Joint modeling for longitudinal covariate and binary outcome via h-likelihood

Joint modeling techniques of longitudinal covariates and binary outcomes have attracted considerable attention in medical research. The basic strategy for estimating the coefficients of joint models is to define a joint likelihood based on two submodels with shared random effects. Numerical integration, however, is required in the estimation step for the joint likelihood, which is computationally expensive due to the complexity of the assumed submodels. To overcome this issue, we propose a joint modeling procedure using the h-likelihood to avoid numerical integration in the estimation algorithm. We conduct Monte Carlo simulations to investigate the effectiveness of our proposed modeling procedures by evaluating both the accuracy of the parameter estimates and computational time. The accuracy of the proposed procedure is compared to the two-stage modeling and numerical integration approaches. We also validate our proposed modeling procedure by applying it to the analysis of real data.