Why Odds Ratios Can Be Tricky Statistics: The Case of Finasteride, Dutasteride, and Sexual Dysfunction

Finasteride and dutasteride are 5α-reductase inhibitor drugs that are used to treat benign prostatic hyperplasia (BPH). Randomized controlled trials (RCTs) conducted in men with BPH show that these drugs impair libido and cause erectile dysfunction. Meta-analyses of the RCTs confirm the findings, estimating odds ratio (OR) values for these adverse effects at around 1.50. A problem with meta-analyses that do not report absolute risks with drug vs placebo and that extract ORs instead of relative risks (RRs) from RCT data is that it is hard for the reader to know how to interpret the findings and communicate them to patients. Had the RR been 1.50, the reader would conclude that the risk with drug is 50% higher than the risk with placebo; this is easily understood because the risk with placebo would be available from the RCTs. In contrast, an OR of 1.50 means that the odds with drug are 50% higher than the odds with placebo; understanding this requires a knowledge of what the odds with placebo are as well as an understanding of what odds mean. Odds are not as easily understood as risks are. Odds are numerically different from risks, and the OR is numerically different from the RR. The difference between the OR and the RR is numerically small when the risks are similar in the two groups and also when the risks are dissimilar but the risk is small in the group of interest. The difference between the OR and the RR becomes increasingly large when the risks are dissimilar in the two groups and when the risk in the group of interest is not small. Smallness of risk, in this context, has been conservatively stated as 10%, but it could be possible to use a higher cutoff, such as 20%. Other issues related to risk, odds, RR, and OR are also discussed.