I am fitting a mixed effects shared parameter which involves fitting a nonlinear mixed-effects model for the response variable Y and a piecewise exponential survival model for the time to dropout T for large clinical trials (e.g., >1,000 subjects with up to 11 observations on subjects that complete the trial). One of the issues is whether a missing at random dropout based on the observed response variable Y is predictive of dropout. Hence I wish to include an internal time-dependent covariate (i.e., Yij) in the piecewise exponential hazard function. The problem is that the partial log-likelihood function requires a double summation across subjects which makes the use of numerically derived derivatives infeasible (I ran it for three days and it was still computing so I decided to try using analytical derivatives of computation for which I can). While I have derived the analytical derivative of the partial log-likelihood, I don't know how one specifies that within NLMIXED thereby bypassing the use of numerically derived derivatives. Any help would be greatly appreciated.
Ed
