I have managed to work out how to manually calculate the Schoenfeld residual for a coxPH model and i am getting the same answers as R.
However – i have absolutely no idea how to calculate the Scaled Schoenfeld residuals.
If anyone has the formula for these Scaled Schoenfeld residuals it would be greatly appreciated!
Best Answer
On page 228 in this book on Survival Analysis by Liu et. al. the formula for the scaled Schoenfeld residual for observation i and covariable m is described as:
$$ r_{im}^{\text{scaled schoen}} = \frac{r_{im}^{schoen}(\beta_m)}{V(\beta_m, t_i)} $$
Where $V(\beta_m, t_i)$ describes the variance of the coefficient for the variable $X_m$. This is estimated via the observed Fisher-Information-Matrix that you presumably already calculated in the Fisher-Scoring-step for the estimation of the coefficients (negative 2nd derivative of Partial log-Likelihood w.r.t. all coefficients).
I think, intuitively this makes sense, as you scale the Schoenfeld residuals by the variance of the coefficient of interest. I am looking forward to your response on that - hope this short paragraph helps!