Estimating the prevalence of atrial fibrillation from a three-class mixture model for repeated diagnoses

Atrial fibrillation (AF) is an abnormal heart rhythm characterized by rapid and irregular heartbeat, with or without perceivable symptoms. In clinical practice, the electrocardiogram (ECG) is often used for diagnosis of AF. Since the AF often arrives as recurrent episodes of varying frequency and duration and only the episodes that occur at the time of ECG can be detected, the AF is often underdiagnosed when a limited number of repeated ECGs are used. In studies evaluating the efficacy of AF ablation surgery, each patient undergoes multiple ECGs and the AF status at the time of ECG is recorded. The objective of this paper is to estimate the marginal proportions of patients with or without AF in a population, which are important measures of the efficacy of the treatment. The underdiagnosis problem is addressed by a three-class mixture regression model in which a patient's probability of having no AF, paroxysmal AF, and permanent AF is modeled by auxiliary baseline covariates in a nested logistic regression. A binomial regression model is specified conditional on a subject being in the paroxysmal AF group. The model parameters are estimated by the Expectation-Maximization (EM) algorithm. These parameters are themselves nuisance parameters for the purpose of this research, but the estimators of the marginal proportions of interest can be expressed as functions of the data and these nuisance parameters and their variances can be estimated by the sandwich method. We examine the performance of the proposed methodology in simulations and two real data applications.