Lifetime Data Analysis

, Volume 21, Issue 4, pp 594–625 | Cite as

The current duration design for estimating the time to pregnancy distribution: a nonparametric Bayesian perspective

  • Dario Gasbarra
  • Elja Arjas
  • Aki Vehtari
  • Rémy Slama
  • Niels Keiding
Article

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).

Keywords

McMC Posterior consistency Data augmentation Logistic process prior Generalized gamma convolution process 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Dario Gasbarra
    • 1
  • Elja Arjas
    • 1
  • Aki Vehtari
    • 2
  • Rémy Slama
    • 3
  • Niels Keiding
    • 4
  1. 1.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  2. 2.Department of Computer ScienceAalto UniversityEspooFinland
  3. 3.French Institute of Health and Medical Research, Team of Environmental Epidemiology applied to Reproduction and Respiratory HealthInserm-Univ. Grenoble AlpesGrenobleFrance
  4. 4.Department of Public HealthUniversity of CopenhagenCopenhagenDenmark

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