What is the formula to calculate the scaled schoenfeld residuals for a coxPH model? 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!
 A: 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!
A: The scaled Schoenfeld residual for time $t_k$ is given by multiplication of the vector of Schoenfeld residuals at time $k$ by the inverse weighted covariance matrix of the (partial likelihood) estimate of the regression coefficients. See here:
(pdf)
at pages 39-42.
Here:
(pdf) you can find the formula: 
$r_{k}^*(\beta) = V^{-1}(\beta, t_k)r_k(\beta)$, where it is highlighted that everything depends on the $\beta$ vector of coefficients from the Cox regression,  $r_k$ is the Schoenfeld residual for events at time $t_k$, $r^*$ expresses scaled Schoenfeld residuals, $V^{-1}(t_k)$ is the covariance matrix of covariates for events at time $t_k$.  
