Births averted by induced abortion: an application of renewal theory.

It is increasingly recognized that few if any populations have undergone the transition from high to low fertility without significant recourse to induced abortion (Davis, 1963; Kirk, 1967). The strategic role played by induced abortion in helping to bring down the birth rate of Japan and the nations of Eastern Europe is well documented (Muramatsu, 1960; Hall, 1970). That its contribution to family planning in the United States will increase is made likely by the legal changes now occurring in several states as well as recent advances in abortion technique. Yet despite the importance of the topic, a mathematical theory of induced abortion and its impact on natality has not been previously developed. For two reasons, an induced abortion cannot be equated with preventing a birth. First, the effect of a particular abortion is conditional upon the potential outcome of the pregnancy it terminates. If the pregnancy might have ended in miscarriage, then essentially nothing is gained; if the pregnancy might have ended in a stillbirth, far from gaining protection, several months of pregnancy and anovulation are being forfeited. Only when the aborted pregnancy might have produced a live birth does an appreciable delay of the next birth ensue. Second, even when the pregnancy aborted was otherwise fated to end in a live birth, that abortion is typically not equivalent to averting a live birth. Months of gestation and anovulation associated with an abortion are fewer than those associated with a live birth. Therefore a woman is returned to fecundable status sooner after an abortion than a live birth. As a result, it is not obvious whether 100 induced abortions are averting 75, 50, or more nearly 35 births. Moreover, one would like to know the manner in which the impact per abortion varies according to the age and fecundity of the woman, the timing of her abortion as measured in terms of missed menstrual periods, and the efficiency of her accompanying contraception. Previous theoretical work (Potter, 1963; Sheps, 1964; Srinivasan, 1967) has