Stochastic EM Algorithm for Joint Model of Logistic Regression and Mechanistic Nonlinear Model in Longitudinal Studies

We study a joint model where logistic regression is applied to binary longitudinal data with mismeasured time-varying covariate that modeled using mechanistic nonlinear model. Multiple random effects are necessary characterize the trajectories of and response variable, leading high dimensional integral in likelihood. To account for computational challenge, we propose stochastic expectation-maximization (StEM) algorithm Gibbs sampler coupled Metropolis–Hastings sampling inference. In contrast previous developments, this uses single imputation missing during Monte Carlo procedure, substantially increasing computing speed. Through simulation, assess algorithm’s convergence compare more classical approaches handling measurement errors. also conduct real-world analysis gain insights into association between CD4 count viral load HIV treatment.