Comparison of statistical tests for assessing the proportionality assumption and estimation of parameters of the cox model

Before adopting the cox proportional hazards model for censored survival data,a prerequisite is to check the validity of the proportional hazards assumption. we compared three test statistics,weighted residuals,regression survival model,and modeling log-log of survival curve,through simulation under proportional hazards and following types of non-proportional hazards: increasing,decreasing,crossing and diverging relative hazards. we compared power and size of these tests at different censoring proportions (0%,10%,30% and 50%) for sample sizes 40,60,100 and 200. the size (α) of all test statistics remained close to the nominal value (α=0.05),and the power was negatively affected by censoring proportions for all three methods. yet,the regression survival model and modeling the log-log of survival curves provided equally good power for detecting nonproportionality. all three methods resulted in similar estimation of parameters. simulation results demonstrated that modeling the log-log of survival curve and regression survival model performed better in terms of power at the cost of higher type i errorcompared to the weighted residual method. all three methods have also been compared using illustrative data from literature. © 2013 pakistan journal of statistics.