Cox model is widely used for analysis of factor effects on censored survival time such as age at first marriage. In most practical situations, the fundamental assumption of the proportionality of hazard in Cox model, which implies that the covariates whose effects are to be investigated have a constant impact on the hazard ratio over the time is not always feasible. For example, the values of some of the covariates for individuals may be different over time and these may cause a break-down of proportionality assumption in the hazard model. Ignoring such violation may result in misleading effects of estimates. In this study therefore, Extended Cox models have been used to analyze data on age at first marriage among Nigerian women between 2013 and 2018 waves of Nigerian Demographic and Health Surveys (NDHS). The standard Cox model as well as Extended Cox models under four distinct time functions, namely, t, t² , log(t) and Heaviside were considered in the analysis and compared using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). The standard Cox model was found to perform worst among all the models considered and Extended model with log(t) time function was best fit for the data.
Key words: Time dependent covariate, Survival time, Baseline hazard, Partial likelihood, Hazard ratio
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