Statistical Implications of Endogeneity Induced by Residential Segregation in Small-Area Modeling of Health Inequities

Health inequities are assessed by health departments to identify social groups disproportionately burdened by disease and by academic researchers to understand how social, economic, and environmental inequities manifest as health inequities. To characterize inequities, group-specific small-area health data are often modeled using log-linear generalized linear models (GLM) or generalized linear mixed models (GLMM) with a random intercept. These approaches estimate the same marginal rate ratio comparing disease rates across groups under standard assumptions. Here we explore how residential segregation combined with social group differences in disease risk can lead to contradictory findings from the GLM and GLMM. We show that this occurs because small-area disease rate data collected under these conditions induce endogeneity in the GLMM due to correlation between the model’s offset and random effect. This results in GLMM estimates that represent conditional rather than marginal associations. We refer to endogeneity arising from the offset, which to our knowledge has not been noted previously, as “offset endogeneity.” We illustrate this phenomenon in simulated data and real premature mortality data, and we propose alternative modeling approaches to address it. We also introduce to a statistical audience the social epidemiologic terminology for framing health inequities, which enables responsible interpretation of results.

卫生部门通过评估健康不公平性，识别疾病负担不成比例的社会群体；学术研究者则借助此类评估，探究社会、经济与环境层面的不公平如何具体转化为健康不公平。为刻画不公平性的特征，针对特定群体的小区域健康数据，常通过对数线性广义线性模型（log-linear generalized linear models, GLM）或带随机截距项的广义线性混合模型（generalized linear mixed models, GLMM）开展建模。在标准假设前提下，这两种方法会估计用于比较不同群体疾病发病率的同一份边际率比。本研究旨在探讨，当居住隔离与疾病风险层面的社会群体差异同时存在时，为何会导致GLM与GLMM得出相互矛盾的结果。我们的研究表明，出现该矛盾的原因在于：在上述情境下收集的小区域疾病发病率数据，会因模型的偏移量（offset）与随机效应之间存在相关性，从而在GLMM中引发内生性问题。这会使得GLMM的估计结果反映的是条件关联而非边际关联。我们将由偏移量引发的内生性命名为‘偏移量内生性（offset endogeneity）’，据我们所知，该现象此前尚未被学界关注到。我们通过模拟数据与真实的过早死亡数据对该现象进行了演示，并提出了可用于解决该问题的替代性建模方法。此外，我们还面向统计学科研人员介绍了用于阐释健康不公平性的社会流行病学术语体系，该体系有助于对研究结果开展负责任的解读。