Hypothesis testing in sequentially randomized designs through artificial randomization

An adaptive treatment strategy (ATS) is an outcome-guided algorithm that allows personalized treatment of complex diseases based on patients' disease status and treatment history. Conditions such as AIDS, depression, and cancer usually require several stages of treatment due to the chronic, multifactorial nature of illness progression and management. Sequential multiple assignment randomized (SMAR) designs permit simultaneous inference about multiple ATSs, where patients are sequentially randomized to treatments at different stages depending upon response status. The purpose of the first part of the dissertation is to develop a sample size formula to ensure adequate power for comparing two or more ATSs. Based on a Wald-type statistic for comparing multiple ATSs with a continuous endpoint, we develop a sample size formula and test it through simulation studies. We show via simulation that the proposed sample size formula maintains the nominal power. The proposed sample size formula is applicable to designs with continuous endpoints and will be useful for practitioners while designing SMAR trials to compare adaptive treatment strategies. Hypothesis testing to compare adaptive treatment strategies are usually based on inverse weighting and g-estimation. However, regression methods that allow for comparison of treatment strategies that flexibly adjusts for baseline covariates are not as straight-forward using these methods due to the fact that one patient can belong to multiple strategies. This poses a challenge for data analysts as it violates basic assumptions of regression modeling of unique group membership. In the second part of the dissertation, we propose an "artificial randomization" technique to make the data appear that each subject belongs to a specific ATS. This enables treatment strategy indicators to be inserted as covariates in a regression model. The properties of this method are investigated analytically and through simulation. Public Health Significance: Chronic diseases such as cancer and mental health problems are becoming a major health care burden that present challenges to caregivers and public health officials. Adaptive treatment strategies are natural way of treating patients as subjects' conditions change repeatedly over a course of treatment. Finding optimal ATS is therefore vital for the benefit of the patient as well as for the society to reduce the health care burden. SMAR (sequential multiple adaptive randomized) trials are convenient methods to compare ATSs. In this dissertation, we provide a sample size formula to help design SMARTs. We also introduce an "artificial randomization" technique that would allow researchers to compare strategies in regression based models. These contributions enhance our understanding of debilitating chronic diseases and will help managing them better