Robust inference in the joint modeling of multilevel zero-inflated Poisson and Cox models

A popular method for simultaneously modeling of correlated count response with excess zeros and time to event is by means of the joint models. In these models, the likelihood-based methods (such as expectation-maximization algorithm and Newton-Raphson) are used for estimating the parameters, but in the presence of contaminations, these methods are unstable. To overcome this challenge, we extend the M-estimator methods and propose a robust estimator approach to obtain a robust estimation of the regression parameters in the joint model. Our proposed algorithm has two steps (Expectation and Solution). In the expectation step, the likelihood function is expected by conditioning on the observed data and in the solution step, the parameters are computed, with solving robust estimating equations. Therefore, this algorithm achieves robustness by applying robust estimating equations and weighted likelihood in the S-step. Simulation studies under various situations of contaminations show that the robust algorithm gives us consistent estimates with a smaller bias than likelihood-based methods. The application section uses data on factors affecting fertility and birth spacing.