Survival analysis for Hispanic ELL students’ access to postsecondary schools: discrete model or Cox regression?

Survival analysis is an advanced statistical method to investigate the occurrence and the timing of an important event such as school access, dropout, and graduation in a longitudinal framework. The aim of our study is to provide practical guidelines for empirical researchers in choosing an appropriate survival analysis model. For this goal, this study chose two major survival analytical models of a discrete-time hazard model and a Cox regression model and compared analytical outcomes considering time metrics, as well as sample sizes and censoring proportions. In the analytical model, the combined specifications of varying factors using two models were adopted to analyse the Educational Longitudinal Study of 2002. We chose the college access of Hispanic English Language Learners to understand the importance of adopting a proper survival model to examine the educational outcome in the educational context. Importantly, we considered the hazard probability for the target event in the model specification which is a fundamental yet often neglected component of survival analysis. We recommended discrete models for the cases with a smaller number of time points, larger time metrics, larger sample size, and smaller proportions of censored observations.