A Bivariate Transformation Model for Time-to-Event Data Affected by Unobserved Confounding: Revisiting the Illinois Reemployment Bonus Experiment

Motivated by empirical studies investigating treatment effects in survival analysis, we propose a bivariate transformation model to quantify the impact of a binary treatment on a time-to-event outcome. The model equations are connected through a bivariate Gaussian distribution, with the dependence parameter capturing unobserved confounding, and are specified as functions of additive predictors to flexibly account for the impacts of observed confounders. Moreover, the baseline survival function is estimated using monotonic P-splines, the effects of binary or factor instruments can be regularized through a ridge penalty approach, and interactions between treatment and observed confounders can be incorporated to accommodate potential variations in treatment effects across subgroups. The proposal naturally provides the survival average treatment effect. Parameter estimation is achieved via an efficient and stable penalized maximum likelihood estimation approach, and intervals constructed using related inferential results. We revisit a dataset from the Illinois Reemployment Bonus Experiment to estimate the effect of a cash bonus on the probability of remaining unemployed at several time points, unveiling interesting insights. The modeling framework is incorporated into the R package GJRM, enabling researchers and practitioners to employ the proposed model and ensuring the reproducibility of results.