Nagelkerke N J, Borgdorff M W, Kim S J
Royal Netherlands Tuberculosis Association (KNCV), The Hague, The Netherlands.
Stat Med. 2001 Apr 15;20(7):1113-24. doi: 10.1002/sim.745.
Interpretation of the Mantoux test for tuberculous infection can be complicated by cross-reactions caused by infection with non-specific mycobacteria. Thus, the distribution of positive indurations is a mixture of two distributions. To estimate tuberculous infection prevalence, the marginal distribution of indurations needs to be separated into its component distributions. Observations from several populations with different mixes of the two types of infection are required. Homogeneity across populations of distributions of indurations for each type of infection is assumed. A logistic model is specified for the probability of having tuberculous infection conditional on the observed induration size. No other assumptions about the two distributions are made. Maximum likelihood is used to estimate the logistic function. Goodness-of-fit criteria are discussed. The method is applied to a series of tuberculin surveys carried out in (South) Korea. Estimated infection prevalence agrees reasonably well with several ad hoc criteria. The goodness-of-fit test rejects underlying assumptions of homogeneity. One reason appears to be a decline over time in induration sizes caused by tuberculous infection. However, not all reasons for this rejection are obvious. The proposed method of mixture analysis provides an additional tool for the interpretation of prevalence survey data where the diagnostic test lacks specificity as a result of cross-reactions.
结核感染的结核菌素试验结果解读可能会因非特异性分枝杆菌感染引起的交叉反应而变得复杂。因此，阳性硬结的分布是两种分布的混合。为了估计结核感染患病率，需要将硬结的边缘分布分离为其组成分布。这需要来自几种具有不同两种感染混合比例人群的观察数据。假定每种感染类型的硬结分布在不同人群中具有同质性。针对基于观察到的硬结大小而感染结核的概率指定了一个逻辑模型。对于这两种分布不做其他假设。使用最大似然法估计逻辑函数。讨论了拟合优度标准。该方法应用于在韩国进行的一系列结核菌素调查。估计的感染患病率与几个特设标准相当吻合。拟合优度检验拒绝了同质性的潜在假设。一个原因似乎是结核感染导致的硬结大小随时间下降。然而，导致这种拒绝的并非所有原因都很明显。所提出的混合分析方法为解释因交叉反应导致诊断测试缺乏特异性的患病率调查数据提供了一个额外工具。
