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The calibration plot for logistic regression is quite intuitive for me because we can directly get the predicted probability. However, in Cox regression model we just get the hazard ratio so how can we transform it into the probability?

Steven Xu
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I cover this in some detail here. Use the smooth calibration method, not the stratified Kaplan-Meier method. See various case studies in Regression Modeling Strategies.

Frank Harrell
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  • Hello Prof. Harrell, thanks for your material. I check for the process and I am just wondering that how can we estimate the survival function（S_hat(t | x)） for each individual based on cox regression? Because cox regression just can estimate the hazard ratio. – Steven Xu Dec 16 '23 at 14:55
  • @StevenXu after a Cox model is fit, you use the coefficient values to estimate the baseline cumulative hazard function $H_0(t)$; see this page, for example. You then adjust the baseline cumulative hazard for covariates $x$ to get $H(t|x)$ and transform to a survival estimate via $S(t|x)=\exp(-H(t|x))$. This page outlines how the smooth calibration method works. – EdM Dec 16 '23 at 16:54
  • Survival probability estimates are easily computed using the R survival package survfit function or the R rms package survest and Survival functions. The latter composes an R function to compute $S(t|X)$ from the linear predictor $X\beta$. – Frank Harrell Dec 16 '23 at 17:31