Confidence intervals for a difference between lognormal means in cluster randomization trials

Abstract

Cluster randomization trials, in which intact social units are randomized to different interventions, have become popular in the last 25 years. Outcomes from these trials in many cases are positively skewed, following approximately lognormal distributions. When inference is focused on the difference between treatment arm arithmetic means, existent confidence interval procedures either make restricting assumptions or are complex to implement. We approach this problem by assuming log-transformed outcomes from each treatment arm follow a one-way random effects model. The treatment arm means are functions of multiple parameters for which separate confidence intervals are readily available, suggesting that the method of variance estimates recovery may be applied to obtain closed-form confidence intervals. A simulation study showed that this simple approach performs well in small sample sizes in terms of empirical coverage, relatively balanced tail errors, and interval widths as compared to existing methods. The methods are illustrated using data arising from a cluster randomization trial investigating a critical pathway for the treatment of community acquired pneumonia.

Confidence interval estimation for treatment effects in cluster randomization trials based on ranks

“…That approach entails regarding the Mann‐Whitney probability as a function of the normal mean difference and variance components. Inferences may be proceed by first constructing confidence limits for components and then apply the method of variance estimates recovery 63 …”

“…Examples include length of hospital stay and health cost data, which are usually right‐skewed. Such data may be more meaningfully analyzed on the raw scale as done by Poirier et al in a cluster randomization trial setting 63 . This is because differences in length of hospital stays or monetary units between treatment arms are relevant to cost‐effectiveness analysis.…”