Statistical methods for recurrent event data in the presence of a terminal event and incomplete covariate information

In many clinical and epidemiological studies, recurrent events such as infections in immunocompromised patients or injuries in athletes often occur. It is of interest to examine the relationship between covariates and recurrent events, however in many situations, some of the covariates collected involve missing information due to various reasons. Under such missingness, a commonly practiced method is to analyze complete cases; this method may be inefficient or result in biased estimates for parameters. In this dissertation, we develop methods to analyze recurrent events data with missing covariate information. These will be useful in reducing the bias and improving the efficiency of parameter estimates. This method is motivated by the need for analyzing recurrent infections in a renal transplant cohort from India in which approximately 19% of patients died and over 13% had missing covariate information. Literature shows that opportunistic infections times and death time may be correlated and need to be adjusted in the estimation process. First, we studied this problem by developing methods using marginal rate models for both recurrent events and terminal events with missing data. We adopted a weighted estimating equation approach with missing data assumed to be missing at random (MAR) for estimating the parameters. Second, we considered a marginal rate model for multiple type recurrent events in the presence of a terminal event. We proposed a weighted estimating equation approach assuming that terminal events preclude further recurrent events. We adjusted for the terminal events via inverse probability survival weights. The asymptotic properties of the proposed estimators were derived using empirical process theory. Third, we extended the marginal rate model for analyzing multiple type recurrent events in the presence of a terminal event to handle missing covariates. The main goal was to examine the relationship between covariates and multiple type recurrent infections broadly classified into bacterial, fungal and viral origin from the aforementioned data. We considered a weighted estimating equation approach to estimate the parameters. Through simulations, we examined the finite sample properties of the estimators and then applied the method to the India renal transplant data for illustration in all three papers