CPH and AFT Models for Time-To-Employment Data in the Presence of Cure Fraction

In this work, we present the use of mixture cure models (MCM) to analyze time-to-employment data of graduates of the statistics department, Kano University of Science and Technology, Nigeria. This is against Cox proportional hazards (CPH) and accelerated failure time (AFT) models that are traditionally used to model such types of data. MCM was used because the Kaplan-Meier (KM) employment curve has suggested the possibility of cure with an estimated unemployment fraction of 33.8%. Here, two MCM were constructed based on CPH and AFT assumptions for the latency part of the model. Weibull was used as the baseline distribution in the AFT Cure model. The Cure models were used to estimate the unemployment fraction, survival function of the employment subgroup, as well as the effects of covariates on time-to-employment and probability of unemployment. Estimates of unemployment fractions by CPH Cure model are closer to the empirical estimate by KM compared to that of Weibull AFT Cure model. In comparing cure and non-cure CPH, some of the covariates (Gender and Age) that were not significant in the non-cure model were found to be significant in the cure model. Likewise Grade, which was found to be significant in the non-cure model, was not significant in the cure model. None of the covariates was found to influence unemployment probability significantly. It is concluded that, since today’s time-to-employment data of graduates mostly consists of groups that would remain unemployed forever (cure fraction), then the use of cure models is superior to their non-cure counterparts in revealing the true effect and significance of a covariate on time-to-employment. In addition, cure models assess the influence of covariates on unemployment probability. Findings may benefit the government and other stakeholders in employment planning policies.