Some Issues and Results on Nonparametric Maximum likelihood
Estimations in Joint Model for Survival and Longitudinal Data.

Fushing Hsieh
Univ. of California, Davis


In study of biomedical dynamics, longitudinal covariate data together
with the survival time of an event of interest is collected from each
individual subject. Separately the longitudinal analysis is biased
due to the truncation at the event time, while sparse and incomplete
covariate history also causes the survival analysis biased even
equipped with practical imputation techniques. To resolve this two-sided
biased issue, the nonparametric maximum likelihood approach is suggested
among many proposals in previous works. However, first, the fundamental
likelihood construction issue is still not yet well settled in the literature
due to the involvement of possible informative generating mechanisms of
the longitudinal time schedule; second, neither a valid nor comprehensive
account of statistical inference under a joint model setting is available.

To fill in these two gaps in this talk, a full likelihood is constructed,
from which a partial and a conditional likelihood are derived
pertaining to conditions on the generating mechanisms. Then, the generalized
maximum likelihood (GMLE) approach and the method of sieves are applied to
derive interval estimations as well as goodness-of-fit testing under various
smoothness conditions.

This is joint work with Jane-Ling Wang in Dept. of Statistics, UC Davis.