When Log-Normal and Gamma Models Give Different Results: A Case Study

The analysis of a simple dataset with two similar models is considered. A generalized linear model assuming a log-normal distribution and a generalized linear model assuming a gamma distribution are two models assuming constant coefficient of variation (CCV). Sources in the literature indicate that these two models are often interchangeable. However, in this real dataset—obtained from a clinical trial of a vaccine product—the two models do not agree. Reasons for this lack of agreement are explored. It is proposed that analyzing a dataset with both of the models may be an ad hoc robustness analysis of the dependence of the conclusions on the assumed model.