Zero-inflated count data are frequently encountered in public health and epidemiology research. Two-parts model is often used to model the excessive zeros, which are a mixture of two components: a point mass at zero and a count distribution, such as a Poisson distribution. When the rate of events per unit exposure is of interest, offset is commonly used to account for the varying extent of exposure, which is essentially a predictor whose regression coefficient is fixed at one. Such an assumption of exposure effect is, however, quite restrictive for many practical problems. Further, for zero-inflated models, offset is often only included in the count component of the model. However, the probability of excessive zero component could also be affected by the amount of ‘exposure’. We, therefore, proposed incorporating the varying exposure as a covariate rather than an offset term in both the probability of excessive zeros and conditional counts components of the zero-inflated model. A real example is used to illustrate the usage of the proposed methods, and simulation studies are conducted to assess the performance of the proposed methods for a broad variety of situations.

在公共卫生和流行病学研究中经常遇到零膨胀计数数据。两部分模型通常用于模拟过多的零点，它们是两个分量的混合：零点质量和计数分布，例如泊松分布。当关注每单位曝光的事件发生率时，通常使用偏移量来解释不同的曝光程度，这本质上是一个回归系数固定为 1 的预测变量。然而，这种曝光效应的假设对于许多实际问题来说是相当有限的。此外，对于零膨胀模型，偏移量通常仅包含在模型的计数组件中。然而，过度零分量的概率也可能受到“暴露”量的影响。因此，我们，建议在零膨胀模型的过度零概率和条件计数组件中将变化的暴露作为协变量而不是偏移项。一个真实的例子被用来说明所提出的方法的使用，并进行了模拟研究来评估所提出的方法在各种情况下的性能。