When modeling health events in small areas, the conditional autoregressive (CAR) framework of Besag, York, and Mollié (BYM) is widely used. For multiple outcomes, the multivariate CAR (MCAR) extension accommodates dependence among diseases that share risk factors, in addition to spatial dependence, and can also jointly model demographic subgroups for a single disease, allowing information to be borrowed across related populations. However, recent studies have shown that the BYM CAR model can be overly informative, leading to excessively precise estimates. While the MCAR model is expected to be more informative due to additional information shared across subgroups, its level of informativeness has not been previously quantified. We propose a framework to measure MCAR model informativeness as an extension of prior work and introduce a method to control it, ensuring the model contributes comparably to each subgroup. We achieve this through a reparameterization of the MCAR model within a computationally efficient framework. We demonstrate how the MCAR model compares with the BYM CAR model in terms of informativeness and oversmoothing and highlight the advantages of the restricted MCAR model using county-level heart disease death data stratified by race and sex.

翻译：在小区域健康事件建模中，贝萨格、约克和莫利耶（BYM）提出的条件自回归（CAR）框架被广泛使用。针对多结果情形，多变量CAR（MCAR）扩展模型在空间依赖性的基础上，进一步纳入了共享风险因素的不同疾病之间的依赖性，并可联合建模单一疾病的人口统计子组别，从而允许在相关人群间借用信息。然而，近年研究表明，BYM CAR模型可能过度提供信息，导致估计结果过于精确。尽管MCAR模型因跨子组共享额外信息而预期更具信息性，但其信息量此前尚未被量化。我们提出一个框架，作为先前工作的扩展，用于衡量MCAR模型的信息量，并引入一种控制方法，确保模型对各子组的贡献度相当。我们通过在计算高效框架内对MCAR模型进行重新参数化来实现这一目标。我们展示了MCAR模型与BYM CAR模型在信息量和过度平滑方面的差异，并利用按种族和性别分层的县级心脏病死亡数据，凸显受限MCAR模型的优势。