaneous model selection and estimation in semiparametric mixed models for longitudinal data. Two types of penalties are jointly imposed on the ordinary log‐likelihood: the roughness penalty on the nonparametric baseline function and a nonconcave shrinkage penalty on linear coefficients to achieve model sparsity. Compared to existing estimation equation based approaches, our procedure provides valid inference for data with missing at random, and will be more efficient if the specified model is correct. Another advantage of the new procedure is its easy computation for both regression components and variance parameters. We show that the double‐penalized problem can be conveniently reformulated into a linear mixed model framework, so that existing software can be directly used to implement our method. For the purpose of model inference, we derive both frequentist and Bayesian variance estimation for estimated parametric and nonparametric components. Simulation is used to evaluate and compare the performance of our method to the existing ones. We then apply the new method to a real data set from a lactation study.