Bayesian Analysis of First-Order Markov Models for Autocorrelated Binary Responses

In many clinical trials, patient outcomes are often binary-valued which are measured asynchronously over time across various dose levels. To account for autocorrelation among such longitudinally observed outcomes, a first-order Markov model for binary data is developed. Moreover, to account for the asynchronously observed time points, nonhomogeneous models for the transition probabilities are proposed. The transition probabilities are modeled using B-spline basis functions after suitable transformations. Additionally, if the underlying dose-response curve is assumed to be non-decreasing, our model allows for the estimation of any underlying non-decreasing curve based on suitably constructed prior distributions. We also extended our model to the mixed effect model to incorporate individual-specific random effects. Numerical comparisons with traditional models are provided based on simulated data sets, and also practical applications are illustrated using real data sets.

Automated summary

In many clinical trials, binary-valued patient outcomes measured asynchronously over time across different dose levels are common. To address autocorrelation among these longitudinally observed outcomes, a first-order Markov model for binary data is developed. Nonhomogeneous models for transition probabilities are proposed to account for asynchronously observed time points, with B-spline basis functions used for modeling the transition probabilities. The model also allows estimation of any underlying non-decreasing curve based on suitable prior distributions, along with the incorporation of individual-specific random effects through a mixed effect model. Numerical comparisons with traditional models are conducted using simulated data sets, as well as practical applications using real data sets.