Design and Analysis Considerations for Comparing Dynamic Treatment Regimens with Binary Outcomes from Sequential Multiple Assignment Randomized Trials

Abstract

In behavioral, educational and medical practice, interventions are often personalized over time using strategies that are based on individual behaviors and characteristics and changes in symptoms, severity, or adherence that are a result of one's treatment. Such strategies that more closely mimic real practice, are known as dynamic treatment regimens (DTRs). A sequential multiple assignment randomized trial (SMART) is a multi-stage trial design that can be used to construct effective DTRs. This article reviews a simple to use 'weighted and replicated' estimation technique for comparing DTRs embedded in a SMART design using logistic regression for a binary, end-of-study outcome variable. Based on a Wald test that compares two embedded DTRs of interest from the 'weighted and replicated' regression model, a sample size calculation is presented with a corresponding user-friendly applet to aid in the process of designing a SMART. The analytic models and sample size calculations are presented for three of the more commonly used two-stage SMART designs. Simulations for the sample size calculation show the empirical power reaches expected levels. A data analysis example with corresponding code is presented in the appendix using data from a SMART developing an effective DTR in autism.

Keywords: Adaptive interventions; Dynamic treatment regimes; Inverse-probability-of-treatment weighting; Sequential multiple assignment randomized trial; sample size.

Figure 1

SMART design from an autism trial [19] including 3 embedded DTRs. The R inside a circle denotes randomization; J denotes joint attention and joint engagement; E denotes enhanced milieu teaching; S denotes speech generating device; X₁ denotes coding for first-stage intervention; X_2R and X_2NR denote coding for second-stage intervention for responders and non-responders, respectively.

Figure 2

Three common SMART designs. Design I includes 8 embedded DTRs, design II includes 4 embedded DTRs, and design III includes 3 embedded DTRs. The R inside a circle denotes randomization; X₁ denotes coding for first-stage intervention; X_2R and X_2NR denote coding for second-stage intervention for responders and non-responders, respectively. The tailoring variable is trial-specific with intermediate outcome denoted here by response and non-response.