Probability of helicobacter pylori infection based on IgG levels and other covariates using a mixture model

To use IgG antibody measurements to detect infection with Helicobacter pylori (H. pylori). one typically defines a cut-off value based on samples of persons presumed to be infected or uninfected. When there are no good 'gold standard' tests to determine infection status, or when laboratory conditions vary, it is useful to have a method based on the IgG measurements themselves to determine infection status.

We present a two component mixture model to analyse serologic data on H. pylori infection. The mixing proportions correspond to the probability that a latent variable, the true, unknown infection status I of a person, is either 0 (uninfected) or 1 (infected). By using a logistic model for these probabilities, we are able to incorporate covariate information.

The model is applied to IgG data from Shandong, China. The distribution of the true infection status given the IgG value and a set of covariates is calculated using the IgG distribution function. An optimal cut-off point is found by minimising the probability of misclassification for the Shandong data. The optimal cut-off point is slightly lower than the pre-defined one.

We contrast results from the mixture model with results from tabulations and from standard logistic regression that are based on fixed cut-points. The mixture model yields information on the probability that a person is truly infected as a function of IgG levels and covariates. In our data, the mixture model indicates that a slightly lower cut-off value than the pre-defined cut-point 1.0 can reduce misclassification rates.