Conditional autoregressive distributions are commonly used to model spatial dependence between nearby geographic units in disease mapping studies. These distributions induce spatial dependence by means of a spatial weights matrix that quantifies the strength of dependence between any two neighboring spatial units. The most common procedure for defining that spatial weights matrix is using an adjacency criterion. In that case, all pairs of spatial units with adjacent borders are given the same weight (typically 1) and the remaining non-adjacent units are assigned a weight of 0. However, assuming all spatial neighbors in a model to be equally influential could be possibly a too rigid or inappropriate assumption. In this paper, we propose several adaptive conditional autoregressive distributions in which the spatial weights for adjacent areas are random variables, and we discuss their use in spatial disease mapping models. We will introduce our proposal in a multivariate context so that the spatial dependence structure between spatial units is shared and estimated from a sufficiently large set of mortality causes. As we will see, this is a key aspect for making inference on the spatial dependence structure. We show that our adaptive modeling proposal provides more flexible and accurate mortality risk estimates than traditional proposals in which spatial weights for neighboring areas are fixed to a common value.

在疾病测绘研究中，通常使用条件自回归分布来对附近地理单元之间的空间依赖性进行建模。这些分布借助于空间权重矩阵来诱导空间依赖性，该空间权重矩阵量化了任意两个相邻空间单元之间的依赖性强度。定义空间权重矩阵的最常见过程是使用邻接标准。在这种情况下，所有具有相邻边界的空间单元对都具有相同的权重（通常为1），其余的非相邻单元的权重都为0。但是，假设模型中的所有空间邻居都具有同等影响力可能是太严格或不合适的假设。在本文中，我们提出了几种自适应条件自回归分布，其中相邻区域的空间权重是随机变量，并且我们讨论了它们在空间疾病映射模型中的用途。我们将在多变量环境中介绍我们的建议，以便可以从足够大的一组死亡原因中共享和估算空间单位之间的空间依赖性结构。正如我们将看到的，这是推断空间依赖结构的关键方面。我们表明，与传统建议相比，我们的自适应建模建议提供了更灵活，更准确的死亡率风险估计，传统建议中，相邻区域的空间权重固定为一个共同值。我们将在多变量环境中介绍我们的建议，以便可以从足够大的一组死亡原因中共享和估算空间单位之间的空间依赖性结构。正如我们将看到的，这是推断空间依赖结构的关键方面。我们表明，与传统建议相比，我们的自适应建模建议提供了更灵活，更准确的死亡率风险估计，传统建议中，相邻区域的空间权重固定为一个共同值。我们将在多变量环境中介绍我们的建议，以便可以从足够大的一组死亡原因中共享和估算空间单位之间的空间依赖性结构。正如我们将看到的，这是推断空间依赖结构的关键方面。我们表明，与传统建议相比，我们的自适应建模建议提供了更灵活，更准确的死亡率风险估计，传统建议中，相邻区域的空间权重固定为一个共同值。