I always associated/used log-rank test to evaluate Hazard Ratios.

However, a well-known professor is using/presenting results of log-rank test for Relative Risk and Risk Ratio. Can anyone explain how these two statistics relate with a Log-rank test?


The log-rank test assumes that two survival time distributions are in proportional hazards, which can also be stated as assuming that one curve is an exponentiation of the other. Log-rank is a special case of the Cox proportional hazards model. Both methods can be used to estimate hazard ratios. Neither has anything to do with risk ratios (relative risk) which are ratios of probabilities. Although you can get a hazard ratio from log-rank it is much preferred to use the Cox model for that purpose. The Cox model can also handle continuous variables and covariate adjustment.

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    $\begingroup$ So, when someone is stating that is calculating Risk Ratio with log-rank then there is some kind of misinterpretation. Am I correct? Also, as I understood, there is no statistics in survival analysis that can give me a Relative Risk between treatments. Did I understand it correctly? $\endgroup$ – yohanna Jun 10 '15 at 14:08
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    $\begingroup$ There are models that model risk ratios but you are correct in the sense that nothing related to the Cox model models risk ratios. Lots of people confuse rate ratios (e.g., hazard ratios) with risk ratios. "Risk" means either a probability, or in economics, the amount of a loss multiplied by the probability of the loss. Risk never refers to an instantaneous change (rate). $\endgroup$ – Frank Harrell Jun 10 '15 at 19:10

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