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.

Sample size considerations for comparing dynamic treatment regimens in a sequential multiple-assignment randomized trial with a continuous longitudinal outcome

“…A working assumption similar to A1(a) is commonly made in developing sample-size formulae for SMARTs with outcomes collected once at the end of the study. 19,20,38 Working assumptions A1(b) and A1(c) impose further constraints on the covariance of the outcome conditional on response and allow for tractable sample size formulae. We believe assumption A1(b) is approximately satisfied in most common definitions of response (see the supplement).…”

“…Equation (18) follows from equation (17) by identifiability assumption I3 and smoothing over Y ðd Þ t 0 , equation (19) arises from the definition of covariance, and equation (20) is a consequence of working assumption A1(b).…”

“…The comparison of two embedded DTRs which recommend different first-stage treatments is a common primary aim for a SMART. 7 There exist data analytic methods for addressing this aim when the outcome is continuous, 7 survival, 18 binary, 19 cluster-level 20 and longitudinal. 21,22 A key step in designing a SMART, as with any randomized trial, is determining the sample size needed to be able detect a desired effect with given power.…”

Optimal allocation to treatments in a sequential multiple assignment randomized trial

“…Multiple ATSs are embedded in a SMART and the main question in the design phase of a SMART is how many subjects should be assigned to each ATS, and whether an unequal allocation is better than an equal allocation. Some recent papers studied the relation between sample size and power for SMART designs, 25,[28][29][30][31][32][33][34] but did not study the optimal allocation of units to treatment sequences and the loss of efficiency of using equal rather than unequal allocation.…”

Ascertaining properties of weighting in the estimation of optimal treatment regimes under monotone missingness

“…Because these methods require complete data, it is often necessary to employ methods to address missing data. A common approach is to apply multiple imputation to complete the data, compute a given estimator of an optimal regime on each of the imputed data sets, and then aggregate these estimators, for example, by averaging or voting 48‐53 . Although estimation of an optimal treatment regime is often but one part of a suite of secondary analyses, the requirement to develop a complete dataset is convenient as it can be used for a variety of other analyses.…”