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Evaluation of the type I error rate when using parametric bootstrap analysis of a cluster randomized controlled trial
Lilian Golzarri-Arroyo1, Stephanie L Dickinson1, Yasaman Jamshidi-Naeini1
1Department of Epidemiology and Biostatistics, Indiana University School of Public Health-Bloomington USA.
Background:
Cluster randomized controlled trials (cRCTs) are increasingly used but must be analyzed carefully. We conducted a simulation study to evaluate the validity of a parametric bootstrap (PB) approach with respect to the empirical type I error rate for a cRCT with binary outcomes and a small number of clusters.
Methods:
We simulated a case study with a binary (0/1) outcome, four clusters, and 100 subjects per cluster. To compare the validity of the test with respect to error rate, we simulated the same experiment with K=10, 20, and 30 clusters, each with 2,000 simulated datasets. To test the null hypothesis, we used a generalized linear mixed model including a random intercept for clusters and obtained p-values based on likelihood ratio tests (LRTs) using the parametric bootstrap method as implemented in the R package "pbkrtest".
Results:
The PB test produced error rates of 9.1%, 5.5%, 4.9%, and 5.0% on average across all ICC values for K=4, K=10, K=20, and K=30, respectively. The error rates were higher, ranging from 9.1% to 36.5% for K=4, in the models with singular fits (i.e., ignoring clustering) because the ICC was estimated to be zero.
Conclusion:
Using the parametric bootstrap for cRCTs with a small number of clusters results in inflated error rates and is not valid.
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