Comparing Tobit and Two-Part Hurdle Models for Semi-Continuous Longitudinal Data with an Application to Clonal Hematopoiesis

Abstract

Zero-inflated nonnegative continuous longitudinal data frequently arise in biomedical studies where outcomes consist of a mixture of excess zeros and positive continuous measurements. Two widely used approaches for analyzing such data are mixed-model versions of Tobit and the two-part hurdle models. The Tobit assumes a latent regression model that is censored below a specified threshold, while the hurdle separately models the continuous positive outcomes and the binary indicator of being positive. The choice between these models has rarely been systematically discussed, and inappropriate model choice may lead to biased estimation and misleading scientific interpretations. In this paper, we derive rigorous mathematical conditions under which the two models are equivalent and show that the Tobit can be viewed as a special case of the hurdle model when the link function for the binary process is probit. Based on simulation studies, we found that the hurdle is more flexible and robust than the Tobit model. On the other hand, if the assumptions of the Tobit are met, this model is easier to interpret since it does not require distinct inferences on both the continuous and binary processes. We therefore recommend that the Tobit model only be used when these assumptions are scientifically plausible and empirically supported; otherwise, the hurdle model is preferable. We applied both models to study the dynamics of somatic mosaicism using longitudinal clonal fraction measurements from the Prostate, Lung, Colorectal, and Ovarian study data while accounting for excess zero values. Estimates obtained from the Tobit and hurdle models were broadly consistent with those from a standard linear model that ignored zero inflation. These findings provide additional support for previously reported associations in studies of clonal hematopoiesis across different types of mosaic chromosomal alterations.