ABSTRACT
D.1 Computing Individual Survival Probabilities after Fitting a Cox Model Estimation of the survival probability πt(x1,x2, . . . , xp) = P(Y ≥ t|x1,x2, . . . , xp) requires, besides estimation of the regression coefficients of the Cox model, obtaining information about the baseline hazard function from the data. The quantity actually used is not directly the baseline hazard function h0(t) but the so-called cumulative baseline hazard function H0(s) =
Estimates for this quantity to be used after fitting a Cox regression model have been provided by Kalbfleisch and Prentice (1973) and Breslow (1972). The Breslow estimate can be expressed explicitly as
where the first sum includes only the uncensored subjects, whereas the second includes also the censored subjects, and Yj is for a censored subject the time point of censoring.
