Department of Statistics, Glasgow University, Glasgow G12 8QQ, UK.
Biostatistics. 2011 Jan;12(1):51-67. doi: 10.1093/biostatistics/kxq040. Epub 2010 Jun 24.
The analysis of large data sets of standardized mortality ratios (SMRs), obtained by collecting observed and expected disease counts in a map of contiguous regions, is a first step in descriptive epidemiology to detect potential environmental risk factors. A common situation arises when counts are collected in small areas, that is, where the expected count is very low, and disease risks underlying the map are spatially correlated. Traditional p-value-based methods, which control the false discovery rate (FDR) by means of Poisson p-values, might achieve small sensitivity in identifying risk in small areas. This problem is the focus of the present work, where a Bayesian approach which performs a test to evaluate the null hypothesis of no risk over each SMR and controls the posterior FDR is proposed. A Bayesian hierarchical model including spatial random effects to allow for extra-Poisson variability is implemented providing estimates of the posterior probabilities that the null hypothesis of absence of risk is true. By means of such posterior probabilities, an estimate of the posterior FDR conditional on the data can be computed. A conservative estimation is needed to achieve the control which is checked by simulation. The availability of this estimate allows the practitioner to determine nonarbitrary FDR-based selection rules to identify high-risk areas according to a preset FDR level. Sensitivity and specificity of FDR-based rules are studied via simulation and a comparison with p-value-based rules is also shown. A real data set is analyzed using rules based on several FDR levels.
对标准化死亡率（SMR）的大数据集进行分析，通过在连续区域的地图上收集观察到的和预期的疾病计数，可以作为描述性流行病学的第一步，以检测潜在的环境风险因素。当在小区域中收集计数时，通常会出现一种情况，即预期计数非常低，并且地图下的疾病风险具有空间相关性。基于泊松 p 值控制假发现率（FDR）的传统 p 值方法可能在识别小区域中的风险方面具有较低的灵敏度。本研究的重点是提出一种贝叶斯方法，该方法对每个 SMR 上不存在风险的零假设进行检验，并控制后验 FDR。实施了一个包括空间随机效应的贝叶斯分层模型，以允许额外的泊松变异性，从而提供不存在风险的零假设为真的后验概率的估计。通过这种后验概率，可以根据数据计算出后验 FDR 的估计值。为了实现控制，需要进行保守估计，这可以通过模拟进行检查。该估计值的可用性允许从业者根据预设的 FDR 水平确定基于 FDR 的选择规则来识别高风险区域。通过模拟研究了基于 FDR 的规则的敏感性和特异性，并显示了与基于 p 值的规则的比较。使用基于几个 FDR 水平的规则对真实数据集进行了分析。
