Accounting for Latent Covariates in Average Effects from Count Regressions

The effectiveness of a treatment on a count outcome can be assessed using a negative binomial regression, where treatment effects are defined as the difference between the expected outcome under treatment and under control. These treatment effects can to date only be estimated if all covariates are manifest (observed) variables. However, some covariates are latent variables that are measured by multiple fallible indicators. In such cases, it is important to control for measurement error of covariates in order to avoid attenuation bias and to get unbiased treatment effect estimates. In this paper, we propose a new approach to compute average and conditional treatment effects in regression models with a logarithmic link function involving multiple latent and manifest covariates. We extend the previously presented moment-based approach in several aspects: Building on a multigroup SEM framework for count variables instead of the generalized linear model, we allow for latent covariates and multiple covariates. We provide an illustrative example to explain the application and estimation in structural equation modeling software.

针对计数型结局变量的治疗效果评估，可借助负二项回归（negative binomial regression）开展，其中治疗效应被定义为治疗组与对照组下的期望结局之差。截至目前，仅当所有协变量均为显式（观测）变量（manifest (observed) variables）时，方可对该类治疗效应进行估计。但部分协变量为潜变量（latent variables），需通过多个存在测量误差的指示变量进行测量。在此类场景下，为避免衰减偏倚（attenuation bias）并获得无偏的治疗效应估计值，对协变量的测量误差进行控制至关重要。本文提出一种全新方法，用于在包含多个潜变量与显式协变量且带有对数连接函数（logarithmic link function）的回归模型中，计算平均治疗效应与条件治疗效应。我们从多个维度拓展了此前提出的基于矩的方法（moment-based approach）：不再沿用广义线性模型（generalized linear model）框架，而是基于计数变量的多组结构方程模型（Structural Equation Model，简称SEM）框架，从而支持潜变量协变量与多协变量的设定。此外，我们提供了一个说明性示例，用以阐释该方法在结构方程建模软件中的应用与估计流程。