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This thesis presents Regenerative Rejection Sampling (RRS), a novel approximate sampling algorithm inspired by classical Rejection Sampling and Markov Chain Monte Carlo methods. The method constructs a continuous-time regenerative process…
Complete randomization balances covariates on average, but covariate imbalance often exists in finite samples. Rerandomization can ensure covariate balance in the realized experiment by discarding the undesired treatment assignments. Many…
Technological advancements in the field of mobile devices and wearable sensors have helped overcome obstacles in the delivery of care, making it possible to deliver behavioral treatments anytime and anywhere. Increasingly the delivery of…
Biomarker-guided designs are increasingly used to evaluate personalized treatments based on patients' biomarker status in Phase II and III clinical trials. With adaptive enrichment, these designs can improve the efficiency of evaluating the…
Background: It has long been advised to account for baseline covariates in the analysis of confirmatory randomised trials, with the main statistical justifications being that this increases power and, when a randomisation scheme balanced…
Various adaptive randomization procedures (adaptive designs) have been proposed to clinical trials. This paper discusses several broad families of procedures, such as the play-the-winner rule and Markov chain model, randomized…
Biased-coin designs are used in clinical trials to allocate treatments with some randomness while maintaining approximately equal allocation. More recent rules are compared with Efron's [Biometrika 58 (1971) 403-417] biased-coin rule and…
Modern randomization methods in clinical trials are invariably adaptive, meaning that the assignment of the next subject to a treatment group uses the accumulated information in the trial. Some of the recent adaptive randomization methods…
A framework for online robust adaptive radiation therapy (ART) is presented. This framework is designed to (i) handle interfractional geometric variations following a probability distribution different from the a priori hypothesis, (ii)…
Data from both a randomized trial and an observational study are sometimes simultaneously available for evaluating the effect of an intervention. The randomized data typically allows for reliable estimation of average treatment effects but…
Clinical trials usually target average treatment effects, but treatment decisions are made for individuals. This tension motivates a common criticism of evidence-based medicine: a treatment that is beneficial on average may be inappropriate…
Estimating the effects of interventions in networks is complicated when the units are interacting, such that the outcomes for one unit may depend on the treatment assignment and behavior of many or all other units (i.e., there is…
Linear regression is arguably the most fundamental statistical model; however, the validity of its use in randomized clinical trials, despite being common practice, has never been crystal clear, particularly when stratified or…
A multi-arm multi-stage trial is a multi-arm trial which includes interim analyses - analysing the data at certain specified points, generally discontinuing treatments which are concluded to not work and proceeding with the remainder. It is…
We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such sub-populations could be defined by a biomarker or risk factor measured at…
It is generally appreciated that a frequentist analysis of a group sequential trial must in order to avoid inflating type I error account for the fact that one or more interim analyses were performed. It is also to a lesser extent realised…
We propose a convex and fast signal reconstruction method for block sparsity under arbitrary linear transform with unknown block structure. The proposed method is a generalization of the similar existing method and can reconstruct signals…
Medical research has evolved conventions for choosing sample size in randomized clinical trials that rest on the theory of hypothesis testing. Bayesians have argued that trials should be designed to maximize subjective expected utility in…
Random allocation is essential for causal inference, but practical constraints often require assigning participants in clusters. They may be stratified pre-assignment, either of necessity or to reduce differences between treatment and…
The win ratio (WR) statistic is increasingly used to evaluate treatment effects based on prioritized composite endpoints, yet existing Bayesian adaptive designs are not directly applicable because the WR is a summary statistic derived from…