Mixture model analysis for establishing a diagnostic cut-off point for pertussis antibody levels

Previous studies of pertussis (whooping cough) that have derived diagnostic cut-off points for pertussis antibody levels have assumed a single distribution for antibody levels and have used small sample sizes. In a recent study of 5409 serum samples from the Third National Health and Nutrition Examination Survey (NHANES III), a finite mixture model was developed to examine the distribution of immunoglobulin G (IgG) antibody levels against pertussis toxin (PT), an antigen specific to the Bordetella pertussis bacterium. The mixture model identified three component populations with antibody levels greater than the quantitative assay's lower limit of quantitation (LLQ) and included a point distribution located at or below the LLQ to account for the excess number of antibody values that fell below the LLQ. The mixture model analysis accounted for the NHANES III design. A cut-off point for anti-PT IgG levels was chosen to have a 99 per cent model specificity based on the two overlapping normal distributions assumed for the two component populations with the highest antibody levels. This cut-off point may have a higher diagnostic sensitivity for acute B. pertussis infection than other cut-off points derived by assuming a single distribution for antibody levels.