Accounting for complex intracluster correlations in longitudinal cluster randomized trials: a case study in malaria vector control

Background: The effectiveness of malaria vector control interventions is commonly evaluated using parallel-arm cluster randomized trials with outcomes assessed using repeated cross-sectional surveys. A key requirement in designing and analyzing cluster randomized trials is to account for the intra-cluster correlation coefficient (ICC). In addition to exchangeable correlation (which assumes a constant ICC over time), correlation structures proposed for longitudinal cluster trials are block exchangeable (which allows a different within- and between-period ICC) and exponential decay (which allows the between-period ICC to decay at an exponential rate). More flexible correlation structures that do not require a decay are available in statistical software packages and, although not formally proposed for longitudinal cluster trials, may offer some advantages. Our objectives were to empirically explore the impact of these correlation structures on treatment effect inferences, identify gaps in the methodological literature, and make practical recommendations for investigators designing and analyzing such trials. Methods: : We obtained data from a longitudinal parallel-arm cluster randomized trial conducted in Tanzania to compare four different types of insecticide-treated bed-nets. Malaria prevalence was assessed in repeated cross-sectional surveys of 45 households in each of 84 villages at baseline, 12 months, 18 months and 24 months post-randomization (19,083 children in total). We re-analyzed the data using mixed-effects logistic regression according to a prespecified analysis plan but under five different correlation structures as well as a robust variance estimator under exchangeable correlation and compared the estimated correlations and treatment effects. Results: : The estimated correlation structures varied substantially across different models. The unstructured model was the best-fitting model based on information criteria. Although point estimates and confidence intervals for the treatment effect were similar, allowing for more flexible correlation structures led to different conclusions based on statistical significance. Use of robust variance estimators generally led to wider confidence intervals. Conclusion: More flexible correlation structures should not be ruled out in longitudinal cluster randomized trials. This may be particularly important in malaria trials where outcomes may fluctuate over time. In the absence of robust methods for selecting the best-fitting correlation structure, researchers should examine sensitivity of results to different assumptions about the ICC.