Mixture-of-exponentials models to explain heterogeneity in studies of the duration of Chlamydia trachomatis infection

Published studies of the duration of asymptomatic Chlamydia trachomatis infection in women have produced diverse estimates, and most reviewers have not attempted an evidence synthesis. We review the designs of duration studies, distinguishing between the incident cases presenting soon after infection in clinic-based studies and prevalent cases ascertained in population screening studies. We combine evidence from all studies under fixed-effect (single clearance rate), random-effect (study-specific clearance rate), and mixture-of-exponentials models, in which there are either two or three classes of infection that clear at different rates. We can identify classes as 'passive' infection and fast-clearing and slow-clearing infections. We estimate models by Bayesian MCMC and compared them using posterior mean residual deviance and the deviance information criterion. The single fixed-effect clearance rate model fitted very poorly. The random-effect model was adequate but inferior to the two-class and three-class mixture of exponentials. According to the two-class model, the proportion in the first class was 23% (95% CI: 16-31%), and the mean duration of C.trachomatis infection is 1.36years (95% CI: 1.13-1.63years). With the three-rate model, duration was similar, but identification of the proportions in each class (19%, 31%, and 49%) was poor. Although the random-effect model was descriptively adequate, the extreme degree of between-study variation in the clearance rate it predicted lacked biological plausibility. Differences in study recruitment and sampling mechanisms, acting through a mixture-of-exponentials model, better explains the apparent heterogeneity in duration.