Distributions of amenorrhoea and anovulation

Abstract

Most statistics of post-partum amenorrhoea are based on retrospective rather than prospective reporting and, except when short (averaging less than six months), exhibit bimodality, negative skewness, and gross heaping on multiples of six months. The two best prospective series, one representing moderately long and the other very long post-partum amenorrhoea, exhibit modest degrees of bimodality and negative skewness. Bimodalty is plausibly explained in terms of sample heterogeneity, that is a combination of the lengths of amenorrhoea of successful lactators which might be expected to be unimodal, with the brief amenorrhoea of non lactators and of mothers experiencing early infant deaths, and sometimes of respondents experiencing pregnancy losses or confusing post-partum bleeding for genuine onset of menstruation. To cope with the problems of bimodality and heaping on multiples of six months, Lesthaeghe and Page have used an ingenious logit regression approach. Logit-fitted curves exhibit positive skewness when the retrospective amenorrhoea series is short or very long, and negative skewness when the series is of intermediate length. For retrospective series averaging between six and nine months, the negative skewness is especially marked, with a second 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 suppressed heaping. Hitherto, in the construction of family-building models, post-partum anovulation has been conventionally represented by Barrett's modified Pascal distribution. It is shown that when amenorrhoea series are long, averaging over a year, this distribution generates excessive variances. A generalization of Barrett's curve, the negative binomial, yields control over the variance as well as the mean, but also unimodal, positively skewed curves of amenorrhoea 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 lengths, 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 amenorrhoea.

The research was financed by NICHD Grant 1 RO1-HD-12100 and National Science Foundation Grant SOC76-12342. The comments of Barbara Anderson, John Bongaarts and John Ross are gratefully acknowledged.

The research was financed by NICHD Grant 1 RO1-HD-12100 and National Science Foundation Grant SOC76-12342. The comments of Barbara Anderson, John Bongaarts and John Ross are gratefully acknowledged.

Notes

The research was financed by NICHD Grant 1 RO1-HD-12100 and National Science Foundation Grant SOC76-12342. The comments of Barbara Anderson, John Bongaarts and John Ross are gratefully acknowledged.

Additional information

Notes on contributors

Frances E. Kobrin

Department of Sociology and the Population Studies and Training Center, Brown University, Providence, Rhode Island, 02912, USA.