Finite Mixture Models in Assessing Anti-thyroglobulin Antibody Positivity as a Marker of Chronic Thyroiditis

Abstract

Positivity of anti-thyroglobulin antibody (TgAb) is one of the markers of chronic thyroiditis (Hashimoto disease). From 2000 to 2003, a thyroid disease prevalence study was conducted at the Radiation Effects Research Foundation, in Hiroshima and Nagasaki. Utilizing the study's results, we show that via EM algorithm log-transformed TgAb level is compatible with a two-component mixture normal distribution, with the smaller normal distribution corresponding to the TgAb negative group but the larger distribution not necessarily corresponding to the TgAb positive group. A subject is determined to be TgAb positive if TgAb level is greater than a given cutoff. We compared the cutoff values from population-based methods and the laboratory method. The population-based methods consist of a simple method, a receiver operating characteristic (ROC) curve method, and a minimum misclassification rate (MMR) method. The simple method is used to determine positivity from only TgAb negative populations. Since the ROC curve and MMR methods are valid only when TgAb positivity and negativity are known but the simple method is valid only when TgAb negativity is known, the simple method was deemed useful for determining the cutoff in our data. In comparison with the simple, population-based method, we show that the cutoff from the laboratory method is appropriate and that the TgAb positive rates from various methods are approximately equal. With the two-component mixture normal distribution in TgAb level, our simple population-based method for determination of cutoff is another more practical example of handling the clinical measurement than the method given in Thompson et al. (Applied Statistics 1998).