Time to pregnancy: a probabilistic method for using the duration of non-conception in fertility assessment

Abstract

Introduction: An important problem in reproductive medicine is determining when people who have failed to achieve a pregnancy without medical assistance should begin investigation and treatment. This study provides a firm theoretical basis for determining what can be deduced about a couple's fertility from the period of time over which they have been trying to conceive. The presentation will provide important insights into the role of probability in the conception process. Material & Methods: The starting point is that there is some uncertainty in a couple's likelihood of conceiving in each cycle. This is modelled as a probability distribution. As the number of cycles increases, if a couple have not yet conceived it is progressively more likely that they are at the low fertility end of the distribution. In other words the distribution changes so that there is relatively more weight at the lower fertility end and less at the higher fertility end. A mathematical method known as Bayes' Theorem enables the probability distribution to be updated. From the original probability distribution, and the number of cycles of non-conception, it is possible to obtain a posterior distribution for the couple's fertility. This in turn enables calculation of the number of cycles of non-conception before various subfertility metrics are reached. A typical such metric is that the probability of conception on the next cycle falls below a given threshold such as 10% or 5%. A computer program has been written in C to put these methods into effect. Results: Four different prior distributions are considered. Three are derived from fits to time-to-conception data for different populations, and a fourth is a hypothetical example representing a mixture of a fertile and a subfertile population. It is found that the number of cycles of non-conception for a given metric to be reached varies somewhat between different populations. For example, the number of cycles before the probability of conception in the next cycle falls below 10% ranges from 8 to 15 among the four examples. It is also found that the predicted conception pattern over time is generally not highly sensitive to the form of distribution fitted to a given dataset. If there are enough data points, these constrain the fitted distribution in such a way that it produces a similar conception pattern when different parametric forms of distribution are used. Results will be presented for beta, triangular and compressed beta distributions. Conclusions: The analysis described in this study illustrates how the duration of non-conception influences a couple's probability of conceiving. A computer program using these methods yields results that appear to be robust. This approach has the potential to contribute to decision support tools which make use of the duration of non-conception for fertility assessment