In clinical studies, longitudinal covariates are often used to monitor the
progression of the disease as well as survival time. Relationship between
a failure time process and some longitudinal covariates is of key interest
and so is the understanding of the pattern of longitudinal process
to learn more about health status of patients, or to get some insight
into the progression of disease. Joint modeling of the longitudinal and
survival data has certain advantages and emerged as an effective way to
gain information from each other. Typically, a parametric longitudinal
model is assumed to facilitate the likelihood approach. However, the
choice of a proper parametric model turns out more illusive than standard
longitudinal studies where no survival end-point occurs. Furthermore,
the computational burden due to both Monte Carlo numerical integration
and EM (Expected Maximum) algorithm is an important concern in the joint
modelling setting.
To deal with those challenges, in the first part of the talk, I will
propose several nonparametric longitudinal models in the joint modelling
setting. Longitudinal process is represented by some basis functions
and a proportional hazard model is then used to link them with the
event-time. Unknown model parameters are estimated through maximizing
the observed joint likelihood, which are iteratively maximized by the
Monte Carlo Expected Maximization (MCEM) algorithm. The simplicity of
the model structure is crucial to have good numerical stability, and
so the parsimonious nonparametric models have computational advantages
and compare well to competing parametric longitudinal approaches. In
the second part of the talk, I will introduce the method of sieves for
joint modelling to illustrate the high dimensionality problem currently
encountered in the joint modelling literature. The asymptotic properties
of the proposed sieve estimator will be discussed.
Meet the speaker in Room 212 Cockins Hall at 4:30
p.m. Refreshments will be served.