Interval estimation of the proportion ratio in repeated binary measurements under a stratified randomized clinical trial with noncompliance.

The proportion ratio (PR) of a positive response between an experimental treatment and a standard treatment (or placebo) is often used to measure the relative treatment efficacy in a randomized clinical trial (RCT). For ethical reasons, it is almost inevitable to encounter some patients not complying with their assigned treatment. Furthermore, when there are confounders in a RCT or meta-analysis, we commonly employ stratified analysis to control the confounding effects on interval estimation of the PR. On the basis of a general risk multiplicative model, we focus our discussion on interval estimation of the PR in repeated binary data under a stratified RCT with noncompliance. We develop seven asymptotic closed-form interval estimators for the PR. We apply Monte Carlo simulation to study the finite-sample performance of these interval estimators in a variety of situations. We note that the two interval estimators with the logarithmic transformation based on the commonly used weighted least squares (WLS) approach can be liberal, while the three interval estimators with the Mantel-Haenszel (MH) weight derived from various methods can consistently perform well. We also note that the two estimators with the estimated optimal weight defined in the context using Fieller's Theorem and a randomization-based approach may not necessarily produce a confidence interval preferable to the MH-type interval estimators for the PR with respect to accuracy and precision.