Using robust non-parametric and semi parametric survival techniques to analyze student dropout in university courses

Abstract

The Kaplan Meier (KM) estimator and the Cox Proportional Hazards(CPH) model have been used extensively to analyze survival data in educational settings, however, these statistical techniques are vulnerable to outliers. This paper explores the robust KM estimator and the robust CPH model to analyze durations of students in university courses before dropout in the presence of influential observations. These outliers can severely impact the parameter estimates and lead to incorrect inferences. The bias-adjusted KM estimator is the first technique used in this paper to overcome the impact of outlier. The estimator uses an empirical likelihood weighting to enforce the equality of the covariate distributions, more specifically the equality of the moments of the covariates between comparison groups. The robust CPR model is the second technique used in this paper to overcome the impact of influential observation. This method, proposed by Bednarski(1993), is based on a smooth modification of the partial likelihood (PL)which yields reliable estimates of the effect sizes of different predictors on survival durations in the presence of data contamination. These robust techniques are used to investigate student dropouts in undergraduate courses at the Faculty of Science in the University of Malta (UOM). Using the student cohort that commenced their studies in 2022, the study examines the impact of a number of predictors on student dropout rates using the bias-adjusted KM estimator and the robust CPR model.The predictors include gender, admission score, and selected subjects. Moreover, the study compares the results obtained from traditional Kaplan Meier and Cox regression analysis with their robust alternative approaches to assess the stability of hazard ratio (HR) estimates. This paper demonstrates that in the presence of outliers and influential observations, the robust KM estimator and the robust CPR approach yield robust parameter estimates without a notable loss of efficiency. One of the findings shows that the number of dropouts peak at the end of the first year of tertiary education but then reduces gradually in subsequent years. Other findings show that pre tertiary academic achievement and the selection of course subjects have a huge impact on dropout rates.