Tobit模型与两部分Hurdle模型在半连续纵向数据中的比较及其在克隆性造血中的应用
Comparing Tobit and Two-Part Hurdle Models for Semi-Continuous Longitudinal Data with an Application to Clonal Hematopoiesis
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中文总结 AI 辅助
本文比较了Tobit模型与两部分Hurdle模型，推导了二者等价的数学条件，通过模拟研究发现Hurdle模型更灵活稳健，将二者应用于克隆性造血研究，得到的结果与标准线性模型大致一致。
中文摘要 AI 辅助
零膨胀非负连续纵向数据常出现在生物医学研究中，这类数据的结局包含过多零值和正连续测量值。分析此类数据的两种常用方法是Tobit模型和两部分Hurdle模型的混合模型版本。Tobit模型假设一个在指定阈值下方被删失的潜在回归模型，而Hurdle模型则分别对正连续结局和是否为正的二元指示变量进行建模。这些模型的选择很少被系统讨论，不当的模型选择可能导致估计结果有偏和科学解释产生误导。本文推导了两种模型等价的严格数学条件，并证明当二元过程的连接函数为probit时，Tobit模型可被视为Hurdle模型的一个特例。基于模拟研究，我们发现Hurdle模型比Tobit模型更具灵活性和稳健性；另一方面，若Tobit模型的假设成立，该模型更易于解释，因为它无需对连续过程和二元过程分别进行推断。因此，我们建议仅在这些假设具有科学合理性且得到实证支持时使用Tobit模型，否则更适合使用Hurdle模型。我们将两种模型应用于研究体细胞嵌合现象的动态变化，使用来自前列腺、肺、结直肠和卵巢（Prostate, Lung, Colorectal, and Ovarian）研究的纵向克隆分数测量值，同时考虑过多零值的情况。Tobit模型和Hurdle模型得到的估计值与忽略零膨胀的标准线性模型的估计值大致一致，这些发现为不同类型嵌合染色体改变的克隆性造血研究中先前报道的关联提供了额外支持。
英文摘要
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.
