Bayesian Methods for SMART Designs With Re-Randomization Based on a Continuous Outcome and Estimating Survival Outcomes When COVID-19 Is a Competing Risk in Cancer Patients

Abstract

Sequential, multiple assignment, randomized trials (SMARTs) typically rely on a binary variable to define response which is used in assigning the next stage treatment assignment. We develop a function of a continuous outcome to assign a probability of staying on the same treatment and then randomly assign the next treatment using a multinomial distribution.

First, we develop a new trial design for small sample SMARTs (snSMARTs). The overall goal of the trial is to determine the optimal first stage treatment. We use a function, called the mapping function, to map the first stage outcome to a probability of staying on the same treatment and Bayesian methods to analyze data from both stages. Re-randomization based on a mapping function of a continuous outcome allows for snSMARTs to be conducted without requiring a binary outcome. We perform simulation studies to compare the proposed design with continuous outcomes to standard snSMART designs with binary outcomes. The proposed design results in more efficient treatment effect estimates and similar outcomes for trial patients. This addresses a gap in rare disease clinical trial methodology by presenting a trial that keeps a continuous outcome continuous, allows patients to either stay or switch treatments based on their outcome, and uses repeated measures for improved statistical properties.

Next, we apply similar concepts to standard size SMARTs with continuous outcomes where the goal is to determine the optimal dynamic treatment regimen (DTR). We present a new trial design for SMARTs that use a tailoring function instead of a binary tailoring variable. Here, we simultaneously develop a tailoring variable and estimate the DTR. We apply methods for developing DTRs from observational data: tree-based regression learning and Q-learning. We compare this to a typical SMART design with a tailoring variable and analyzed with generalized estimating equations. This project addresses a gap in clinical trial methodology by presenting SMARTs where second stage treatment is based on a continuous outcome. We demonstrate that data from a SMART using a tailoring function can be used to efficiently estimate the DTR and is more flexible under varying scenarios than a SMART with a tailoring variable.

Finally, we develop Bayesian methods to estimate overall survival for cancer patients when COVID-19 presents a competing risk. First, we forecast local epidemic trends and daily infection risk for an individual by implementing a truncated Dirichlet state space model. We combine the infection risk with COVID-19 cause-specific mortality to obtain predicted COVID-19 cause-specific mortality. We then combine the COVID-19 cause-specific mortality as a competing risk with Bayesian, pre-COVID-19 overall survival estimates in cancer patients. Our main outcome of interest is the difference in restricted mean survival time under immediate treatment (7 days after diagnosis) versus delayed treatment (60 days after diagnosis). We present example cases to demonstrate the use of our methods. The goal of our method is to create an overall personalized predicted survival curve with posterior prediction intervals to allow health care providers to make more informed decisions on immediate versus delayed treatment for cancer patients.