Comparing Tobit and Two-Part Hurdle Models for Semi-Continuous Longitudinal Data with an Application to Clonal Hematopoiesis
This study addresses the lack of systematic guidance in choosing between Tobit and two-part hurdle models for zero-inflated semicontinuous longitudinal data. It rigorously derives, for the first time, the precise mathematical conditions under which the two models are equivalent, revealing that the Tobit model is a special case of the hurdle model when the binary component employs a probit link. Through theoretical analysis, Monte Carlo simulations, and an empirical application to clonal fraction data from the PLCO clonal hematopoiesis cohort, the authors propose a model selection criterion grounded in the plausibility of underlying assumptions. Findings indicate that while the hurdle model offers greater flexibility and robustness, the Tobit model provides more parsimonious interpretation when its assumptions hold. Both approaches yield consistent substantive conclusions in practice and substantially outperform standard linear models that ignore zero inflation, thereby corroborating established biological insights.