Estimation of time independent Cox proportional hazard model with correlated unordered categorical covariates

Abstract

Many studies have been carried out since the development of Cox model(1972). Little or no attention on the performance of Cox model with correlated unordered categorical data exists in literature. The paper is aimed at investigating the behavior of the parameter estimates and the model under varied collinearity ( p =0.2, 0.6, 0.9) between discrete independent variablse. Two discrete independent data were generated using binomial distribution with the considered levels of collinearity for sample size of 10, 30, 100 and 500.Survival time was generated with estimated baseline hazard function. The paper shows that regression coefficients with small standard errors are statistically significant when sample
size is large at low collinearity as against small sample size. There is evidence of non proportional hazard assumptions when there exists collinearity between unordered categorical data. Moreso, Cox model is statistically significant at all levels of collinearity considered for varied sample size except when sample size is 30 in the study.