A Sample Size Calculator for SMART Pilot Studies

Abstract

In clinical practice, as well as in other areas where interventions are provided, a sequential individualized approach to treatment is often necessary, whereby each treatment is adapted based on the object s response. An adaptive intervention is a sequence of decision rules which formalizes the provision of treatment at critical decision points in the care of an individual. In order to inform the development of an adaptive intervention, scientists are increasingly interested in the use of sequential multiple assignment randomized trials (SMART), which is a type of multistage randomized trial where individuals are randomized repeatedly at critical decision points to a set treatment options. While there is great interest in the use of SMART and in the development of adaptive interventions, both are relatively new to the medical and behavioral sciences. As a result, many clinical researchers will first implement a SMART pilot study (i.e., a small-scale version of a SMART) to examine feasibility and acceptability considerations prior to conducting a full-scale SMART study. A primary aim of this paper is to introduce a new methodology to calculate minimal sample size necessary for conducting a SMART pilot.

Use of Sequential Multiple Assignment Randomized Trials (SMARTs) in oncology: systematic review of published studies

“…It is undoubtedly that power analyses for SMART designs present relevant challenges because of the correlation structure between the embedded DTRs [ 29 ]. Several approaches have been proposed in the last years to undertake such issues in the SMART design [ 29 – 31 ] without definitive solutions. However, if the primary aim of a SMART study is to identify the best DTR, it follows that the sizing should be done to be able to detect the optimal DTR.…”

Sample size calculation based on precision for pilot sequential multiple assignment randomized trial (SMART)

“…This approach serves as a complementary method to currently available sample size approaches for pilot SMARTs (Almirall et al., 2012; Kim, 2015; Tamura et al., 2016). As mentioned in Section 1, we further emphasize that the intended specific end‐goal or feasibility aspects for these approaches are different and hence we may not necessarily have a smaller sample size than those existing methods.…”

“…(2012)'s approach as the feasibility‐based approach. A follow‐up work on this presented an alternative precision‐based approach that allows the researchers to observe the response or nonresponse rate, by ensuring the rate is confined within a prespecified margin of error (Kim, 2015).…”

Bayesian Sample Size Calculations for SMART Studies

“…Using the calculations developed in Kim (2016), we determined the sample size of the simulated pilot studies in order to guarantee that at least 6 individuals are observed in each treatment sequence with a 90% probability, which resulted in a sample size of 66 in Scenarios 1 and 4, 114 in Scenario 2, and 64 in Scenario 3. Finally, the type I error was assessed by sizing the full-scale trial in order to identify a minimal detectable difference between strategy means of 2 points in the continuous outcome setting and 0.14 points in the binary outcome setting when there is indeed no difference.…”

“…The major drawback of this approach lies in the specification of the variance of the strategy means' estimator, which, contrary to frequentist calculations, needs to be specified. Although the use of crude estimates from pilot studies of the variance components needed for sample size computations is controversial (Vickers, 2003;Browne, 1995;Bell et al, 2018), and SMART pilot studies are generally sized to ensure that a sufficient number of subjects for each treatment sequence is observed with high probability (Kim, 2016) rather than through precision-based approaches (although an alternative has recently been introduced in Yan et al ( 2021)), we propose to marginalize the Bayesian power function over the posterior distribution of the variance components estimated on pilot data in order account for their variability. The paper is structured as follows.…”