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I'm curious about interpreting the coefficients of dummy variables within a Cox Proportional Hazards (PH) model. Consider a scenario where I have a sample comprising both male and female patients, and I aim to include a dummy variable to represent females. In linear models, interpreting such dummy variables is straightforward due to the presence of an intercept that captures the reference group (in this case, males). However, in Cox models, the intercept isn't included.

Hence, I'm seeking clarification on how to interpret dummy variables in the absence of an intercept within a Cox PH model. Any insights or guidance on this matter would be greatly appreciated.

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Say $b$ is the regression coefficient of an indicator dummy of some category, say category 2, of your nominal predictor. Then $e^b$ has as interpretation: the hazard of category 2 is $e^b$ as large as the hazard in the reference category. Only these hazard ratio's are estimated, not the hazards themselves.

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The interpretation of a dummy variable is similar to that of other variables. It is an estimate of the multiplicative change in the hazard when it is 1 vs. when it is 0. For your case, what is the ratio of hazards for women vs. men?

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