| cox.sat.dev {glmnetr} | R Documentation |
Calculate the CoxPH saturated log-likelihood
Description
Calculate the saturated log-likelihood for the Cox model using both the Efron and Breslow approximations for the case where all ties at a common event time have the same weights (exp(X*B)). For the simple case without ties the saturated log-likelihood is 0 as the contribution to the log-likelihood at each event time point can be made arbitrarily close to 1 by assigning a much larger weight to the record with an event. Similarly, in the case of ties one can assign a much larger weight to be associated with one of the event times such that the associated record contributes a 1 to the likelihood. Next one can assign a very large weight to a second tie, but smaller than the first tie considered, and this too will contribute a 1 to the likelihood. Continuing in this way for this and all time points with ties, the partial log-likelihood is 0, just like for the no-ties case. Note, this is the same argument with which we derive the log-likelihood of 0 for the no ties case. Still, to be consistent with others we derive the saturated log-likelihood with ties under the constraint that all ties at each event time carry the same weights.
Usage
cox.sat.dev(y_, e_)
Arguments
y_ |
Time variable for a survival analysis, whether or not there is a start time |
e_ |
Event indicator with 1 for event 0 otherwise. |
Value
Saturated log likelihood for the Efron and Breslow approximations.