Whence Healthy Children? | Mini-Monograph

Methodologic and Statistical Approaches to Studying Human Fertility and Environmental Exposure Candace Tingen,1 Joseph B. Stanford,2 and David B. Dunson1 1Biostatistics Branch, National Institute of Environmental Health Sciences, National Institutes of Health, Department of Health and Human Services, Research Triangle Park, North Carolina, USA; 2Health Research Center, Department of Family and Preventive Medicine, University of Utah, Salt Lake City, Utah, USA

2000) and exposure to lead (Apostoli et al. Although there has been growing concern about the effects of environmental exposures on human 2000; Sallmen et al. 1995), pesticides (Curtis fertility, standard epidemiologic study designs may not collect sufficient data to identify subtle effects et al. 1999; Larsen et al. 1998; Thonneau et al. while properly adjusting for confounding. In particular, results from conventional time to pregnancy 1999), organic and chemical solvents (Sallmen studies can be driven by the many sources of bias inherent in these studies. By prospectively collect- et al. 1998; Wennborg et al. 2001), and ing detailed records of menstrual bleeding, occurrences of intercourse, and a marker of ovulation day cigarette smoking (Weinberg et al. 1989). in each menstrual cycle, precise information on exposure effects can be obtained, adjusting for many However, in studies to date, exposure has been of the primary sources of bias. This article provides an overview of the different types of study assessed only retrospectively, and these results designs, focusing on the data required, the practical advantages and disadvantages of each design, were based mostly on small sample sizes. and the statistical methods required to take full advantage of the available data. We conclude that Sexual behavior. One of the main difficul- detailed prospective studies allowing inferences on day-specific probabilities of conception should be ties in studying human fertility is the large considered as the gold standard for studying the effects of environmental exposures on fertility. Key behavioral component. There is a tremendous words: conception, fecundability, menstrual cycle, ovulation, reproductive epidemiology, statistical interplay between behavior and biology, both methods, study design, time to pregnancy. Environ Health Perspect 112:87–93 (2004). of which need to be considered when assessing doi:10.1289/ehp.6263 available via http://dx.doi.org/ [Online 24 September 2003] etiologic end points. The ages at which couples attempt conception vary substantially between different socioeconomic and ethnic groups There is increasing concern about the effects Throughout the article, we use the term (Morabia and Costanza 1998; O’Connell and of environmental exposures on human fertil- “fecundity” to refer to a couple’s probability of Rogers 1982; Pearce et al. 1999; Taffel 1977). ity (Baird and Strassmann 2000). At least pregnancy with regular intercourse without the Over the last several decades there has been a 10% of couples in the United States have had use of contraception. In other words fecundity steady increase in the age of the mother at first difficulty achieving pregnancy (Chandra and is the inherent capacity to conceive. Depending birth (Morabia and Costanza 1998; Pearce Stephen 1998). Investigators are worried that on the context, fecundity can be assessed for et al. 1999; Ventura et al. 2000, 2001), largely fertility may be declining, and there is corre- women, for men, or for couples. The related due to women delaying childbirth while focus- sponding concern in the general public term from demography, “fecundability,” is the ing on careers. Such trends may be more preva- (Carlsen et al. 1992; Pearce et al. 1999; Swan specific probability of conception within a sin- lent among couples in certain demographic et al. 2000; United Nations 1997). The gle menstrual cycle with noncontracepted inter- groups, making it important to carefully adjust increased public focus on fertility problems course. We use the term “fertility” to refer to for age and behavior in analyses of environmen- has resulted partly from the increasing num- the ability of a couple to achieve a pregnancy tal effects. In particular, including only age as a bers of women who delay attempting preg- that survives to birth. covariate in a time to pregnancy (TTP) model nancy until their midddle to late 30s, ages at may not adequately adjust for differences which a substantial proportion of couples will Factors Affecting Fertility between groups in the timing and frequency of fail to conceive within a year and hence be Age and environmental exposures. It is gener- intercourse. Fertility data analysis is also biased categorized as clinically infertile (Dunson ally accepted that female fecundity declines by the “survival” effect, where more fertile cou- et al. In press). Many of these couples will with age (Sauer 1998). However, limited data ples conceive early in their reproductive years, resort to assisted reproduction techniques, are available on the rate of decline (Schwartz resulting in an age-dependent increase in the which pose potential concerns about safety and Mayaux 1982; Stovall et al. 1991; proportion of subfertile couples among the and impact on perinatal and child health van Noord-Zaadstra et al. 1991) and on factors couples attempting pregnancy. (Mitchell 2002). Despite broad interest in the contributing to the decline (Abdalla et al. 1997; Because there are no realistic animal models scientific community and in the general pub- Rosenwaks et al. 1995). Even less is known (Amann 1982; Working 1988) or universally lic, surprisingly little is known about key fac- about aging effects on male fecundity, with the accurate biomarkers (Barnhart and Osheroff tors related to human fertility and fecundity, available data pertaining mostly to declines in such as age, environmental exposures, sexual the elderly years (Kidd et al. 2001). A recent This article is part of the mini-monograph behavior, and lifestyle (Joffe 2003; Olsen and study reported that female fecundity starts to “Understanding the Determinants of Children's Rachootin 2003). In this article we first decline in the late 20s and male fecundity in Health.” review broadly the factors known to affect fer- the late 30s, controlling for timing of inter- Address correspondence to D. Dunson, Biostatistics Branch, NIEHS, MD A3-03, NIH, tility. We then discuss methodologic and sta- course (Dunson et al. 2002), but more data are DHHS, PO Box 12233, Research Triangle Park, tistical issues involved in studying fecundity, needed to validate this result and investigate NC 27709 USA. Telephone: (919) 541-3033. Fax: with an emphasis on the advantages, necessary causes. In particular, little is known about the (919) 541-4311. E-mail: [email protected] design elements, and statistical methods for impact of environmental exposures on the vari- We acknowledge the helpful comments of mem- detailed prospective preconception cohort ability in fecundity among young couples and bers of the Fertility and Early Pregnancy Working studies. We also comment on the need in the rate of decline with age. Some studies Group of the National Children's Study. The authors declare they have no competing to integrate the study of human fecundity have reported lower fecundity associated with financial interests. with the study of other aspects of human environmental factors, such as parental Received 6 February 2003; accepted 2 September reproduction and development. consumption of contaminated fish (Buck et al. 2003.

Environmental Health Perspectives • VOLUME 112 | NUMBER 1 | January 2004 87 Mini-Monograph | Tingen et al.

1998; 1999; Berardono et al. 1993; Scott and More precisely, women are asked to recount abortion or ectopic pregnancy, which may be Hofmann 1995) of human fecundity, it is nec- their contraceptive and sexual history, from related to some environmental exposures, essary to study humans attempting pregnancy. which the number of noncontracepted cycles cannot be accurately assessed, and this also The number of menstrual cycles of noncontra- to conception can be derived. Other data on introduces confounding with regard to TTP. cepting intercourse required to achieve concep- environmental exposures, smoking and alcohol In addition to obtaining information on tion, or the TTP, is a useful, commonly use, medical history, family income, education current pregnancies, investigators in retrospec- employed measure of a couples’ fecundity. level, and pregnancy history may also be col- tive studies may also interview women about However, there are a number of important sta- lected (Baird 1988). Interviews can take place previous pregnancies. A longer time until recall tistical and methodological issues to consider. during a pregnancy, near the time of birth, or may lead to information bias, although a high In particular, complete assessment of the several years after a birth. level of accuracy in recall has been reported effects of sexual behavior requires the collection Bias in recruitment, recall, and behavior or (Joffe et al. 1993). Digit preference, bias in of prospective daily information about the exposure trends are all possible in retrospective which women are inclined to choose a rounded occurrence of vaginal–penile sexual intercourse studies of TTP. Recruitment for retrospective digit such as 3 or 6 when retrospective studies and the timing of ovulation, and the use of this studies is often done when women present to ask them to remember how many menstrual information to estimate day-specific probabili- obstetric clinics for prenatal care. This method cycles occurred before they conceived, has been ties of conception relative to ovulation. These introduces selection bias into the study if dif- noted in some fertility studies (Jain 1969; Linn issues are summarized below, in the context of ferences in prenatal care are linked to the inves- et al. 1982). Additionally, in retrospect, couples methodologic design options to study human tigated environmental exposure. For example, may change how they feel about a pregnancy fecundity (Table 1). if women who were heavily exposed to an and say it was planned even if the pregnancy environmental factor were more worried about resulted from a birth control failure, leading to Time to Pregnancy their pregnancies, this group would be more the inclusion of data from a pregnancy that Time to pregnancy is generally defined as the apt to present early for prenatal services (and occurred during the use of contraception. number of menstrual cycles it takes a couple use them more frequently over a longer period Currently, there is no method to adjust for the with regularly occurring, noncontracepted of time) and could be overrepresented in the effect of the use of contraception on fecundity, intercourse to achieve pregnancy. Since the study. Conversely, if a decrease in fecundability and therefore pregnancies that occur during the 1980s TTP has been used in epidemiologic (or an increased probability of early sponta- use of contraception must be excluded. studies as a measure of fecundability, the prob- neous abortion) were linked to an increase in Women who experience longer TTP and ability of conception in a menstrual cycle for a exposure, heavily exposed women would be suspect themselves to be subfertile may change couple at risk of conception (Baird et al. 1986). underrepresented among those using prenatal their behavior (quit smoking, decrease caffeine TTP can be obtained retrospectively, by asking care services, making the effect harder to detect or sugar intake) in a way they believe is more pregnant women how long it took to become in the study. Juul et al. (2000) warn against conducive to conception. Bias is thus intro- pregnant, or prospectively, either by enrolling selection bias in choosing only pregnant sam- duced if exposure is analyzed using day of con- couples at the time they stop contraception to ples because of error it causes when studying ception as the index day. In the same manner, attempt conception or by following couples at age-dependent effects on fecundity. Their a time trend bias is introduced if a woman’s risk for pregnancy, ideally regardless of preg- study found that using only completed preg- exposure to an environmental factor increases nancy intentions at enrollment. Most of the nancies, a common practice in retrospective over time. A woman with a shorter TTP will studies of environmental exposures have been studies, could lead to the incorrect assumption report less exposure, whereas one with a longer based on retrospective studies. However, signifi- that TTP decreases with age. In addition, TTP will report a greater exposure, even if the cant biases can occur in retrospective studies. because typically only pregnant woman are exposure had no direct effect on TTP. Retrospective studies of time to pregnancy. recruited, no allowance is made in studies for a Despite obvious bias, retrospective studies In retrospective interviews women are asked to sterile subpopulation. Therefore, associations are often used because of the ease and low cost recall the number of menstrual cycles or the between environmental exposures and sterility of collecting data. They may be particularly number of calendar months it took them to cannot be studied using such a design. Further, suitable for exploratory studies or for ongoing conceive from the cessation of contraception. early pregnancy outcomes such as spontaneous population surveillance (Joffe 2003; Olsen and Rachootin 2003). However, because retrospec- Table 1. Research designs to study human fecundity. tive methods are subject to these biases and do Type of study Advantages Disadvantages not account for sexual behavior, they are inade- Retrospective study of TTP Inexpensive; suitable for exploratory Multiple potential biases in quate to definitively assess the effects of envi- studies recruitment, recall, behavior, and ronmental exposures on human development. exposure trends. Outcomes Conventional prospective studies of time to generally limited to completed or pregnancy. In conventional prospective studies advanced pregnancy. investigators follow women from the time of Conventional prospective Fewer biases than retrospective studies; Higher cost and time commitment study of TTP can accurately assess outcomes of than retrospective studies. Some discontinuation of contraception until concep- sterility and spontaneous abortion potential biases remain, including tion or until a set time if conception does not biases arising from planning, occur. Study participants in conventional recognition, medical intervention, prospective studies are often asked to give data and the “unhealthy worker” on intercourse frequency, menstrual bleeding, phenomenon. Cannot adjust contraception history, and exposure(s) of inter- for timing of intercourse. Detailed prospective study Can assess full spectrum of Cost may be more than est. This approach enables investigators to of fecundity, with day-specific reproductive outcomes including early conventional prospective studies. study fecundity, impaired fecundity (e.g., preg- probabilities of conception pregnancy (embryonic) loss. Higher burden for subject nancy loss, ectopic pregnancy), and infertility Can fully adjust for sexual behavior participation. Participants might be (i.e., absence of pregnancy). including the timing of intercourse. less representative of target The prospective design corrects many population. problems inherent in retrospective studies.

88 VOLUME 112 | NUMBER 1 | January 2004 • Environmental Health Perspectives Mini-Monograph | Studying human fertility and environmental exposure

Problems with recall such as digit preference longer TTP, leading more fecund women to Sheps (1964) proposed a model for TTP that are no longer factors. Because a prospective have fewer occupational exposures. assumed a beta distribution for the probability study is based on conception attempts, not Conventional prospective TTP studies do of pregnancy per menstrual cycle. successes, a sterile subpopulation may be pre- not allow for confounding effects of timing of Weinberg and Gladen (1986) extended this sent and later accounted for in the analysis intercourse and the increased chance of concep- beta-binomial model to include couple-specific (Weinberg and Gladen 1986). Information on tion on days close to ovulation (Wilcox et al. covariates and allow for a sterile subpopulation exposures would be collected for the duration 1995), the timing of which varies substantially (those with a zero probability of conception). of the study, allowing investigators to account from cycle to cycle (Wilcox et al. 2000). This Ridout and Morgan (1991) proposed an exten- for any change in prevalence. problem is addressed in more detailed pro- sion that allowed for digit preference among Prospective studies can also accurately spective studies, described below. Overall, women. Boldsen and Schaumburg (1990) sug- ascertain a much broader array of pregnancy prospective designs allow for more accurate, gested an alternative model that treats TTP as a outcomes, such as ectopic pregnancy, sponta- time-specific data on exposure, contraceptive continuous variable. neous abortion, and stillbirth. This allows for a method, intercourse frequency, and menstrual None of the previously mentioned models more complete assessment of potential out- pattern than does the retrospective design allow for time-dependent covariates such as age comes from environmental exposure, as well as (Bonde et al. 1998). Measurement of environ- or accruing environmental exposure. In a more accurate portrayal of TTP. mental exposures, including exposures to both response to this problem, discrete time survival Some of the potential biases inherent in parents, can be studied prospectively, adding models have been proposed (Clayton and retrospective studies such as pregnancy plan- important insight in areas where knowledge is Ecochard 1997; Dunson and Neelon 2003; ning bias, pregnancy recognition bias, medical currently very limited. When more definitive Scheike and Jensen 1997). intervention bias, and unhealthy worker bias assessments are sought for the effects of envi- may still be present in conventional prospective ronmental exposures, the advantages of the Detailed Prospective Studies TTP studies (Baird 1988; Baird et al. 1986; prospective design outweigh the logistical draw- Table 2 summarizes data necessary for a Weinberg et al. 1993, 1994a). The practice of backs, particularly the higher cost and larger detailed prospective study of human fecundity. only using planned pregnancies in TTP studies time commitment than retrospective studies. These include data collected at the level of the (Baird 1988) could introduce pregnancy plan- Statistical models for conventional time to couple, the cycle, and each day in the study. ning bias if exposed couples are more or less pregnancy studies. Retrospective and prospec- The couple-level data include well-established likely to attempt conception than unexposed tive TTP studies generally obtain the same factors that can impact human fecundity and couples. If exposed couples are less fecund, type of data on contraception and cycles until have been described adequately in previous they will be less likely to experience unexpected conception. If pregnancies resulting from con- reviews (Baird and Strassman 2000; Baird et al. pregnancy during the use of contraception and traceptive failure are excluded, both retrospec- 1986). The cycle-level and day-level data are therefore may ultimately be more likely to seek tive and conventional prospective data may be described in more detail below. to plan a pregnancy. Bias in pregnancy recog- analyzed in the same manner (Weinberg and It is highly desirable to obtain more precise nition can occur if an exposed group is more Gladen 1986). Because each menstrual cycle data on intercourse frequency and timing to likely to have irregular menstrual cycles or less provides one conception opportunity, it is con- adjust for the differences in conception proba- likely to buy home pregnancy kits. If recogni- sidered the natural time unit for TTP analysis. bilities by day in the cycle. From the time of tion of pregnancy is delayed by an exposure, If duration is more easily remembered in Ogino (1930) and Knaus (1929), who esti- the TTP may seem longer, even though months in retrospective studies, the length of mated that ovulation occurred approximately the exposure has no direct link to TTP. the average menstrual cycle can be used to esti- 14 days before the start of the next menstrual Additionally, if early spontaneous abortions go mate the interval in menstrual cycles. cycle, it has been known that most of the varia- unnoticed, participants may have two or more Because models that allow for heterogeneity tion in cycle length (both between women and pregnancies before a pregnancy is detected, in fecundity among the population are more within the same woman) occurs in the preovu- leading the group to appear less fecund. realistic than those that assume homogeneity, latory (follicular) phase of the menstrual cycle, Assisted reproductive techniques may increase the odds of conception for some couples, so Table 2. Data elements to include in detailed prospective studies of human fecundity. any medical intervention may lead to a higher Couple-level data fertility rate among couples who seek assis- Age and other demographic data Reproductive, gynecologic, andrologic, and other medical history tance. Some couples may enhance their proba- Past use of contraception and hormonal therapies bilities of conception by using aids for selecting Occupational exposure timing of intercourse, such as urine luteinizing History of alcohol, tobacco, and other drug use hormone (LH) testing or urinary estrogen Semen analysis (with repeated time-referenced measures) metabolite testing (both available over the Cycle-level data a counter) or monitoring signs of fertility, such Occurrence and estimated day of ovulation (derived from day-level data) Occurrence of conception (derived from day-level data)a as vaginal mucus discharge or basal body tem- Reproductive intentions perature (Stanford et al. 2002). It is therefore Use of assisted reproduction techniques or home techniques to enhance conception essential that any interventions used by the Day-level data couple to enhance conception be identified Menstrual or other vaginal bleeding and be accounted for in analysis. (Such inter- Sexual intercourse or genital contacta vention cycles could either be excluded from Use of barriers, withdrawal, or spermicidea Marker of ovulation, such as urinary hormones, vaginal mucus observation, or basal body temperaturea analysis or included with the interventions Marker of conception, such as serum or urine human chorionic gonadotropina noted as covariates.) Finally, the unhealthy Estrogen or metabolites (serum, urine, or saliva) worker bias is particularly problematic in Progesterone or metabolites (serum, urine, or saliva) studies of occupational exposures. Women Biological exposure assessments (serum, urine, or saliva) with reference to day of collection who are successful in conceiving quickly may Use of alcohol, tobacco, drugs, or herbs leave the workforce earlier than those with aIndicate essential core elements for analysis of day-specific probabilities of conception.

Environmental Health Perspectives • VOLUME 112 | NUMBER 1 | January 2004 89 Mini-Monograph | Tingen et al. whereas the postovulatory (luteal) phase is mucus peak can be learned easily by women rigorous assessment of the outcome of concep- relatively constant at approximately 14 days. from a variety of socioeconomic backgrounds tion itself. Many conceptions result in sponta- The later finding that, while in the reproduc- (World Health Organization 1981). In addi- neous pregnancy loss, which may not be tive tract, the human ovum can only be fertil- tion to having low cost, a clear advantage of recognized as a spontaneous abortion. A num- ized for a window of approximately 12–48 hr mucus-based methods is that the presence and ber of studies have assessed these outcomes (Siegler 1944) led to the hypothesis that an quality of mucus discharge provides additional using sensitive assays for human chorionic increased chance of conception would occur in information about the probability of sperm sur- gonadotropin, an early marker of implantation the days surrounding ovulation. A prospective vival and conception, independent of the tim- (Wang et al. 2003; Wilcox et al. 1988b). Early study in the 1960s (Barrett and Marshall ing of ovulation (Dunson et al. 2001a; Hilgers pregnancy factor, now identified as a protein 1969) of 221 married British couples was and Prebil 1979; Stanford et al. 2003) that is a close homolog to chaperonin-10, has among the first to test this hypothesis. Chances Studies that attempt to identify day of ovu- been used to identify conception prior to of conception were low in the early part of the lation must consider important differences implantation, but it is not yet sufficiently spe- menstrual cycle; conception probabilities between methods. For example some of the cific for use in large epidemiologic studies increased to a peak 2 days before the estimated methods of determining the timing of ovula- (Cavanagh 1996; Morton et al. 1992). day of ovulation. After the day of ovulation the tion will alert couples to the days they are more Because of the relatively high proportion of conception probabilities decreased to near zero. likely to be fertile, whereas other methods will conceptions that end prior to clinical recogni- A later study by Wilcox et al. (1995), which not. If couples are alerted to the days of fertil- tion of pregnancy, a complete assessment of collected first morning urine data on each day ity, this may alter their sexual behavior and reproductive outcomes should include the of the menstrual cycle for hormonal analysis, hence their TTP (Hilgers et al. 1992; Stanford measurement of a biochemical marker of con- found that intercourse was unlikely to result in et al. 2002; World Health Organization 1983). ception in the postovulatory phase of the men- a conception unless it occurred in the 6-day A number of studies have used daily urine col- strual cycle. At present, the best candidate is interval ending on the day of ovulation. lections analyzed in a central laboratory for the human chorionic gonadotropin. Detailed prospective TTP studies such as the occurrence and timing of ovulation without A final advantage of the detailed prospective European Study of Daily Fecundability feedback to couples during the study, thus TTP design is the ability to examine interac- (Colombo and Masarotto 2000) have con- eliminating this bias (Waller et al. 1996; Wang tions between exposure effects and the age of firmed the relatively narrow interval of days et al. 2003; Wilcox et al. 1985). If accurate the gametes. Such interactions are plausible, as immediately preceding ovulation when inter- records of the days with intercourse relative to aged gametes may be more susceptible to expo- course may result in pregnancy. These studies the identified ovulation day are collected and sures. Wilcox et al. (1998) noted an increase in allow one to adjust for the confounding effects inferences are based on day-specific probabili- early pregnancy loss among conceptions that of the timing and frequency of intercourse in ties of pregnancy (further described below), occurred when the ovum had the opportunity studying biological effects of covariates such as methods that prospectively inform the couples to age prior to conception. Potentially, gametes age (Dunson et al. 2002). about their fertile days can then be used with- damaged by exposure to a toxicant may degrade Such studies require daily data collection to out biasing the results. Methods that provide more quickly with age. It is also plausible that determine the days of ovulation and intercourse information to the couples about their fertile sperm damaged by an exposure may have a (Table 2). Methods of estimating day of ovula- days should be preferable for couples attempt- higher probability of surviving and transporting tion include direct ultrasonographic monitoring ing pregnancy and those who wish to avoid themselves to the ovum if introduced on days to determine time of follicular rupture, the use pregnancy without using hormonal or barrier with high levels of estrogenic mucus, whereas of surrogates such as the LH surge in urine or methods of contraception. only the most progressively motile sperm have a serum, the last day of hypothermia prior to the Daily analysis of urine, serum, or saliva for chance of fertilizing the egg on days with sub- postovulatory rise in basal body temperature ovarian hormones, pituitary reproductive hor- optimal mucus. This hypothesis is plausible, (BBT), the cervical mucus peak day (the last mones, or their metabolites has been used in because sperm survival and transport are regu- day of slippery or stretchy vaginal discharge), prospective studies to assess ovarian function lated by cervical mucus secretions which vary and the rapid decline in the ratio of estrogen to beyond the simple occurrence of ovulation. during the menstrual cycle (Katz 1991). progesterone metabolites in the urine (day of Such hormonal profiles are predictive of both However, daily records of mucus and inter- luteal transition) (Baird et al. 1991). These maternal outcomes (Waller et al. 1996) and course are necessary to investigate this. methods differ in their accuracy, cost, and time reproductive outcomes (Baird et al. 1999). Methods of analysis. Taken together, the commitment. Ultrasound monitoring is the Although some researchers suspect that data necessary for a prospective study of gold standard, but cost is prohibitive in larger exposure to alcohol, tobacco, and caffeine human fertility necessitate statistical methods studies. Detection of the LH surge and the day decreases human fertility (Curtis et al. 1997; developed specifically to accommodate the of luteal transition require assaying and collec- Dunson 2001; Hakim et al. 1998; Weinberg complex and multilevel nature of the data tion of daily first morning urine samples. Some et al. 1989; Wilcox et al. 1988a), the exact structure. The concept of day-specific proba- studies have attempted to use calendar calcula- nature of these associations is hard to charac- bilities of pregnancy allows the integration of tions based on previous or expected cycle length terize in retrospective studies and has been the these data into a meaningful measure of to estimate the daily probabilities of concep- source of some controversy. In addition, human fecundity that can be used to assess the tion, but estimates from such calculations are despite widespread use of herbal products in effects of various exposures, demographic fac- very imprecise, even among women with a his- the United States (Eisenberg et al. 1993), tors, behavioral factors, and their interactions. tory of regular menstrual cycles (Wilcox et al. almost nothing is known about the effects of Day-specific probabilities have the advantage 2000). BBT and mucus-based methods are these products on human fertility and human of not depending on intercourse behavior, somewhat less accurate than hormonal meas- development. A detailed prospective study unlike the per-menstrual-cycle probabilities of ures but much more accurate than calendar cal- could collect such exposure information on a conception and the TTP. Thus, the day- culations, making them cost effective for large daily basis and allow a more precise examina- specific probabilities provide a more direct studies (Guida et al. 1999). Vaginal observation tion of these effects. measure of biologic fecundity. Knowledge of of mucus discharge for purposes of predicting An additional advantage of detailed the biology of the menstrual cycle can be used the fertile days of the cycle and the cervical prospective studies is the opportunity for a in developing statistical models for the daily

90 VOLUME 112 | NUMBER 1 | January 2004 • Environmental Health Perspectives Mini-Monograph | Studying human fertility and environmental exposure probabilities. In particular, ovulation is the key day of ovulation (Dunson et al. 2001b; probabilities than cycles with a single inter- event in the menstrual cycle that determines Dunson and Weinberg 2000b). In addition, course act. In the latter case, the intercourse act the timing of the fecund interval during which Royston (1982) and Weinberg and Wilcox responsible for the conception is known, so intercourse can result in a pregnancy with non- (1995) developed parametric versions of the there is less uncertainty. negligible probability. If intercourse occurred Schwartz model by assuming distributions for In the study by Wilcox et al. (1995), the only once in each menstrual cycle under study, the survival times of the sperm and egg. sample size was sufficient to obtain precise esti- it would be straightforward to estimate day- Royston and Ferreira (1999) later proposed an mates of covariate effects on the cycle viability specific probabilities and to relate these proba- approximation of Equation 2 that assumes that probability (Dunson and Zhou 2000), but bilities to covariates using logistic regression, sperm introduced into the reproductive tract there was low power to detect interactions ideally with a couple-specific random effect on any given day have no chance of fertilizing between timing in the fecund window and the included to account for within-couple depen- the ovum and thus no effect on the conception effect of a covariate. Even in analyses that did dency. However, in a menstrual cycle with outcome if intercourse occurs on a more fertile not adjust for covariates, 95% confidence limits multiple acts of intercourse occurring within day. Potentially, these models could be general- for the day-specific conception probabilities the fertile window, it is not possible to ized to accommodate time-varying exposure ranged almost from zero to one. The high attribute conception to a single act. effects by using a time-varying coefficient degree of uncertainty is partly due to the large To account for this problem, Barrett and model (Hastie and Tibshirani 1993; Verweij proportion of cycles with multiple intercourse Marshall (1969) applied a model suggested by and van Houwelingen 1995). acts, as the couples in the Wilcox et al. study Peter Armitage, which assumes that batches As previously stated, the incorporation of (1995) were attempting conception. However, of sperm introduced into the reproductive male and female factors into both pk and A another important factor is the type of statistical tract on different days commingle and then makes it difficult to determine which biological methods used to analyze the data. Prior to the compete independently in attempting to fer- factors relate directly to each. In addition, it approach of Dunson (2001), analyses did not tilize the egg. Their model has the following tends to be difficult to separately estimate A incorporate constraints on the pks and hence mathematical form: and the maximum pk because of colinearity in were subject to the problems discussed above. these two parameters. In the special case where As illustrated by Dunson (2001), by incorporat- =−Π ()Xik Pij11kk–, p [1] there is a single intercourse act in each cycle, ing biologically reasonable parameter con- the Schwartz model is not estimable, and one straints on the pks, one can greatly reduce where Pij is the probability of conception for of the parameters must be fixed to fit the uncertainty in the estimates and increase power couple i in cycle j, k is the day in the cycle model. As the highest pk is close to one for each to assess covariate effects. Applying this relative to ovulation (k =0 on day of ovula- of the available data sets, a reasonable modifi- approach to the Wilcox et al. (1995) data tion), Xik is an indicator variable that equals 1 cation of the Schwartz model that solves the revealed evidence of an interaction between the if intercourse occurred on day k and 0 other- estimability and colinearity problems is to set effect of caffeine exposure on reducing fecund- wise, and pk is the probability of conception in the highest pk equal to one. Dunson (2001) ability and the timing of intercourse. a cycle with intercourse only on day k. proposed such an approach within the frame- Standard formulas used for sample-size Schwartz et al. (1980) modified this model work of a Bayesian hierarchical model that also calculations do not apply here, and it is diffi- by including a susceptibility multiplier A to incorporates the constraint that the pks increase cult to formulate general guidelines because of allow menstrual cycle characteristics other to a peak and then decrease. The Dunson complex interactions between the sample size than intercourse to have an effect on the prob- (2001) approach accommodates variability needed to obtain a given power, the couples’ ability of conception: among couples in the day-specific conception intercourse behavior, the numbers of cycles of probabilities and covariate effects on both the follow-up, the distribution of fecundability in =−Π ()Xik maximum day-specific probability and the the population, and the prevalence of the expo- Pij A{}11kk–, p [2] duration of the fertile interval. A further advan- sure(s). As a rule of thumb, small studies tage of this model is that it enhances statistical involving fewer than 100 couples are not rec- where A is typically referred to as the cycle power to study the effects of covariates such as ommended unless one is willing to use viability probability and pk is the probability of follicular phase length or age on fecundity. Bayesian methods with informative priors cho- conception in a viable cycle with intercourse Hence, it is a useful approach in applications sen based on historical studies in the analysis. only on day k. The term cycle viability proba- (Dunson et al. 2002; Stanford et al. 2002). For couples attempting conception (assuming bility is somewhat misleading because it An important issue in designing and that one does not want to incorporate histori- implies that A includes only woman-specific analyzing studies of day-specific pregnancy cal data from previous studies that might be factors such as uterine receptivity and oviduct probabilities is sample size. The two classic informative), an excess of 100 couples followed function. However, like pk, cycle viability (A) studies in this area, the Barrett and Marshall until conception or at least 6–12 months if not also includes male factors (e.g., the presence of (1969) study and the study by Wilcox et al. conceiving is needed to investigate common motile sperm) and interaction effects (ability of (1995), had data for slightly more than exposures possibly associated with overall sperm to fertilize ovum, survival of embryo to 200 couples, a sample size that has proven suf- fecundability. The use of day-specific detection), making it difficult to distinguish ficient to produce many important results. probabilities for the analysis will adjust for the which biological factors relate directly to A and However, the number of couples is not the effects of sexual behavior (i.e., timing of inter- which relate to pk (Dunson 2001). only important issue, as estimation of day-spe- course) while allowing for an overall assessment Variations of the model of Schwartz et al. cific probabilities relies on the availability of of the effect of exposure on fecundability. To have been proposed to allow covariate effects conception and nonconception cycles having a investigate more detailed interactions between on A (Weinberg et al. 1994b), covariate effects variety of intercourse days within the fecund the exposure effect and timing of intercourse on pk (Zhou and Weinberg 1996), hetero- window. Menstrual cycles with no acts of by day relative to ovulation, sample sizes need geneity among couples in A (Dunson and intercourse within the fecund window do not to be much larger. To obtain estimates of Zhou 2000; Zhou et al. 1996), missing data contribute to the analysis. In addition, cycles power under a given scenario, one can conduct on intercourse (Dunson and Weinberg 2000a), with multiple acts of intercourse contribute less a simulation study. Although it did not assess and measurement error in identifying the true information to the estimation of day-specific environmental exposures per se, the European

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Study of Daily Fecundability (Colombo and such as sterility or spontaneous abortion are not day-specific probabilities of conception. Masarotto 2000), with 881 couples and 7,017 included among the outcomes assessed. For Prospective studies, particularly detailed menstrual cycles, had sufficient sample size to example, it is possible that an environmental prospective studies outlined here, will be neces- examine the effect of some demographic and exposure could be misclassified as having a sary to expand our understanding of the effects reproductive factors (age, parity, prior use of weak effect or no effect on the continuum of of environmental exposures on human fertility. oral contraceptives, and follicular phase length) human reproduction when in fact it has a The prospective designs also have an important on day-specific probabilities. strong effect. In addition, if an exposure tends role in addressing the growing interest in The role of pregnancy planning. Most to differentially affect those embryos with a effects of early exposure on later outcomes of prospective studies of TTP exclude couples higher overall susceptibility to adverse out- human development: large cohort studies such who are not planning pregnancy, an exclusion comes, as seems likely, then there can even be as the National Children’s Study and others that may lead to the pregnancy planning bias an apparent beneficial effect of an adverse expo- (Eaton 2002) are currently being proposed. described earlier. Demographic research indi- sure on later developmental outcomes (Dunson The methodological and statistical methods cates that about half of all pregnancies in the and Perreault 2001). Therefore, to accurately reviewed in this article should prove useful in United States are considered unintended assess the lifetime effects of environmental these lines of inquiry. (Henshaw 1998). 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