Models relating the timing of intercourse to the probability of conception and the sex of the baby

The probability that conception will result from intercourse on particular days of the menstrual cycle is of biological, demographic, and personal interest to many. We describe an existing model for conception as related to the timing of intercourse, and develop a method for fitting it by means of the expectation-maximization (EM) algorithm, using widely available software (GLIM). We then generalize the model to allow for effects on its parameters due to reproductively toxic exposures. A further extension allows one to address the question of whether the pattern of intercourse in a conception cycle has an influence on the sex of the resulting baby. We illustrate the methods by application to data from a prospective study of couples trying to begin a pregnancy.