Evaluating the impact of stratification on the power and cross-arm balance of randomized phase 2 clinical trials

Abstract

Background/aimsRandomized clinical trials often use stratification to ensure balance between arms. Analysis of primary endpoints of these trials typically uses a "stratified analysis," in which analyses are performed separately in each subgroup defined by the stratification factors, and those separate analyses are weighted and combined. In the phase 3 setting, stratified analyses based on a small number of stratification factors can provide a small increase in power. The impact on power and type-1 error of stratification in the setting of smaller sample sizes as in randomized phase 2 trials has not been well characterized.MethodsWe performed computational studies to characterize the power and cross-arm balance of modestly sized clinical trials (less than 170 patients) with varying numbers of stratification factors (0-6), sample sizes, randomization ratios (1:1 vs 2:1), and randomization methods (dynamic balancing vs stratified block).ResultsWe found that the power of unstratified analyses was minimally impacted by the number of stratification factors used in randomization. Analyses stratified by 1-3 factors maintained power over 80%, while power dropped below 80% when four or more stratification factors were used. These trends held regardless of sample size, randomization ratio, and randomization method. For a given randomization ratio and sample size, increasing the number of factors used in randomization had an adverse impact on cross-arm balance. Stratified block randomization performed worse than dynamic balancing with respect to cross-arm balance when three or more stratification factors were used.ConclusionStratified analyses can decrease power in the setting of phase 2 trials when the number of patients in a stratification subgroup is small.

Keywords: Stratified randomization; block randomization; dynamic balancing; power; stratification; stratified analysis.

Figure 1.

Power for different design and analysis scenarios. The number of stratification factors used for randomization varied between 0 and 6 (down rows). The number of stratification factors accounted for in the analyses varied between 0 and the number of stratification factors used for randomization (across columns). All stratification factors were distributed 50/50.

Figure 2.

Power when stratification factors have no prognostic value.