Citation
Kiani, Kaveh
(2012)
Parametric survival models with time-dependent covariate for mixed case interval-censored data.
Doctoral thesis, Universiti Putra Malaysia.
Abstract
The aim of this research is to analyze parametric survival models in the presence
of left, right, interval and doubly interval censored data with time-dependent
covariates. In this research we utilize and extend two important parametric survival
models, the Gompertz and the exponential, to accommodate these censoring
schemes and time-dependent covariates.
The analysis starts with the extension of the Gompertz model to incorporate
time-dependent covariates in the presence of right-censored data. Then, the performance
of the model is compared with the fixed covariate model. Following
that, comparison is made when a fixed covariate model was fitted wrongly to a
data set with time-dependent covariate. In addition, two methods of constructing
confidence intervals, the Wald and jackknife are explored for the parameters of
this model. Conclusions are drawn based on the coverage probability study.
In the next step, the Gompertz model is further extended to incorporate time dependent covariates with left, right and interval censored data as well as uncensored
data. The model is then investigated thoroughly at dependent and
independent covariate levels through a comprehensive simulation study. Following
that, the model is compared with a fixed covariate model. Then, two methods
of constructing confidence intervals the Wald and likelihood ratio are investigated
for the parameters of the model and conclusions are drawn based on the coverage
probability study.
Finally, a parametric survival model that accommodates doubly interval-censored
data with time-dependent covariates is developed and studied. In order to formulate
this censoring scheme let V and W be the times of two related consecutive
events where both of them are interval-censored and V ≤ W. Then, the survival
time of interest could be defined as, T = W −V . Here it is assumed that the time
to the first event, V , and the survival time, T, follow the exponential distribution
(special case for Gompertz distribution).
In order to get to this final model, we had to explore three separate models in
advance. Firstly, a simple model consisting doubly interval-censored data without
any covariate was studied. Following that, a model with doubly interval-censored
data and fixed covariates is considered. Lastly, a model with fixed covariates is
studied where some of the covariates affect T and the others affect V . All these
models are studied by the simulation study and two methods of constructing
confidence intervals, the Wald and jackknife are explored for the parameters of
the models.
The results indicate that the Gompertz model with left, right and interval censored
data with a time-dependent covariate works rather well despite its complexity.
Similarly, although doubly interval-censored data with a time-dependent
covariate requires more computational effort, the model will perform well if both V and T are exponentially distributed.
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