Bayesian semiparametric modeling for HIV longitudinal data with censoring and skewness.

In biomedical studies, the analysis of longitudinal data based on Gaussian assumptions is common practice. Nevertheless, more often than not, the observed responses are naturally skewed, rendering the use of symmetric mixed effects models inadequate. In addition, it is also common in clinical assays that the patient's responses are subject to some upper and/or lower quantification limit, depending on the diagnostic assays used for their detection. Furthermore, responses may also often present a nonlinear relation with some covariates, such as time. To address the aforementioned three issues, we consider a Bayesian semiparametric longitudinal censored model based on a combination of splines, wavelets, and the skew-normal distribution. Specifically, we focus on the use of splines to approximate the general mean, wavelets for modeling the individual subject trajectories, and on the skew-normal distribution for modeling the random effects. The newly developed method is illustrated through simulated data and real data concerning AIDS/HIV viral loads.

Nonparametric Bayesian covariate-adjusted estimation of the Youden index.

A novel nonparametric regression model is developed for evaluating the covariate-specific accuracy of a continuous biological marker. Accurately screening diseased from nondiseased individuals and correctly diagnosing disease stage are critically important to health care on several fronts, including guiding recommendations about combinations of treatments and their intensities. The accuracy of a continuous medical test or biomarker varies by the cutoff threshold (c) used to infer disease status. Accuracy can be measured by the probability of testing positive for diseased individuals (the true positive probability or sensitivity, Se(c), of the test), and the true negative probability (specificity, Sp(c)) of the test. A commonly used summary measure of test accuracy is the Youden index, YI=max{Se(c)+Sp(c)-1:c∈ℝ}, which is popular due in part to its ease of interpretation and relevance to population health research. In addition, clinical practitioners benefit from having an estimate of the optimal cutoff that maximizes sensitivity plus specificity available as a byproduct of estimating YI. We develop a highly flexible nonparametric model to estimate YI and its associated optimal cutoff that can respond to unanticipated skewness, multimodality, and other complexities because data distributions are modeled using dependent Dirichlet process mixtures. Important theoretical results on the support properties of the model are detailed. Inferences are available for the covariate-specific Youden index and its corresponding optimal cutoff threshold. The value of our nonparametric regression model is illustrated using multiple simulation studies and data on the age-specific accuracy of glucose as a biomarker of diabetes.