Two-Stage Nonparametric Bootstrap Sampling with Shrinkage Correction for Clustered Data

This article describes a new Stata command, tsb, for performing a stratified two-stage nonparametric bootstrap resampling procedure for clustered data. Estimates for uncertainty around the point estimate, such as standard error and confidence intervals, are derived from the resultant bootstrap samples. A shrinkage estimator proposed for correcting possible overestimation due to second-stage sampling is implemented as default. Although this command is written with cost effectiveness analyses alongside cluster trials in mind, it is applicable to the analysis of continuous endpoints in cluster trials more generally. The use of this command is exemplified with a case study of a cost effectiveness analysis undertaken alongside a cluster randomized trial. We also report bootstrap confidence interval coverage by using data from a published simulation study.