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Effects of Collinearity on Cox Proportional Hazard Model with Time Dependent Coefficients: A Simulation Study

Background: The Cox proportional hazard model has gained ground in Biostatistics and other related fields. It has been extended to capture different scenarios, part of which are violation of the proportionality of the hazards, presence of time dependent covariates and also time dependent co-efficients. This paper focuses on the behaviour of the Cox Model in relation to time coefficients in the presence of different levels of collinearity. 
Objectives: The objectives of this study are to examine the effects of collinearity on the estimates of time dependent co-effiecients in Cox proportional hazard model and to compare the estimates of the model for the logarithm and the square functions of time. 
Materials and methods: The Algorithm based on a binomial model was extended in order to incorporate the different correlation structures required for the study. The scaled Schoenfeld residuals plots revealed the behaviour of the estimated betas at different degrees of collinearity. Results and conclusions are based of outcome of simulation study performed only. 
Results: The estimated betas were compared to the true betas at the different level of collinearity in graphical pattern. 
Conclusion: The study shows that collinearity is a huge factor that influences the correctness of the estimates of the regressors within the framework of Cox model.