The probability of conception on different days of the cycle with respect to ovulation: an overview
Several mathematical models have been developed over the past thirty years to investigate how the probability of conception changes on the different days of the cycle with respect to ovulation. A problem general to all models is to estimate the day of ovulation. Since the most fertile days are those close to ovulation, less precise estimates of this event will lead to less accurate estimates of the probability of conception on a given day of the cycle.
Given that a reference point for ovulation is available, the first model considered conception as dependent only on the timing of intercourse. Conception was found to be most likely to occur on only six days in each cycle. However, the model is biologically unrealistic because it assumes that all ova can be fertilized and lead to a viable pregnancy. There are other factors that affect the probability of conception, including whether the ovum is viable or not. Recent models have extended the idea of cycle viability to allow for differences between cycles within couples and for the introduction of couple specific covariates. In a second group of models the probability of conception depends mainly on the time of intercourse and the survival times of sperm and ovum.
A graphical summary of the results available in the literature is presented. Conception probabilities have been found to be significantly different from zero from five days before ovulation to the day of ovulation itself. On average, less than half of the cycles are viable in women, although recent studies suggest that different cycle viability between women should also be taken into account. Survival times for sperm and the ovum have been estimated to be 1.4 days and 0.7 days, respectively. Sperm would have a 5% probability of surviving more than 4.4 days and a 1% probability of surviving more than 6.8 days.
KeywordsPublic Health Mathematical Model Survival Time Reference Point Accurate Estimate
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- 1.Weinberg CR, Gladen BC. The Beta-Geometric distribution applied to comparative fecundability studies. Biometrics. 1986; 42: 547–60.Google Scholar
- 2.Barrett JC, Marshall J. The risk of conception on di¡erent days of the menstrual cycle. Popul Stud. 1969; 23: 455–61.Google Scholar
- 3.Royston P. Basal body temperature, ovulation and the risk of conception, with special reference to the lifetimes of sperm and egg. Biometrics. 1982; 38: 397–406.Google Scholar
- 4.Wilcox AJ, Weinberg CR, O'Connor JF et al. Incidence of early loss of pregnancy. N Engl J Med. 1988; 319: 189–94.Google Scholar
- 5.World Health Organization. Task Force on Methods for the Determination of the Fertile Period, Special Programme of Research, Development and Research Training in Human Reproduction. A prospective multicentre trial of the ovulation method of natural family planning. III. Characteristics of the menstrual cycle and of the fertile phase. Fertil Steril. 1983; 40: 773–8.Google Scholar
- 6.McCullagh P, Nelder JA. Generalised linear models. Monographs on statistics and applied probability, 2nd edition. London: Chapman and Hall, 1989.Google Scholar
- 7.Schwartz D, MacDonald PDM, Heuchel V. Fecundability, coital frequency and the viability of ova. Popul Stud. 1980; 34: 397–400.Google Scholar
- 8.Weinberg CR, Gladen BC, Wilcox AJ. Models relating the timing of intercourse to the probability of conception and the sex of the baby. Biometrics. 1994; 50: 358–67.Google Scholar
- 9.Zhou H, Weinberg CR. Modelling conception as an aggregated Bernoulli outcome with latent variables via the EM algorithm. Biometrics. 1996; 52: 945–54.Google Scholar
- 10.Liang KY, Zeger SL. Longitudinal data analysis using generalised linear models. Biometrika. 1986; 73: 13–22.Google Scholar
- 11.Zhou H, Weinberg CR, Wilcox AJ, Baird DD. A random-e¡ects model for cycle viability in fertility studies. J Am Statist Assoc. 1996; 91: 1413–22.Google Scholar
- 12.Weinberg CR, Wilcox AJ. A model for estimating the potency and survival of human gametes in vivo. Biometrics. 1995; 51: 405–12.Google Scholar
- 13.Wilcox AJ, Weinberg CR, Baird DD. Timing of sexual intercourse in relation to ovulation. N Engl J Med. 1995; 333: 1517–21Google Scholar
- 14.May K. The Unipath Personal Contraceptive System Proceedings of a Symposium held at the XIV FIGO World Congress of Gynecology and Obstetrics, September 1994, Montreal, Canada. New York: Parthenon Publishing Group, 1996.Google Scholar