Time to pregnancy is the duration from the time a couple starts trying to become pregnant until they succeed. It is considered one of the most direct methods to measure natural fecundity in humans. Statistical tools for designing and analysing time to pregnancy studies belong to the general area of survival analysis, but several features require special attention. Prospective designs are difficult to carry out and retrospective (pregnancy-based) designs, being widely used in this area, do not allow efficiently including couples remaining childless.

A third possible design starts from a cross-sectional sample of couples currently trying to become pregnant, using current duration (backward recurrence time) as basis for the estimation of time to pregnancy or time to the end of the pregnancy attempt. Regression analysis is then most conveniently carried out in the accelerated failure time model. This paper surveys some practical and technical-statistical issues in implementing this approach in a large telephone-based survey, the Epidemiological Observatory of Fecundity in France (Obseff).

The statistical inference is quite sensitive to observations near zero; indeed the nonparametric maximum likelihood estimator is inconsistent at zero. (Recent unpublished results by Groeneboom & Jongbloed and by Arjas, Gasbarra & Vehtari have solved this problem with illustrations from Obseff). 

Two further telephone surveys allowed prospective follow-up of the couples trying at first interview and of a sample of those not currently trying. Using left truncation of those currently trying, we thus have a prevalent cohort study, whose fecundability estimates can be empirically compared to those from the current duration approach based only on the first questionnaire data.

This is joint work with Ditte Nørbo Sørensen (Copenhagen) and Rémy Slama (Grenoble).