Budgeting SMART: Sample size and repeated measures with a cost constraint in a longitudinal sequential, multiple-assignment randomized trial

Abstract

Clinical practice often involves delivering a sequence of treatments which adapts to a patient’s changing needs. A dynamic treatment regimen (DTR) is a sequence of pre-specified decision rules which, based on a patient’s ongoing data, recommend interventions at multiple stages of treatment. The sequential, multiple-assignment randomized trial (SMART) is a tool which can be used in the development of a high-quality DTR. Often, SMARTs involve longitudinal outcomes collected over the course of the trial. An important consideration in the design of a longitudinal-outcome SMART, as with any trial, is both the sample size and number of measurement occasions. We develop sample size formulae for a common SMART design with a longitudinal outcome in which the primary aim is to compare, at end-of-study, two embedded DTRs which recommend different first-stage treatments. We discuss practical and statistical considerations in choosing between adding individuals or measurement occasions, subject to a fixed cost constraint, while respecting the unique features of a SMART, including modeling constraints and over/under-representation of sequences of treatment among participants.