Interval estimation of odds ratio in a stratified randomized clinical trial with noncompliance

It is not uncommon to encounter a randomized clinical trial (RCT), in which we need to account for both the noncompliance of patients to their assigned treatment and confounders to avoid making a misleading inference. In this paper, we focus our attention on estimation of the relative treatment efficacy measured by the odds ratio (OR) in large strata for a stratified RCT with noncompliance. We have developed five asymptotic interval estimators for the OR. We employ Monte Carlo simulation to evaluate the finite-sample performance of these interval estimators in a variety of situations. We note that the interval estimator using the weighted least squares (WLS) method may perform well when the number of strata is small, but tend to be liberal when the number of strata is large. We find that the interval estimator using weights which are not functions of unknown parameters required to be estimated from data can improve the accuracy of the interval estimator based on the WLS method, but lose precision. We note that the estimator using the logarithmic transformation of the WLS point estimator and the interval estimator using the logarithmic transformation of the Mantel-Haenszel (MH) type of point estimator can perform well with respect to both the coverage probability and the average length in all the situations considered here. We further note that the interval estimator derived from a quadratic equation using a randomization-based method can be of use as the number of strata is large. Finally, we use the data taken from a multiple risk factor intervention trial to illustrate the use of interval estimators appropriate for being employed when the number of strata is small or moderate.