How would a decline in sperm concentration over time influence the probability of pregnancy?

Background: Reports have suggested a decline in sperm concentration during the second half of the 20th century. The effect of this decline on fecundability (the monthly probability of pregnancy) could be detected in principle by a study of time to pregnancy. In practice, the amplitude of this expected effect is not well known and the statistical power of time-to-pregnancy studies to detect it has not been explored. Methods: We developed a nonparametric model to describe a temporal decline in sperm concentration using data on French semen donors. We then applied this model to 419 Danish couples planning a first pregnancy in 1992, to predict their time to pregnancy as if the pregnancy attempt had begun during earlier decades with higher sperm concentrations. Finally, we used bootstrap simulations to estimate the statistical power of prospective or retrospective studies that compared fecundability (estimated from time to pregnancy) across these time periods. We express the change in fecundability over time as a fecundability ratio (FR), with values less than 1 indicating decreased fecundability. Results: We estimate that the median sperm concentration decreased by 21% from 1977 to 1992 and by 47% from 1947 to 1992. The estimated decline in fecundability with those semen changes was 7% from 1977 to 1992 (FR = 0.93, adjusted) and 15% from 1947 to 1992 (FR = 0.85, adjusted). The total numbers of couples that would be needed in prospective studies of time to pregnancy to detect these changes in fecundability (with a power of 80%) were 12,000 when comparing 1977 to 1992, and 2000 when comparing 1947 to 1992. Retrospective studies of the same size that excluded childless couples had much lower statistical power and were biased toward the null. Conclusion: The effect of realistic declines in sperm concentration on time to pregnancy may be observed only with studies that include several thousand couples.