Mindel Sheps: Physician, Health Care Activist, Theoretical Demographer

Pioneering the mathematical demography of fertility and family building was Mindel Sheps’ third career. Her interest in demography was based on her strong social conscience, recognition of links between poverty, social inequality, and health, and a belief that theoretical understanding of family building could clarify issues of women’s rights and equality and promote beneficial policy decisions.

Mindel Cherniack was born in Winnipeg, Manitoba, on May 20, 1913. Her parents were Russian Jewish immigrants to Canada. Despite quotas on women and Jews, Mindel was admitted to the University of Manitoba Medical School, graduating in 1936. She and fellow medical school student and lifelong outstanding health activist Cecil G. Sheps married the following year (Sheps & Sheps 2009). Their son, Sam Sheps, followed in their footsteps and is Professor Emeritus, University of British Columbia School of Population and Public Health.

Her first career was as a practicing physician. After internship and residency, the Sheps went to England in 1938, where Mindel worked for a year at the Marie Curie Hospital. Returning to Winnipeg, she spent three years in general practice, becoming active in the Winnipeg Birth Control League (later Planned Parenthood) and going door-to-door teaching women about then-illegal methods of birth control. Later, when the Sheps moved to Chapel Hill, North Carolina in 1947, she was medical director of student health services at North Carolina College, an historically black college in Durham (now North Carolina Central University). These experiences in medical practice and her direct observation of the effects of poverty on health shaped her life and her professional future (Sheps & Sheps 2009).

Mindel came from a left-leaning socialist politically active family: her parents supported liberal political parties, and her brother, Saul Cherniack, served for nearly two decades in the Manitoba Legislature and as Minister of Finance for part of that time. In her second career as health care activist, Mindel took her turn at politics. After the Cooperative Commonwealth Federation party (CCF) came into power in Manitoba, she was elected to the Winnipeg School Board in 1942, chaired the CCF research committee on health, and served on the CCF national health research committee. In 1944, the Sheps moved to Saskatchewan for Mindel to serve as secretary of the Health Services Survey Commission. In that capacity, she and Commission chair Henry Sigerist were the key authors of Saskatchewan’s first blueprint for socialized medicine. As a result, Sasketchewan enacted the first government hospital insurance plan in North America in 1945 (Sheps 1945a,b). Although Sheps and Sigerist had hoped for more extensive health coverage, the plan provided medical and hospital care for “some of the most economically vulnerable” groups, “those receiving provincial assistance payments, such as pensioners, women receiving mothers’ allowances, and the blind” (Jones 2019). Later, in 1962, Sasketchewan enacted full socialized medical care for all – again a first in North America. In 1947, the Sheps left for Yale, where Cecil earned an MPH degree. They had planned to return to Canada, but neither was reappointed to government positions, some say due to stances on health care too radical for their time (Jones 2015, 2019).

That’s when the Sheps moved to Chapel Hill, where Cecil began his academic career in health policy and Mindel received her MPH degree at UNC-Chapel Hill in 1950, concentrating in biostatistics. In 1957, the Sheps left for Boston, where Mindel became assistant professor of preventive medicine at Harvard Medical School and research associate at the Harvard School of Public Health. She next became professor of biostatistics at University of Pittsburgh (1960), then at Columbia University School of Public Health (1965), and finally at UNC-Chapel Hill (1968), where she served as professor until her death in 1973.

By the early 1960s, public concern about rapid population growth was at its height. Support grew for family planning programs intended to reduce fertility. Yet there was no clear consensus on best approaches either to reducing fertility at the population level or to assisting people in having the numbers of children they wanted. Models, both mathematical and simulation-based, seemed an appropriate approach to understanding human population dynamics. Many of the “greats” of human population theory – Lotka (1965), Coale (1972), Keyfitz (1968), and others - worked at the population level, studying interactions of sets of birth and death rates and their resulting growth rate and population age distribution. But their work did not increase understanding of how birth rates themselves are determined and can change – an understanding that was crucial to efforts to reduce population growth. Mindel focused on family building – the process that results in a sequence of births to a woman and the intervals that space them apart - and on determinants of variation in this process. In this endeavor, she followed in the footsteps of only a few others: Corrado Gini (1924), Raymond Pearl (1933), Jean Bourgeois-Pichat (Festy, 1991), perhaps most importantly the French demographers Louis Henry (Sheps & Lapierre-Adamcyk 1972) and Paul Vincent (1961), V.M. Dandekar (1955), William Brass (1958), and Robert Potter (Bongaarts & Potter 1983). Like her predecessors, Mindel assumed that social, economic, and psychological factors are the principal determinants of fertility, but that their influences ultimately work through biological structures.

Collaborating with Edward Perrin, she began developing mathematical models of fertility (Perrin & Sheps 1964) and thus began her third career. In a remarkable burst of intellectual activity, she published 8 articles in 1962–64 that laid out a basic conceptual model of family building and its implications (Sheps 1963, 1964a, 1964b, 1964c; Perrin & Sheps 1962, 1964; Sheps & Perrin 1963, 1964; full bibliography: Keyfitz & Menken 1973). In 1966, I had the great good fortune to become her research associate at Columbia University and to work closely with her until her death.

Her theoretical models are based on a renewal process framework of repeated events and the intervals between them. The reproductive span begins with the later of biological capacity to conceive and sexual debut, and it ends with the earlier of sterility and cessation of sexual relations. Within that span are successive live births. Fig. 1 illustrates the simplest formulation of a family building model based on components of birth intervals. When a woman enters the reproductive span, she can be considered susceptible to conception. The interval to conception, or waiting time to conception, depends on fecundability, the monthly conception probability. Upon conceiving, she enters the pregnant state – here differentiated according to whether the pregnancy will end in a live birth or not. The end of pregnancy is followed by a postpartum nonsusceptible period in which ovulation or sexual relations have not yet both resumed, after which the woman returns to the susceptible state. Pregnancy and postpartum period associated with a non-live birth are usually short and are combined in Fig.1. There may be several non-live births before the woman starts a pregnancy leading to a live birth, postpartum period, and return to the susceptible state. The birth interval is the time between exits from the live-birth pregnant state; the number of live births a woman experiences is the cumulative number of such exits. Using additional simplifying assumptions that the distributions of durations in these states and the transition probabilities do not change over time, Perrin and Sheps (1964) derived expressions for the expected value of the birth interval, the number of births by a specified time, and the birth rate among women during the reproductive span. With Jeanne Clare Ridley, Mindel also developed simulation models in which these quite strict assumptions could be relaxed (Ridley & Sheps 1966).

Fig. 1.

A Simple Family Building Model

Mindel’s driving concern was not mathematics itself but increasing understanding of fertility in a way that could inform policy and practice. Conclusions from her theoretical formulations – sometimes startling - remain relevant today, both for basic understanding of family building and for family planning policy. Important questions can be addressed using even the simplest version of the model in Fig. 1, one in which the monthly probability of conception is constant and equal to ρ, the probability that conception leads to a non-live birth is α, and the duration of pregnancy plus postpartum is w for a non-live birth and m for a live birth. In this case, the mean time in the susceptible state (the mean time to conception) is 1/ρ and the monthly birth rate, B, among women in the reproductive span reaches an equilibrium value (Sheps & Menken 1973, p.201):

$$B=\rho (1-\alpha )/(\rho G+1-\rho )\text{where}G=m(1-\alpha )+w\alpha .$$ (1)

Five questions that she and her colleagues addressed illustrate her theoretical investigations and their practical application:

• Using highly effective contraception, can women/couples avoid accidental pregnancy over long periods of time? The probability of not conceiving within k months is simply (1−ρ)^k and the probability of conceiving within that period is the complement. Were fecundability reduced by a 95% effective contraceptive, say from 0.20 to 0.01 per month, the probability of an accidental pregnancy within 5 years (60 cycles) is 45%, 10 years 79%, and 15 years 84% (c.f. Sheps & Menken 1973 p.226). Reproductive health implications are clear. People practicing reasonable family planning will have accidental pregnancies by chance alone. Some will choose abortion. Some will choose sterilization as the only sure way of preventing pregnancy. Mindel and I often laughed that this very simple example was a sure-fire way to gain rapt attention from an introductory statistics class! But those involved in today’s family planning debates still encounter the uninformed opinion that all accidental pregnancies are preventable. The lesson here is that, in societies where people want only a few children, for a large proportion of her reproductive span, a woman is biologically susceptible to conception but does not want to conceive. Only a method that reduces fecundability to near zero will prevent accidental pregnancy over that long period.

• In terms of family planning program design, what is the difference in birth rate reduction between a program in which a fairly small proportion of women uses highly effective contraception vs one in which a larger proportion uses less effective contraception? Sheps and Perrin (1963) showed that the highly effective contraception design can produce a greater reduction. When fecundability is 0.20 per month, the mean time to conception is only 5 months. A 95% effective contraceptive increases the mean to 100 months while a 50% effective contraceptive increases it only to 10 months. The accumulating numbers of accidental pregnancies over many cycles under less effective contraception lead to a comparatively small reduction in the lifetime fertility. Both the individual goal of controlling one’s own fertility and the population goal of reducing the birth rate may be better served by increasing access to highly effective contraception, even if promoting less effective contraception reaches larger numbers.

• What role does induced abortion play in reducing fertility? Induced abortion alone is a poor way to control fertility. If it is the primary means of fertility control, women are likely to have many abortions in their lifetimes - at physical welfare and economic cost. Sheps and Menken (1973 p. 302–303) compared two models in which the birth rate was reduced by 40% and found an average of 4.5 abortions over a 10-year period would be required to match the effect of a moderately effective (65–70%) contraceptive. Abortion as a back-up measure when contraception fails has a much larger effect on birth rates, due to effective contraception greatly prolonging the time to next conception. While this conclusion may seem obvious to the mathematically astute, it was not obvious in the family planning community that was debating which methods to promote in their programs.

• Can long postpartum periods substantially brake fertility? The sensitivity of the birth rate B to duration w of the live birth pregnancy + postpartum period is clear in equation (1). This mathematical result highlighted the need for empirical research to document the extent to which this period varied in human populations and the causes of variation. Studies starting in the late 1960s found a close biologic relationship between breastfeeding and postpartum amenorrhea (absence of menstrual periods indicating absence of ovulation). The average duration of amenorrhea was 1.5–2 months for U.S. women who did not breastfeed (Salber et al. 1966) and over 18 months in Bangladesh where breastfeeding continued until or even through the next pregnancy (Chen et al. 1974). According to Bongaarts (1982), postpartum period differences account for a large portion of variation in lifetime fertility in populations that do not practice extensive birth control.

• What happens when access to abortion suddenly disappears? A sudden shock, such as Romania’s 1966 abrupt termination of legal abortion, its main means of fertility control, does not lead to a simple change in birth rate but rather a series of oscillations before a new constant birth rate is reached. Sheps and Menken (1971, 1973 p 273–282) extended the basic model in Fig. 1 to allow for time dependency in the probability of a non-live birth, α. In tracing out the effect of an abrupt decline in α, we showed that the birth rate would rise sharply several months later, when those who had expected to have an abortion would instead have a live birth. But at the same time, transitions back into the susceptible state would decline, so that at some point the birth rate would decline. It would rise again as women who had had a live birth returned to susceptibility and would oscillate until a new equilibrium was reached. Similarly, an abrupt increase in effective contraceptive use would suddenly decrease the probability of conception and therefore the birth rate some months later. But as more women returned or remained in the susceptible state, the birth rate would rise and then oscillate to a new equilibrium. According to Joel Cohen (1974), this result “warns effectively against believing that the early results of programs designed to affect the birth rate will be the same as the long-term results.”

On a personal note, Mindel was my mentor, colleague, and dear friend. We found that our interests coincided and that we thought in the same way about the importance of fertility and the contributions theoretical mathematical models can make. The impact of the three rich years we spent together at Columbia and our long-distance work after we both left New York City has reverberated throughout my career to the present day. “The experience of bouncing ideas across a table or by phone and then solving the mathematical problems posed was always exhilarating. We were able to live in a world of ideas based on the shared set of questions we wanted to answer - and a shared sense of humor” (Menken 2018).

Mindel died of cancer at age 59 on January 15, 1973. In dedicating our book (Sheps & Menken 1973) to her, I wrote “She combined excellence in scholarship with warmth, integrity, a capacity to inspire close associates to explore their talents to the fullest, and a deep concern for social problems.” Receiving a 1971 honorary degree from the University of Manitoba (Fig. 2), Mindel said (Sheps, 1971) “it would be well to approach all human problems with humility, with a strong sense of the limitations of our knowledge and of the existence of large areas of ignorance, and with readiness to admit the errors we may make… The only hope of solving the problems of this planet lies in the application of scientific understanding and skills in the service of human dignity, freedom and welfare. Neither science nor high ideals can do the job alone”. This perspective and the models she produced are her legacy to theoretical population biology and to all of population science.

Fig. 2.

Mindel Sheps 1971, receiving a University of Manitoba Honorary Doctor of Science Degree