| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 93 === In this thesis, a more flexible and easily explained joint latent varying-coefficient model
is used to model the relationship between time-dependent responses and a failure time.
Here, the dependence mechanism within time-dependent responses, between time-dependent responses
and a failure time, and the heterogeneity among different subjects on
time-dependent responses and failure times are established
through a non-parametric latent process.
Based on the longitudinally measured responses and survival time data, we mainly propose an estimation
procedure for the time-dependent parameter functions. In our estimation approach, the parameter functions are
first approximated via the corresponding basis function expansions.
Trough the estimates of parameters in the basis function expansions,
the estimated parameter functions are then obtained.
Moreover, the asymptotic risks
of the estimated functions are developed in this study. A Monte-Carlo simulation is conducted to examine the
finite sample properties of the proposed estimated functions. Finally, some additional topics of interest
are considered and a possible extension of our proposed model to more complicated joint processes is discussed.
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