The spatial variation in population-level disease rates can be estimated from aggregated disease data relating to $N$ areal units using Bayesian hierarchical models. Spatial autocorrelation in these data is captured by random effects that are assigned a Conditional autoregressive (CAR) prior, which assumes that neighbouring areal units exhibit similar disease rates. This approach ignores boundaries in the disease rate surface, which are locations where neighbouring units exhibit a step-change in their rates. CAR type models have been extended to account for this localised spatial smoothness, but they are computationally prohibitive for big data sets. Therefore this paper proposes a novel computationally efficient approach for localised spatial smoothing, which is motivated by a new study of mental ill health across $N=\text{32,754}$ Lower Super Output Areas in England. The approach is based on a computationally efficient ridge regression framework, where the spatial trend in disease rates is modelled by a set of anisotropic spatial basis functions that can exhibit either smooth or step change transitions in values between neighbouring areal units. The efficacy of this approach is evidenced by simulation, before using it to identify the highest rate areas and the magnitude of the health inequalities in four measures of mental ill health, namely antidepressant usage, benefit claims, depression diagnoses and hospitalisations.

人口水平疾病发生率的空间变化可以根据与以下疾病相关的汇总疾病数据来估计：$氮$使用贝叶斯分层模型的面积单位。这些数据中的空间自相关性是通过分配条件自回归 (CAR) 先验的随机效应捕获的，该先验假设相邻区域单位表现出相似的发病率。这种方法忽略了疾病发生率表面的边界，这些边界是相邻单位的发生率发生阶跃变化的位置。CAR 类型模型已被扩展以解释这种局部空间平滑性，但它们在计算上对于大数据集来说是令人望而却步的。因此，本文提出了一种新颖的计算有效的局部空间平滑方法，该方法的动机是一项关于心理疾病健康的新研究$氮=\text{32,754}$英格兰较低的超级输出区域。该方法基于计算高效的岭回归框架，其中疾病发生率的空间趋势由一组各向异性空间基函数建模，这些函数可以表现出相邻区域单位之间值的平滑或阶跃变化过渡。这种方法的有效性通过模拟得到证明，然后用它来确定四项精神疾病健康指标（即抗抑郁药物的使用、福利索赔、抑郁症诊断和住院治疗）的最高比率区域和健康不平等的程度。