Bayesian semiparametric regression for longitudinal binary processes with missing data

Abstract

Summary Longitudinal studies with binary repeated measures are widespread in biomedical research. Marginal regression approaches for balanced binary data are well developed, while for binary process data, where measurement times are irregular and may differ by individuals, likelihood-based methods for marginal regression analysis are less well developed. In this article, we develop a Bayesian regression model for analyzing longitudinal binary process data, with emphasis on dealing with missingness. We focus on the settings where data are missing at random, which require a correctly specified joint distribution for the repeated measures in order to draw valid likelihood-based inference about the marginal mean. To provide maximum flexibility, the proposed model specifies both the marginal mean and serial dependence structures using nonparametric smooth functions. Serial dependence is allowed to depend on the time lag between adjacent outcomes as well as other relevant covariates. Inference is fully Bayesian. Using simulations, we show that adequate modeling of the serial dependence structure is necessary for valid inference of the marginal mean when the binary process data are missing at random. Longitudinal viral load data from the HIV Epidemiology Research Study (HERS) are analyzed for illustration.

Predicting Panel Data Binary Choice with the Gibbs Posterior

“…We also provide some results in Tables 3 and 4 (for the case P(Y = 1) = 0.15), when a more commonly used normal prior is used for β (Erkanli et al, 2001;Su & Hogan, 2008). The results are qualitatively similar to the corresponding results in Tables 1 and 2.…”

“…On the other hand, compared to the more traditional Bayesian approach, which uses a likelihood-based posterior (Erkanli et al, 2001;Su & Hogan, 2008), the Gibbs posterior approach is more robust against model misspecification. This is because the latter is constructed directly from the empirical riskR(b) in equation 1.1, which does not require construction of a likelihood function based on the true probability model of (y it , z it ).…”

“…For example, Hsiao (2003) summarizes the National Longitudinal Surveys of Labor Market Experience with T's ranging from 3 to 20 and with n ranging from about 5000 to 12,000. Biostatistical studies of longitudinal data can also have the number of subjects n being much larger than the number of repetitions T (see Erkanli, Soyer, &Angold, 2001 andSu &Hogan, 2008, who study Bayesian modeling of binary longitudinal data).…”

Modeling of Multivariate Monotone Disease Processes in the Presence of Misclassification

“…Justified by the existence of easy/difficult-to-diagnose subjects, the relaxation of some of the assumptions (A.1)-(A.6) could be of interest; for instance, a possible improvement of the scoring behavior of the examiners across the study could be considered. The inclusion of time-dependent within-and across-time association parameters or their dependence on covariates, along the lines of the work by Su and Hogan (2008), can also be pursued. Finally, the extension of the proposed models for handling multinomial data or higher orders of dependence is the subject of ongoing research.…”

A nested semiparametric method for case‐control study with missingness

“…However, a prespecified functional form increases the chance of model misspecification (Si & Reiter, 2013), and misspecifications will lead to biased results (Chen & Ibrahim, 2014). In order to improve the robustness, modifications have been made in both MLE and Bayesian methods, such as incorporating a spline into the algorithm to estimate the nonparametric components (Rizopoulos & Ghosh, 2011; Su & Hogan, 2008). The modified MLE and modified Bayesian methods are alternative approaches to our semiparametric imputation approach.…”