Blog Post

Where did the odds ratios go?

May 28, 2024

Reviewing recent FDA approvals, you may be struck by the total absence of odds ratios. Browsing the labels from the 2023 novel approvals, you can find proportions, differences in proportions, Chi-Squared analyses, CMH and variants, but logistic regression and odds ratios have practically disappeared from labeling. What gives?

There has been a push by FDA to have easily understandable labeling; odds ratios lack the simple and intuitive interpretation that a difference in proportions can provide. Consider this simple example: a drug has a response rate of 75%, while placebo has a response rate of 50%. The difference in proportions is 25%; this is simple and easy to understand. What is the odds ratio in this example? THREE. Someone seeing an odds ratio of 3 in a label may conclude they’re 3 times as likely to respond on drug, but this is clearly not the case. Too often, I’ve heard statisticians describe an odds ratio wrong and somehow we are expecting patients, clinicians, and drug reps to get this right!

So: The odds ratio is unintuitive. Why use it in the first place? One of the main advantages of the odds ratio is that it can be estimated in a logistic regression with covariate adjustments to potentially improve the power of a treatment comparison. However, again, those covariate adjustments in logistic regression are tricky to interpret and the appropriate estimates from the model are not always straightforward. FDA provides some examples of how this can go wrong and suggested approaches in their recent covariate guidance (section III, C).  Bottom line is that you have tricky modeling that yields an odds ratio that no one understands.

This difficulty may or may not be the motivation underlying the scarcity of odds ratios in recent labels, but FDA has absolutely been giving recent feedback for sponsors to consider other methodology when odds ratios and logistic regression are proposed.

What to use then?

A difference in proportions Z test is simple and everyone can understand the difference between two proportions.  It yields things like an estimate, standard error, and z score, so if you have multi-stage designs that require combination of summary statistics (Cui, Hung, Wang sample size re-estimation, for example) or multiple imputation, it can readily be adapted for those.  This simple test can be extended for multiple stratification variables; Stokes, Davis, Koch “Categorical Data Analysis Using SAS” and Agesti “Categorical Data Analysis” are excellent resources and many of the methods described can easily be implemented in common analysis software such as SAS and R.

Need help choosing the right analysis for your phase III trials? Contact us to speak with one of our Biometrics Regulatory Experts.

Ben Vaughn, Chief Strategist Biostatistics and Protocol Design, has demonstrated leadership excellence in the industry for more than 20 years. In his role, he utilizes his extensive expertise to guide sponsors through marketing applications, regulatory interactions, and the design and analysis of analgesia trials. Mr. Vaughn has supported more than 75 pain trials, 30+ marketing applications, and 6 FDA advisory committee meetings (both back room and bullpen) over the course of his career. He has represented sponsors in more than 50 Type A/B/C meetings with FDA.