Accounting for expected attrition in the planning of cluster randomized trials for assessing treatment effect heterogeneity

Abstract

Background: Detecting treatment effect heterogeneity is an important objective in cluster randomized trials and implementation research. While sample size procedures for testing the average treatment effect accounting for participant attrition assuming missing completely at random or missing at random have been previously developed, the impact of attrition on the power for detecting heterogeneous treatment effects in cluster randomized trials remains unknown.

Methods: We provide a sample size formula for testing for a heterogeneous treatment effect assuming the outcome is missing completely at random. We also propose an efficient Monte Carlo sample size procedure for assessing heterogeneous treatment effect assuming covariate-dependent outcome missingness (missing at random). We compare our sample size methods with the direct inflation method that divides the estimated sample size by the mean follow-up rate. We also evaluate our methods through simulation studies and illustrate them with a real-world example.

Results: Simulation results show that our proposed sample size methods under both missing completely at random and missing at random provide sufficient power for assessing heterogeneous treatment effect. The proposed sample size methods lead to more accurate sample size estimates than the direct inflation method when the missingness rate is high (e.g., ≥ 30%). Moreover, sample size estimation under both missing completely at random and missing at random is sensitive to the missingness rate, but not sensitive to the intracluster correlation coefficient among the missingness indicators.

Conclusion: Our new sample size methods can assist in planning cluster randomized trials that plan to assess a heterogeneous treatment effect and participant attrition is expected to occur.

Keywords: Cluster randomized trial; Heterogeneity of treatment effect; Intracluster correlation coefficient; Missing at random; Missing completely at random; Missing data; Power calculation.

Fig. 1

Heatmap of the ratio of sample size estimated based on the proposed formula under MCAR to that obtained from the direct inflation method under the follow-up rate of $\pi =0.6.$, the cluster size of $m\in \left\{20,,,100\right\}$ and the missingness ICC of $\tau \in \left\{\text{0.05,0.6,1}\right\}$

Fig. 2

A schematic roadmap for executing the Monte Carlo approach for sample size calculation with the HTE analysis in cluster randomized trials under the missing at random assumption