Distributions of Amenorrhoea and Anovulation

Most statistics of postpartum amenorrhea are based on retrospective rather than prospective reporting and except when short (averaging less than 6 months) exhibit bimodality negative skewness and gross heaping on multiples of 6 months. The 2 best prospective series 1 representing moderately long and the other very long postpartum amenorrhea exhibit modest degrees of bimodality and negative skewness. Bimodality is plausibly explained in terms of sample heterogeneity that is a combination of lengths of amenorrhea of successful lactators which might be expected to be unimodal with the brief amenorrhea of nonlactators and of mother experiencing early infant deaths and sometimes of respondents experiencing pregnancy losses or confusing postpartum bleeding for genuine onset of menstruation. To cope with the problems of bimodality and heaping on multiples of 6 months Lesthaeghe and Page have used an ingenious logit regression amenorrhea approach. Logit-fitted curves exhibit positive skewness when the retrospective amenorrhea series is short or very long and negative skewness when the series is of intermediate length. For retrospective series averaging between 6 and 9 months the negative skewness is especially marked with a 2nd mode several months later than the mean. A key issue is whether this feature reflects a real phenomenon related to extreme sample heterogeneity or is an artifact of partially surpressed heaping. Hitherto in the construction of family building models postpartum anovulation has been conventionally represented by Barretts modified Pascal distribution. It is shown than when amenorrhea series are long averaging over a year this distribution generates excessive variances. A generalization of Barretts curve the negative binomial yields control over the variance as well as the mean but also unimodal positively skewed curves of amenorrhea that grossly underestimate the left tail of the distribution. A mixed geometric-negative binomial distribution is proposed which ensures bimodality avoids the deficit of short length and produces a much more moderate degree of positive skewness for series of intermediate length. The present analysis makes clear that considerably more prospective data are needed to prove decisively that the degree of bimodality depends primarily on sample heterogeneity; or to decide whether the strong negative skewness found in some logit-fitted curves is artifactual or real. Correspondingly more prospective data including information about the timing of infant deaths are a prerequisite to exploring how well mixed distributions can simulate bimodal distributions of amenorrhea. (Authors)