title: The current duration design for estimating the time to pregnancy distribution: a nonparametric Bayesian perspective.
abstract: This paper was inspired by the studies of Niels Keiding and co-authors on estimating the waiting time-to-pregnancy (TTP) distribution, and in particular on using the current duration design in that context. In this design, a cross-sectional sample of women is collected from those who are currently attempting to become pregnant, and then by recording from each the time she has been attempting. Our aim here is to study the identifiability and the estimation of the waiting time distribution on the basis of current duration data. The main difficulty in this stems from the fact that very short waiting times are only rarely selected into the sample of current durations, and this renders their estimation unstable. We introduce here a Bayesian method for this estimation problem, prove its asymptotic consistency, and compare the method to some variants of the non-parametric maximum likelihood estimators, which have been used previously in this context. The properties of the Bayesian estimation method are studied also empirically, using both simulated data and TTP data on current durations collected by Slama et al. (Hum Reprod 27(5):1489-1498, 2012).
authors.affiliation: Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland. dario.gasbarra@helsinki.fi.
authors.forename: Dario
authors.initials: D
authors.lastname: Gasbarra
authors.affiliation: Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland. elja.arjas@helsinki.fi.
authors.forename: Elja
authors.initials: E
authors.lastname: Arjas
authors.affiliation: Department of Computer Science, Aalto University, Espoo, Finland. aki.vehtari@aalto.fi.
authors.forename: Aki
authors.initials: A
authors.lastname: Vehtari
authors.affiliation: French Institute of Health and Medical Research, Team of Environmental Epidemiology applied to Reproduction and Respiratory Health, Inserm-Univ. Grenoble Alpes, Grenoble, France. remy.slama@ujf-grenoble.fr.
authors.forename: Rémy
authors.initials: R
authors.lastname: Slama
authors.affiliation: Department of Public Health, University of Copenhagen, Copenhagen, Denmark. nike@sund.ku.dk.
authors.forename: Niels
authors.initials: N
authors.lastname: Keiding
mesh_terms: D001499:Bayes Theorem; D056808:Biostatistics; D003430:Cross-Sectional Studies; D005260:Female; D005298:Fertility; D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D011247:Pregnancy; D018709:Statistics, Nonparametric; D013997:Time Factors
keywords: Data augmentation; Generalized gamma convolution process; Logistic process prior; McMC; Posterior consistency