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I fitted a cox proportional hazards model in R using the coxph(). My explanatory variables include; gender, residence, antenatal care, tetanus injection, iron tablets, size at birth, place of delivery and Caesarean section. The model provided hazard Ratios for the variables mentioned. How do I know the hazard Ratio associated with a response/level within a variable. For instance, HR(gender) = 1.08950. How do I know the HR for males and also females. Or how do I know if males have a relative high risk than females or vise versa and at what proportion does it increase. I encoded “females” = 1 and “males” = 2

I was expecting the model to give separate hazard ratios for males and females as well as any response in the other variables. But I only see hazard ratio for the variables and not the responses. Although, I have the coefficient estimates, p-values and the confidence intervals from the cox model. But I am emphasizing on the hazard ratio's because I need clear interpretations.

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Similarly to how ordinary linear regression has an intercept that represents the predicted outcome for a baseline set of predictor values, a Cox regression assumes a baseline hazard function that represents the distribution of event times for a baseline set of predictor values.

Just as the coefficients in linear regression represent differences of outcome from the intercept that are associated with differences in predictor values, the coefficients in a Cox regression represent differences in log-hazard from the baseline. Your hazard ratios (HRs) are exponentiations of those log-hazards.

Each of the Cox regression coefficients is thus the log of a hazard ratio for the difference between the actual value of a predictor versus its baseline value. If you "encoded 'females' = 1 and 'males' = 2" as numeric, then the Cox regression coefficient is for a 1-unit increase in gender, or for males versus females. The HR is thus for males versus females. For continuous predictors modeled linearly, the HR is that associated with each one-unit increase in the predictor.

After the Cox model has been fit, you can get the estimated distribution of survival times for the baseline set of predictor values, or for any other specified set of predictor values. If you do that, I recommend that you use the same software as you used for fitting the Cox model, as the internal representation of "baseline" values might not be what you would expect and differs among implementations.

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