🤖 AI Summary
This study addresses the bias in parameter estimation arising from complete separation when modeling categorical covariates within joint models for longitudinal and time-to-event data. To mitigate this issue, the authors introduce Firth’s penalized likelihood into the joint modeling framework for the first time, embedding it within an Expectation–Maximization (EM) algorithm. The proposed approach effectively alleviates estimation failure under separation and substantially reduces parameter bias. Extensive simulations and an analysis of real-world data from a German vocational training program demonstrate that the method yields robust estimates of covariate effects and uncovers both direct and indirect influences of socioeconomic factors on dropout risk. This work thus provides a reliable frequentist solution for joint modeling scenarios afflicted by complete separation.
📝 Abstract
Joint Models for longitudinal and time-to-event data are frequently used to model endogenous longitudinal covariates alongside a time-to-event outcome. However, the model class borrows some limitations of the survival submodels, including the necessity for non-separation for each category of categorical covariates. We therefore incorporate Firth's correction into the frequentist estimation procedure of joint models in order to make the model class applicable in settings with separation cases. We derive the needed quantities for the correction term and implement it in the Expectation-Maximization Algorithm for the parameter estimation in joint models. Our simulation study shows, that in data situations with separation issues, the Firth-corrected estimation procedure yields less biased estimates and the respective coefficients approach the estimated values observed in the non-separation cases. The application on a data set on satisfaction with and dropouts from vocational training demonstrates the advantages of the Firth-corrected joint model in a real world data set with separation. The results add to the literature on dropout from vocational training in Germany by explicitly modeling direct effects of socioeconomic and training-specific factors on the risk of dropout as well as their indirect contribution via satisfaction with the training.