Response adaptive intervention allocation in stepped-wedge cluster randomized trials

Abstract

Background: Stepped-wedge cluster randomized trial (SW-CRT) designs are often used when there is a desire to provide an intervention to all enrolled clusters, because of a belief that it will be effective. However, given there should be equipoise at trial commencement, there has been discussion around whether a pre-trial decision to provide the intervention to all clusters is appropriate. In pharmaceutical drug development, a solution to a similar desire to provide more patients with an effective treatment is to use a response adaptive (RA) design.

Methods: We introduce a way in which RA design could be incorporated in an SW-CRT, permitting modification of the intervention allocation during the trial. The proposed framework explicitly permits a balance to be sought between power and patient benefit considerations. A simulation study evaluates the methodology.

Results: In one scenario, for one particular RA design, the proportion of cluster-periods spent in the intervention condition was observed to increase from 32.2% to 67.9% as the intervention effect was increased. A cost of this was a 6.2% power drop compared to a design that maximized power by fixing the proportion of time in the intervention condition at 45.0%, regardless of the intervention effect.

Conclusions: An RA approach may be most applicable to settings for which the intervention has substantial individual or societal benefit considerations, potentially in combination with notable safety concerns. In such a setting, the proposed methodology may routinely provide the desired adaptability of the roll-out speed, with only a small cost to the study's power.

Keywords: adaptive design; clinical trial; interim analysis; multi-stage; sequential allocation.

FIGURE 1

The empirical rejection probability (ERP) and empirical average proportion of cluster‐periods spent in the intervention condition (EACP), as functions of w and $\theta$, of the response adaptive (RA) stepped‐wedge cluster randomized trial (SW‐CRT) designs with $\eta =0$, $\gamma =2.5$, and $\{p_1,\dots ,p_L\}=\{3,6\}$, in trial design scenario 1 (TDS1). The dashed lines in the ERP plot indicate the desired type‐I and type‐II error‐rates. In the EACP plot they indicate the minimal, initially planned, and maximal values of the EACP based on $X=X_{p_1}$

FIGURE 2

The empirical average final allocation matrix (${\bar{X}}_P$), as a function of $\theta$, of the response adaptive (RA) stepped‐wedge cluster randomized trial (SW‐CRT) design with $\eta =0$, $\gamma =2.5$, $w=1/2$, and $\{p_1,\dots ,p_L\}=\{3,6\}$, in trial design scenario 1 (TDS1). The dashed lines indicate the timing of the interim analyses

FIGURE 3

The empirical probability mass function of the proportion of cluster‐periods spent in the intervention condition, as a function of $\theta$, of the response adaptive (RA) stepped‐wedge cluster randomized trial (SW‐CRT) design with $\eta =0$, $\gamma =2.5$, $w=1/2$, and $\{p_1,\dots ,p_L\}=\{3,6\}$, in trial design scenario 1 (TDS1)

FIGURE 4

The empirical rejection probability (ERP), as a function of w and $\theta$, of the response adaptive (RA) stepped‐wedge cluster randomized trial (SW‐CRT) designs with $\{p_1,\dots ,p_L\}=\{3,6\}$ for different combinations of $\eta$ and $\gamma$, in trial design scenario 1 (TDS1). The dashed lines indicate the desired type‐I and type‐II error‐rates

FIGURE 5

The empirical average proportion of cluster‐periods spent in the intervention condition (EACP), as a function of w and $\theta$, of the response adaptive (RA) stepped‐wedge cluster randomized trial (SW‐CRT) designs with $\{p_1,\dots ,p_L\}=\{3,6\}$ for different combinations of $\eta$ and $\gamma$, in trial design scenario 1 (TDS1). The dashed lines indicate the minimal, initially planned, and maximal values of the EACP based on $X=X_{p_1}$

FIGURE 6

The empirical standard deviation of the proportion of cluster‐periods spent in the intervention condition (ESDCP), as a function of w and $\theta$, of the response adaptive (RA) stepped‐wedge cluster randomized trial (SW‐CRT) designs with $\{p_1,\dots ,p_L\}=\{3,6\}$ for different combinations of $\eta$ and $\gamma$, in trial design scenario 1 (TDS1)

FIGURE 7

The empirical rejection probability (ERP), average proportion of cluster‐periods spent in the intervention condition (EACP), standard deviation of cluster‐periods spent in the intervention condition (EACP), bias (EB), and root‐mean‐square error (RMSE), as functions of w and $\theta$, of the response adaptive (RA) stepped‐wedge cluster randomized trial (SW‐CRT) designs with $\eta =0$ and $\gamma =2.5$, for different values of $\{p_1,\dots ,p_L\}$, in trial design scenario 1 (TDS1). The dashed lines in the ERP plot indicate the desired type‐I and type‐II error‐rates. In the EACP plot they indicate the minimal, initially planned, and maximal values of the EACP based on $X=X_{p_1}$