A generalized logrank-type test for comparison of treatment regimes in sequential multiple assignment randomized trials

Abstract

The sequential multiple assignment randomized trial (SMART) is the ideal study design for the evaluation of multistage treatment regimes, which comprise sequential decision rules that recommend treatments for a patient at each of a series of decision points based on their evolving characteristics. A common goal is to compare the set of so-called embedded regimes represented in the design on the basis of a primary outcome of interest. In the study of chronic diseases and disorders, this outcome is often a time to an event, and a goal is to compare the distributions of the time-to-event outcome associated with each regime in the set. We present a general statistical framework in which we develop a logrank-type test for comparison of the survival distributions associated with regimes within a specified set based on the data from a SMART with an arbitrary number of stages that allows incorporation of covariate information to enhance efficiency and can also be used with data from an observational study. The framework provides clarification of the assumptions required to yield a principled test procedure, and the proposed test subsumes or offers an improved alternative to existing methods. We demonstrate performance of the methods in a suite of simulation studies. The methods are applied to a SMART in patients with acute promyelocytic leukemia.

Keywords: augmented inverse probability weighting; dynamic treatment regime; estimating function; potential outcomes.

FIGURE 1

Schematic depicting the design of Study C9710. Solid circles represent points of randomization. The 4 embedded regimes implied by this design are of the form “Give consolidation therapy initially; if consolidation is completed before the event occurs, give maintenance therapy ,” where ATRA or ATRA+Arsenic Trioxide and ATRA or ATRA+MP+Mtx.

FIGURE 2

Schematic depicting the design of a 2-stage SMART with , in which subjects who do not experience the event prior to Decision 2 are classified as responders or nonresponders to Decision 1 treatment and are randomized to stage 2 treatments within feasible subsets of depending on their stage 1 treatment and response status; here, . Solid circles represent points of randomization. The 8 embedded regimes implied by this design are of the form “Give Trt initially; if the event does not occur before Decision 2 and response, give Trt , otherwise if the event does not occur before Decision 2 and no response, give Trt ,” where the 8 regimes correspond to .

FIGURE 3

Schematic depicting the design of 2 possible 2-stage SMARTs, without and with a control (“standard of care”) regime to which subjects can be randomized up front. In the former design, with no control regime, ; in the latter, control}. In either design, subjects who receive stage 1 options Trt 0 or 1 and do not experience the event prior to Decision 2 are classified as nonresponders or responders to Decision 1 treatment, nonresponders continue stage 1 treatment, and responders are randomized to either continue stage 1 treatment or switch; thus, for such subjects , where 0 indicates continue and 1 indicates switch. Solid circles represent points of randomization. The 4 embedded regimes excluding the possible control regime are of the form “Give Trt initially; if the event does not occur before response status is ascertained and nonresponse, continue; else if response, give ,” where the 4 regimes correspond to .