Contributions to the Analyses of Recurrent Events and Competing Risk

There is a growing interest in the analysis of recurrent events data. Recurrent events are frequently considered as an outcome when a subject could possibly experience more than one event over follow-up period. Thus, It is important to consider previous events history to explore the relationship between the effects of covariates and the correlated failure times. We extend the Cox-type model with time-varying effect depending on the number and the gap time between previous events to enhance both model fit and prediction. Parameter estimation and statistical inference can be achieved via the partial likelihood. A statistical test procedure is provided to assess the existence of the triggering effects. We demonstrate our approach via comprehensive simulation studies and chronic pseudomonas infections in young cystic fibrosis patients’ data. Significantly, our model provides better predictions than the existing models. When some patients do not adhere to their assigned treatments in a randomized trial, the standard intention-to-treat analysis may not properly estimate the effect of treatment on the outcome. Also, considering only received treatment without accounting for unmeasured confounders could be biased. Therefore, it is challenging to obtain the true treatment effect, which can be observed when all subjects comply their assigned regime. Instrumental variable methods help us to consistently estimate the average causal effect of an exposure on some outcome of interest even in the presence of latent confounding. We apply Abadie's weighting scheme to estimate corresponding local average response functions in survival analysis. The method is demonstrated by simulation studies and the colorectal cancer screening data, designed and sponsored by the National Cancer Institute. Competing risks also occur when subjects can experience one or more events which compete with the outcome of interest. In these cases, the competing risk inhibits to observe the event of interest or modifies the chance that this event occurs. We extend existing parametric approaches to estimate the cumulative incidence function for considering both left truncation and interval in competing risks settings. This parametric method is applied to data from the study of osteoporotic fractures to bone mineral density testing interval with age as time scale.Doctor of Philosoph