I am getting into survival analysis and am a bit confused about the definition of hazard ratio and odds ratios. This question implies that there is a clear difference between hazard ratios and odds ratios and that it is not straightforward to compute odds ratios from hazard ratios.
Now, I found the paper of Heimer (2016) who report the following results of a coc hazard model:
They compute the odds ratio as the exponential of the coefficient retreived from the hazard model. For example, in column (1), the odds-ratio is retreived by exp(0.295). I though the exponent of the coefficient of a hazard model is the hazard ratio and not the odds ratio. They interpret the odds ratio as "the rate at which trades are closed increases by 34% if the position is a gain".
Are they correct in defining the odds ratio as the exponential of the coefficient? Is their interpretation of the odds ratio correct?
References:
Heimer, R. Z. (2016). Peer pressure: Social interaction and the disposition effect. The Review of Financial Studies, 29(11), 3177-3209.
Best Answer
You are correct that these authors should have called the exponentiation of the Cox regression coefficient the "hazard ratio," not the "odds ratio." In practice, however, the values might not be so different from each other, as @Glen_b explains:
Despite this frequent similarity in values, however, there is no reason to use terminology that isn't correct. As the report was of a Cox proportional hazards regression, "hazard ratio" is the correct terminology. For more detail on these frequently confused terms, see for example: George A, Stead T S, Ganti L (August 26, 2020) What’s the Risk: Differentiating Risk Ratios, Odds Ratios, and Hazard Ratios?. Cureus 12(8): e10047. doi:10.7759/cureus.10047