In Mplus 7.11 I was able to include cases with partial covariate data into Cox regression models by explicitly estimating their variances and obtain both parameter estimates and standard errors. When I try to do the same in version 7.3, I get estimates but no standard errors and the message, "THE STANDARD ERRORS FOR THIS SURVIVAL MODEL ARE NOT AVAILABLE DUE TO NUMERICAL INTEGRATION AND AUXILIARY PARAMETERS IN THE MODEL.YOU CAN USE THE BASEHAZARD=ON OPTION WITHOUT THE SURVIVAL=(ALL) SPECIFICATION TO RESOLVE THIS PROBLEM." I was curious why this change was made and whether there is a way to obtain SE's from the non-parametric Cox model with incomplete covariate data include in the analysis under MAR missingness assumption.
Section 9 in http://statmodel.com/download/Survival.pdf explains the change. To summarize, the standard errors in 7.11 were not correct for certain special models. We introduced a new type of survival variable: "semi-parameteric" which doesn't have the SE problem and performs as well as the (ALL) version. We changed the language a bit so now the best way to specify a survival variable is "survival=T;" and Mplus automatically decides what the best specification is.
You can also use imputation (as an alternative) for the partial covariates and you won't run into this issue.
It appears from reading Section 9 in the helpful document you referenced that what I would need to do is turn on the basehazard and specify some reasonable number of jumps, say 30, following the survival time variable to approximate the Cox model closely. E.g., if my survival time variable is "adobst", then my survival statement would be survival = adobst(30); Does that sound right? Thanks again.