Extended Survival Models by Incorporating Time Varying Covariate and Coefficient Effect

Volume 1 - Issue 4

Yemane Hailu Fissuh^1,2*, Tsegay Giday Woldu³, Tarekegn Gebreyesus Abisso⁴, Abebe Zewdie Kebebe⁵ and Idriss Abdelmajid Idriss Ahme¹

Received: June 03, 2019;   Published: June 18, 2019

DOI: 10.26717/CTBB.MS.ID.000118

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Abstract

Background: Survival analysis is a major area of interest in the vast disciplines including biostatistics and biomedical researches. Survival data are the observations that systematically arise when the duration from a defined time origin until the occurrence of event for each individual item. Proportionality problems are the key challenges in survival models. The proportionality problems may arise when the coefficient effect varies over time intervals. Thus, to fill this gap and to relax the proportionality assumption, the article is focused on the comparison of proportional hazards models with and without including time-varying coefficient effect and time-varying covariate.

Results: After a comparison of four models, the findings have proved that the statistical significance was highly improved when the time-varying coefficient was considered (P-value≤0.001). However, the findings indicated that despite its improvement in P-value, in general, the addition of time-varying covariate did not provide statistically significant results except when both timevarying covariate and time-varying coefficients were considered as a general model.

Conclusion: To sum up the study, the more general review and rough comparison were done on four cases by using simulated data of a small sample. After systematic evaluation and comparisons of four models with and without time-varying covariates and time-varying coefficient effects. Eventually, the more general model was employed by incorporating both time-varying covariate and time-varying coefficient effects. The results have shown that the last model was partially significant with small P-value for the first regression coefficient. The overall result indicated that consideration of time-varying effect in both coefficient and covariates can give us reasonably robust results but in the case of nonproportionality, considering the time-varying coefficient provides much more robust solutions in general.

Keywords: Cox Model; General Model; Simulations; Time-Varying Co- variates; Time-Varying Coefficient Effect

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