Academic journal article
By Weinberg, Clarice R.; Dunson, David B.
Journal of the American Statistical Association , Vol. 95, No. 449
While the human population continues to grow, depleting natural resources and reducing biodiversity, scientists have become concerned about our continued capacity to reproduce (perhaps a testament to the enduring value that we place on procreation). Several lines of evidence have contributed to this concern. Ecologists have documented reproductive abnormalities, including malformations and effects on sexual dimorphism and behavior, in certain species exposed to polluted waters (Burkhart et al. 1998; Guillette et al. 1994). Some reports describe declines in the concentrations and quality of human sperm over the past several decades (Swan, Elkin, and Fenster 1997), and increases in rates of testicular cancer and the birth defect cryptorchidism (undescended testicles). Laboratory studies document that certain chemicals can mimic and/or disrupt reproductive hormones, and research on endocrine disruption is flourishing, both epidemiologically and in the laboratory (Daston et al. 1997).
Interest in statistical assessment of reproduction dates back to Galton (1869) and Fisher (1958). Trying to understand why the families of the English aristocracy suffered from subfertility, Galton concluded that subfertility confers a selective aristocratic advantage by tending to concentrate a family's wealth in the estates of fewer descendents. Fisher studied families and inferred (correctly) that fertility must be highly heterogeneous across couples, an observation with important implications for models.
In this article we discuss statistical methods for identifying and characterizing factors that can modify human fertility, through either unintended effects, as with reproductively toxic exposures, or through intended interventions, such as contraceptive methods or clinical treatments for infertility.
Reproductive systems are highly variable across species. Human females do not have an estrous cycle. We are not reflex ovulators, like rabbits, that release ova in response to coitus. We do not normally give birth to litters. In fact, species display such a diversity of reproductive strategies that there is no good animal model for human fertility; we must study humans.
Under regulation by the hypothalamus and pituitary, one of a woman's two ovaries releases a mature egg once each menstrual cycle, an event called ovulation. If the egg is properly swept into the fallopian tube, encounters healthy sperm, is successfully fertilized, implants in a receptive uterine lining, and avoids rejection by the maternal immune system, then pregnancy may ensue; otherwise, the uterine lining is menstrually sloughed, and the cycle must begin again.
Human fertility is inherently hard to study. First, the unit of study is the couple (a complication in itself), and couples vary in their fertility. Empirically, the conception rate among couples followed after discontinuing contraception decreases markedly over time. This decline reflects sorting, where the more fertile couples conceive rapidly and are absent from later risk sets. Determining the sources of such heterogeneity among couples has long been of interest to demographers (Sheps and Mencken 1973) and remains a primary challenge for fertility research. A second complicating factor is that human couples exercise a great deal of control over their reproduction. A third complication is that humans get multiple opportunities (some intended, some not) to evidence their fertility, and self-selection plays an important role.
The interplay of these phenomena creates novel forms of confounding. For example, among couples recruited for prospective study, an exposure under study may be correlated with past use of contraception. If smokers have historically taken more risks than nonsmokers, then the smokers with higher fertility may have had all of their desired pregnancies through unintended conceptions, leaving only the relatively subfertile smokers to be at risk of a self-identified planned conception. …