Triggering-Effect Models for Multi-Type Recurrent Events and Biased Coin Randomization for Biomarker-Stratified Multiarm Trials

Multi-type recurrent events frequently arise in lifetime data analysis. It is reasonable to assume that previously occurred events can trigger more events to come, either of homogeneous or heterogeneous categories. Previous work has focused on non-linear triggering models when there is only a single event type. We propose a general Cox-type structure for modeling the triggering effects among multiple types of events. In Chapter 2, we introduce the general structures of the triggering-effect models for single-event data and multi-type event data. We derive partial likelihood estimators and establish the consistency and asymptotic normality of the estimators, as well as provide plug-in variance estimators. We develop an algorithm to efficiently compute the partial likelihoods, gradients, and Hessian matrices of the models. We demonstrate a good performance of the methods through a series of simulation experiments. The models are applied to a cohort of patients with Li-Fraumeni syndrome (LFS) to analyze the triggering effects between breast cancers versus non-breast cancers. In Chapters 3, we introduce the frailty extension of the triggering-effect models to adjust for cluster effects and unobserved heterogeneity. We use the penalized partial likelihood approach to set up the estimation and inference procedures. We derive the penalized partial likelihoods for the main parameters of interest, and the profile likelihood for the variance parameters. We derive corresponding estimation procedures, and adjust the inference methods accordingly. We develop a two-loop algorithm to implement the estimation process. Simulation experiments are carried out to demonstrate the feasibility of proposed methods. We apply the models to LFS data to investigate the family heterogeneity among patients. In Chapter 4, as a separate topic, we describe how to implement a biased coin design to achieve the desired allocation ratios across interventions and between the number of biomarker-positive and biomarker-negative participants assigned to each intervention. We discuss about how the algorithm performs in terms of the balance of covariates prevalence and the situation of crossover studies. We simulate several scenarios to illustrate the proposed method with the randomization algorithm implemented in the Precision Interventions for Severe and/or Exacerbation-prone Asthma (PrecISE) trial.