# Parametric survival models with time-dependent covariate for mixed case interval-censored data

## 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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FS 2012 114 IR.pdf