I was taught, that when we deal with data of multiplicative nature, following the log-normal distribution, like in pharmacokinetic analyses, we should log the data first to enable classic parametric tests. The bonus was that the back-transformed tests of means (of log-transformed data) was about the ratio of geometric means (of raw data). We like the geometric means and standard deviations in the pharmaceutical industry, especially because it is equal to medians. Actually, even the regulatory guidelines advise to use the log transformation. This is just an industry standard.
But recently I had a talk with a statistician, who recommended the gamma regression with log link. He plained me why the outcomes of the two are not equivalent. It was not only about the predicted outcome, but also the fact, that GLM handles the mean-variance relationship, which is not handles by log (which changes both mean and variance of the data), does not bias the outcomes (as back-transformed confidence intervals on log data) and still gives nice interpretation in terms of multiplicative change of the response for unit change in predictors.
But, since the models are not equivalent, which one would you advise me to work with log-normal data? Do you know, if the pharmaceutical regulators allow the gamma regression for that? Are the predicted LS-means the geometric means, as when I just run OLS on log-transformed data? As the two models are different, I bet it is not. So what is this?