Modelling population heterogeneity in sensitivity and specificity of a multi-stage screen for objective sleep apnoea

We propose a model-based approach for modelling population heterogeneity in terms of sensitivity and specificity of multi-stage screening procedures that consists of multiple tests ordered according to criteria such as cost and invasiveness. It is assumed that a patient proceeds to the next test only if they test positive for the current test. An overall positive result occurs if a patient tests positive for all tests. A dropout occurs when a subject tests positive for a test but does not proceed to subsequent tests. Chinchilli proposed estimates of sensitivity and specificity based upon ratios of multinomial sample probabilities for such a multi-stage procedure in a homogeneous population. The method proposed here accommodates population heterogeneity with generalized linear models and transformation-based confidence intervals. In contrast to the approach of Chinchilli, such an approach provides model-based tests of population differences, narrower confidence intervals that satisfy boundary constraints, and a method for accommodating dropouts without the need for prespecified weights. The proposed method is motivated by the need to assess age differences in the accuracy of a multi-stage test for obstructive sleep apnoea.