Epidemiologic Approaches for Studying Recurrent Pregnancy Outcomes: Challenges and Implications for Research

Epidemiologic Approaches for Studying Recurrent Pregnancy Outcomes: Challenges and Implications for Research

Cande V. Ananth, PhD, MPH

The study of recurrence of pregnancy-related complications and outcomes can offer powerful insights to understanding patient-related risks for subsequent pregnancies. Such studies, when designed, analyzed, and interpreted correctly, can help distinguish genetic from environmental causes that portend increased recurrence of a particular pregnancy complication (eg, recurrence of gestational diabetes) or a perinatal outcome (eg, recur- rence of preterm birth or preeclampsia). Recurrence risk studies can be challenging in other dimensions, including inherent biases, generalizability of findings, inadequate study size, and inappropriate use of analytic models to study recurrence. Other common mis- perceptions in studies of recurrence risk are highlighted, including issues with terminology and interpretation of recurrence risks. A review of available epidemiologic study designs is presented and the usefulness and applicability of each design for addressing specific etiologic questions as they relate to recurrence risks are contrasted. Semin Perinatol 31:196-201 © 2007 Elsevier Inc. All rights reserved.

KEYWORDS recurrence risk, heterogeneity, epidemiology, clustered data, case-crossover design, prospective cohort, cohort studies

M rent events in pregnancy are highlighted with particular

ost diseases in medicine do not tend to recur. Preg-

nancy is perhaps the only state that provides the op- emphasis on: (1) challenges in accurately defining the end- portunity to study recurrence risks. The study of recurrence

point being observed; (2) choosing an appropriate epidemi- of pregnancy-related complications and outcomes can offer

ologic design for studying patterns of recurrence risks; (3) powerful insights to understanding patient-related risks for

confounding; (4) limitations contributed through various bi- subsequent pregnancies. Whereas recurrent outcome re-

ases in epidemiologic studies; (5) sample size, statistical search can help guide clinical care for future pregnancies, it

power, and analytic models; (6) a note on terminology; and also affords a unique opportunity to explore disease etiolo-

(7) interpretation of recurrence risks. Finally, an outline of gies through the study of heterogeneity in risk factors or

some unifying concepts in studies on recurrence is presented. those that change across successive pregnancies.

The fundamental ideas and concepts espoused in this pa- This paper provides an overview of some of the fundamen-

per regarding epidemiologic approaches to studying recur- tal concepts in studying recurrence, focusing largely on avail-

rent pregnancy outcomes stem, in part, from discussions able epidemiologic and statistical approaches. In addition,

from the “Second International Symposium on Successive Preg- some of the common misperceptions about recurrence re-

nancy Outcomes: A Decade of Progress”, which was held in New search in human reproduction (broadly defined) are ad-

Brunswick, NJ, in August 2005, and the proceedings of this dressed. In particular, several challenges in studying recur-

symposium that are due to be published in a forthcoming issue of Paediatric and Perinatal Epidemiology. 1

Division of Epidemiology and Biostatistics, Department of Obstetrics, Gy- necology, and Reproductive Sciences, UMDNJ-Robert Wood Johnson Medical School, New Brunswick, NJ.

Why Study Recurrence?

Address reprint requests to Cande V. Ananth, PhD, MPH, Division of Epidemi- ology and Biostatistics, Department of Obstetrics, Gynecology, and Repro-

For epidemiologists as well as clinicians, studying recurrence

ductive Sciences, UMDNJ-Robert Wood Johnson Medical School, 125

provides an opportunity to examine etiologic heterogeneity.

Paterson Street, New Brunswick, NJ 08901-1977. E-mail: cande.

One fundamental, yet much underappreciated, advantage to

ananth@umdnj.edu

studying recurrence is the ability to separate “low-risk”

196 0146-0005/07/$-see front matter © 2007 Elsevier Inc. All rights reserved.

doi:10.1053/j.semperi.2007.03.008 doi:10.1053/j.semperi.2007.03.008

cinctly illustrated by Wilcox, 2 who made a compelling argu-

ment that what separates low risk from high risk of recur- rence is driven by the etiology of the initial clinical event or complication. When characteristics of persons in the low- and high-risk groups differ, then depending on the strength and magnitude, these differences may provide some clues about disease causation.

As an illustration, consider a study to examine differences in risk factors associated with spontaneous and indicated preterm births. Some studies have shown a few differences between these two clinical subtypes of preterm birth. 3-5 The ability to separate preterm birth based on the underlying clinical subtypes addresses issues related to etiologic hetero- geneity in studying preterm birth. 4,6 The similarities in risk factors between the two subtypes suggest that these two con-

ditions may overlap in terms of similar etiologic profiles. 7 Yet,

studying the recurrence of preterm birth provides one oppor- tunity to examine separately and in greater detail the risk profiles between low-risk women (women with a previous term birth) and high-risk women (those with a prior preterm birth). Whereas the data regarding increased recurrence (of either spontaneous or indicated preterm birth) suggest a di- rect biologic influence of the previous preterm birth, other observed (both fixed and transient) and unobserved factors that are shared between the two pregnancies also probably contribute to this increased recurrence.

The heterogeneity in recurrence risks is derived through variable contributions of genetic effects, environmental influ- ences, their interaction, and “time.” A genetic contribution to the recurrence of an adverse reproductive endpoint can be contributed by the mother such as is seen with inherited thrombophilias and venous thromboembolism risk. An en- vironmental effect (eg, smoking during pregnancy) can op- erate through either, or both, of the pregnancies within which the recurrence is studied. An interaction between genes and environment is one when the effect of genotype on disease risk depends on the type and level of exposure to an environmental factor, or vice versa. A good example is the risk of recurrence for neural tube defects in siblings in rela- tion to a genetic polymorphism (in the folate metabolism pathway) and the variability in environmental exposure to folate supplementation. The “time” factor in recurrence stud- ies, although important to understand heterogeneity in dis-

ease etiologies, is highly complex. 8 Exposures or risk factors

inevitably operate through time with varying windows of opportunity: a short exposure window (eg, exposure to a teratogen during organogenesis), throughout the pregnancy (eg, cumulative exposure to smoking throughout preg- nancy), or a lifetime of exposure (eg, inadequate nutrition

through harsh social conditions 9 or across generations).

For example, attempts to separate biologic aging effects (such as maternal age) from those of aging of the uterine environment contributed through repeated pregnancies (a

parity effect) on the risk of placental abruption, 10 although

straightforward in theory, are challenging to separate in cross-sectional studies. Consider the task of separating the

biologic aging effects from other influences on the recurrence of a pregnancy complication using the interpregnancy inter- val as the important “time” factor. Both short and long inter- vals between pregnancies have been associated with adverse pregnancy outcomes. 11-14 Although short intervals can be as- sociated with the biologic effect of possible inadequate uter- ine recovery between pregnancies, there may also be a ten- dency for couples with an adverse outcome to have another pregnancy sooner, something known as selective fertility. Conversely, a long interpregnancy interval may allow ade- quate replenishment of nutrients to ensure a subsequent suc- cessful pregnancy, but may be associated with the develop- ment of a medical disease (such as diabetes or hypertension) and possibly a change in partner between the two pregnan- cies. It is extremely difficult to separate the relative effects of each of these components on the recurrence of a particular pregnancy complication. Taken together, all these factors in- evitably contribute to recurrence risks, are highly inter- twined, and complex to disentangle.

Challenge 1: The Importance of Accurately Defining Exposures and End Points

One of the fundamental tenets of any research is to be able to define both the exposure and the outcome of interest with high degree of precision. The challenges in defining out- comes accurately have serious implications both in data an- alytic approach and in the interpretation of study findings. Most of the outcomes in perinatal epidemiology and, more broadly in obstetrics and gynecology, are fairly well defined and can be measured accurately. Whereas some outcomes, such as preterm birth, gestational diabetes, and preeclamp- sia, are easy to define accurately, others are not (eg, preterm birth clinical subtypes).

Several conditions and reproductive end points present a challenge regarding an acceptable definition. Intrauterine growth restriction refers to a fetus that has not been growing adequately, and is thought to be the result of an underlying

pathological process. 15 Because true intrauterine growth re- striction is very difficult to assess in population-based stud- ies, a proxy, small-for-gestational age, has instead been used. The latter refers to infants (at birth) that weigh below a cer- tain threshold (usually the 10th centile) for a given gesta- tional age. Although small-for-gestational age is used as a proxy of “true” in utero fetal growth restriction, not all babies that are “small” for their gestational age are truly growth restricted. Thus, inaccuracies in defining an end point can have serious implications as to how data on recurrence risks can be interpreted.

Challenge 2: Study Designs for Studies of Recurrence

Several epidemiologic study designs are available to study recurrence of a specific disease or outcome. A prospective cohort study is one that has been a commonly applied design

Studying recurrent events in pregnancy 197

C.V. Ananth

to study recurrence of pregnancy complications. With this is a risk factor for the outcome being examined among design, women having an index pregnancy are followed lon-

those unexposed; (2) the factor must be associated with gitudinally over time to record their outcome in subsequent

the exposure in the population from which the subjects pregnancies. Existing registry-based data can be used to de-

arose; and (3) the variable is not in the causal pathway of sign a prospective cohort study assuming an ability to iden-

the exposure– outcome relationship. 18 Adjustment for po- tify and link women having more than one pregnancy. This is

tential confounders in any analysis eliminates bias (caused the most commonly used design in studies of recurrent preg-

by those confounders) that could otherwise distort the nancy outcomes.

exposure– disease association. In a cross-sectional or a For some types of recurrent pregnancy complications,

case-control study, adjustment for available confounders newer hybrid study designs may offer some advantages.

is straightforward; however, the issue of confounder ad- Most notably, the case-crossover study design is one that

justment gets more complicated in studies of recurrence. offers great promise for studying the effect of transient

Consider, as an illustration, if one is interested in quanti-

fying the extent to which preeclampsia recurs between the answer the question: “Was an outcome triggered by some

exposures on the risk of outcomes. 16 This design helps

first and the second pregnancy. Should one adjust for specific exposure that occurred immediately preceding the

potential confounders present in the first pregnancy, sec- outcome (ie, an antecedent exposure)?” The distinguish-

ond pregnancy, or both?

ing characteristic of this design is that each case serves as Confounders largely fall into two broad types: time- its own control, and is analogous to a crossover experi-

independent and time-varying (or time-dependent). In the ment viewed retrospectively. This means that the investi-

former, when the value of a variable for subjects under gator does not control when a patient starts being exposed

study does not change over time (eg, race/ethnicity), the

variable is said to be time-independent. On the contrary, some similarities to a traditional matched-pair case-con-

to a potential trigger. 17 The case-crossover design has

when the value of the variable changes with time (eg, trol study. 18 In both types of designs, each case has a

parity, maternal smoking or prepregnancy body mass in- “matched” control. However, in a traditional matched

dex across successive pregnancies), the variable is consid- case-control study, the control is a different individual at a

ered time-dependent. The type of variable being consid- similar time. As in the case in the case-crossover design,

ered for adjustment during statistical analysis, presumably the control is the same person, but observed at a different

to minimize confounding, has implications in studies of time. The case-crossover design applies best when the ex-

recurrence.

posure is intermittent, the effect of risk is immediate and Although sophisticated statistical models have been de- transient, and the outcome is abrupt. Therefore, it may be

veloped for correcting time-varying confounders, 20,21 sim- helpful to examine the effects of an abdominal trauma on

pler approaches can also be undertaken. Consider a sce- the risk of placental abruption among women with a pre-

nario where one is interested in estimating the risk of vious abruption and those with prior normal pregnancy

recurrence of placental abruption, and maternal smoking outcomes.

(as a binary factor denoting if the women was a smoker or One of the inherent strengths of the case-crossover de-

nonsmoker) is a potential confounder. One efficient ap- sign is the implicit control for confounding bias. Since

proach to fully adjust for the confounding effects of smok- every subject in a case-crossover study serves as their own

ing is to construct a four-level factor as follows: non- “control,” confounding is less of an issue relative to studies

smoker in both pregnancies (coded 0), smoker in the first that incorporate other designs. This phenomenon was el-

but not the second (coded 1), smoker in the second, but

not the first (coded 2), and smoker in both pregnancies dom effectiveness study in preventing infections, where

egantly illustrated by Warner and colleagues 19 in a con-

(coded 3). The construction of the new variable is similar they demonstrated that epidemiologic studies confounded

to allowing an interaction effect of smoking status between by unmeasured differences between condom users and

the first and second pregnancies. Adjustment for this vari- nonusers underestimate condom effectiveness against cer-

able in the regression model will ensure control for con- tain infections. For instance, prospective cohort studies

founding as opposed to adjusting for smoking effects in suffer from unmeasured confounding (a term also referred

the first or in the second pregnancy alone. to as “residual confounding”), often leading to distorted

estimates of the exposure– disease relationship. The case- crossover method, however, provided a technique for re-

Challenge 4: Biases

ducing unmeasured confounding in studies of condom

in Studies of Recurrence

effectiveness. 19

A couple’s decision to achieve a desired family size introduces

Challenge 3: Confounding a bias in studies of recurrence. Selective fertility, the tendency

to control fertility on the basis of previous pregnancy out-

A confounder is, by definition, a factor that distorts the comes, 22 is one such phenomenon that can affect studies of association between an exposure and the outcome unless

recurrence risks. 23 Specifically, couples that experience peri- adjusted. Three essential criteria for a variable to be clas-

natal losses in the first pregnancy tend to go on to have sified as a confounder include: (1) the variable in question

additional pregnancies to achieve a desired family size. This additional pregnancies to achieve a desired family size. This

older women. Skjaerven and coworkers 23 suggest that, al-

though women differ in their inherent risks for perinatal losses, selective fertility leads to an overrepresentation of high-risk women at higher birth orders.

Other biases often operate in studies of recurrence, with bias due to selection being one of the more important of biases. When a study of recurrence of a reproductive out- come is restricted to successive singleton live births, for ex- ample, women with pregnancy losses or stillbirths, either before the first singleton live birth or between two successive live births, are inevitably excluded. These inclusion and ex- clusion criteria have implications to studies on recurrence, including generalizability or clinical relevance of the find- ings. Although this is not a critical limitation, careful atten- tion to such biases must be considered while drawing infer- ences from such studies.

Challenge 5: Choosing the Appropriate Study Size and Analytic Approach

Most published research on recurrent pregnancy outcomes come from large, population-based data. These studies mostly come from the Scandinavian countries, notably, Nor- way, Sweden, and Denmark, and others in Europe such as Scotland. Data collection from these countries date back sev- eral decades with perhaps the Norwegian birth registry dat- ing back to the mid-1960s. Similar data from within the United States are few, and are largely based on identifying and linking biologic mothers to their successive pregnancies. In the United States, these data come primarily from vital statistics registers that are based on birth and death (fetal and infant) certificates.

The advantages of using large, population-based registries to address specific research on recurrent pregnancy out- comes is the large sample size which, in turn, affords excel- lent statistical power to discern patterns of recurrence risk. In addition, such studies offer greater generalizability since they are population-based. One of the inherent difficulties with smaller studies on recurrence of a particular pregnancy com- plication is adequate study size. As an illustration, consider if one is interested in estimating the risk of recurrence of uter- ine rupture. Uterine rupture has a reported incidence of 1.6 per 1000 pregnancies in women with a previous cesarean

delivery attempting a subsequent vaginal birth. 24 If the goal is

to estimate the recurrence risk of uterine rupture, then the study should exclude women who have undergone hysterec- tomy and include only women with a repaired uterine rup- ture in the first pregnancy who then go on to have a second pregnancy that again results in a uterine rupture. The rarity of this sequence of events would require hundreds of thousands of women to adequately study. To be successful, a study of this magnitude would need several large registries, perhaps a collaborative effort of all population-based registries. Smaller studies will inevitably lead to conclusions being affected by

lack of statistical power (type II error). Therefore, picking an outcome that is observable with an available study popula- tion is paramount to a successful study.

One of the important assumptions of any statistical test is the “independence” of observations. Thus, studying a recur- rent pregnancy-related event entails evaluation of the event in the same woman twice. Studies dealing with the recur- rence of an outcome clearly violate this assumption of inde- pendence. Consider, for example, studies dealing with the risk of recurrence of fetal growth restriction, a topic reviewed

extensively by Kinzler and Kaminsky in this issue. 25 Since a woman contributes data on two successive pregnancies, with each pregnancy resulting in a growth-restricted or appropri- ately grown infant, the responses (fetal growth) tend to be “correlated.” This tendency of “clustering” gives rise to an intracluster correlation (the woman, in this instance, is said to constitute a cluster), which will produce incorrect esti- mates of variance parameters when left unadjusted. 26-28 In other words, although the odds ratio for the exposure– dis- ease relationship will remain unaffected due to ignoring the intracluster correlation, the 95% confidence interval for the odds ratio will be biased on either direction (depending on the strength and direction of the intracluster correlation). This, in turn, will affect significance tests, and eventually diminish the scientific merit of the intended research. Several analytic models and methods have been developed to ac- count for this clustering phenomenon. Although description of these methods fall well beyond the scope of this paper, interested readers are referred to papers on this topic with specific applications to studies on human reproduction. 5,29

Challenge 6:

A Note on Terminology

Unfortunately, the terms “multivariable” and “multivariate” have been used interchangeably in the medical literature. However, these terms have distinct implications that are im- portant for recurrence research. Consider, as an illustration, the setting of a cross-sectional (or case-control) study, where the goal is to estimate the risk of preeclampsia in relation to nulliparity (with parous women as the reference). A regres- sion model to derive an estimate of the relative risk (or odds ratio) for preeclampsia in relation to nulliparity after adjust- ing for potential confounders is, by definition, a multivari- able model. On the other hand, if one is interested in estimat- ing the effect of change in paternity on the recurrence risk of preeclampsia, then a study of successive births is required. Because preeclampsia is repeatedly assessed (ie, in each of the two pregnancies), a regression model that is adjusted for potential confounders is a “multivariate” model. Researchers have used the two terms “multivariable” and “multivariate” casually, and the medical literature has paid little attention to its correct usage. Correct use and understanding of terminol- ogy will facilitate communication among all parties involved in recurrence research.

Studying recurrent events in pregnancy 199

C.V. Ananth

Challenge 7: Interpretation

recurrence risks. More importantly, incorrect models to an-

of Recurrence Risks alyze data arising from correlated responses will likely yield

incorrect statistical and biologic inferences. Finally, correct One of the fundamental issues common to studies on recur-

interpretation of recurrence risks will greatly enhance our rence of pregnancy outcomes pertains to interpretation. The

ongoing pursuits for studying recurrence of adverse out- biggest challenge is to successfully translate the results of

comes in pregnancy-related conditions, which is best ap- epidemiologic observations on recurrence risk to clinical de-

proached through a collaborative environment. cision making for individual patients. Most studies on recur- rence are population-based, which is a strength in many

Acknowledgments

ways, but population-based recurrence risks do not readily lead to customized risks for an individual patient. Aside from

The author extends special thanks to Russell Kirby, PhD, conceptual differences in the regression models for popula-

Morgan Peltier, PhD, John Smulian, MD, MPH, and Anthony tion-based versus subject-specific approaches to risk estima-

Vintzileos, MD, for their thoughtful suggestions and valuable tion, 30,31 the rich set of factors that shape risk in an individual

comments that helped improve the paper. Dr. Ananth is par- patient limits the direct translation of population-derived

tially supported through a grant (HD038902) from the Na- risks to individuals.

tional Institutes of Health awarded to him. As an illustration, consider the following scenario. The

recurrence risk for stillbirth in a large study is fourfold higher

References

among women with a previous stillbirth. Let us assume that

1. Ananth CV: Second International Symposium on Successive Pregnancy

one is interested in applying this recurrence risk to an indi-

Outcomes: a decade of progress. Paediatr Perinat Epidemiol 21(Suppl)

vidual patient with gestational diabetes that had experienced

2007, in press

a previous stillbirth. But this particular patient may have lost 2. Wilcox AJ: The analysis of recurrence risks as an epidemiologic tool.

Paediatr Perinat Epidemiol 21(Suppl) 2007, in press

weight, maintained extremely good glycemic control inter-

3. Berkowitz GS, Blackmore-Prince C, Lapinski RH, et al: Risk factors for

conceptionally, or was managed differently in the next preg-

preterm birth subtypes. Epidemiology 9:279-285, 1998

nancy. This is in addition to other contributing factors that

4. Savitz DA, Blackmore CA, Thorp JM: Epidemiologic characteristics of

may have been altered, but are difficult to ascertain. That the

preterm delivery: etiologic heterogeneity. Am J Obstet Gynecol 164:

recurrence risk for stillbirth for this patient is fourfold higher

467-471, 1991

5. Ananth CV, Platt RW, Savitz DA: Regression models for clustered bi-

is clearly misleading. This illustration highlights the chal-

nary responses: implications of ignoring the intracluster correlation in

lenge in applying population-based risk profiles to individual

an analysis of perinatal mortality in twin gestations. Ann Epidemiol

patient settings. Smulian 32 provides a clinical perspective on

15:293-301, 2005

many of the issues surrounding interpretation of research in

6. Ananth CV, Vintzileos AM: Maternal-fetal conditions necessitating a

recurrent pregnancy complications. medical intervention resulting in preterm birth. Am J Obstet Gynecol

195:1557-1563, 2006

7. Ananth CV, Getahun D, Peltier MR, et al: Recurrence of spontaneous versus medically indicated preterm birth. Am J Obstet Gynecol 195:

Conclusions

643-650, 2006

8. Basso O: Options and limitations in studies of successive pregnancy

No research can be accomplished in isolation, and a study on

outcomes: an overview. Paediatr Perinat Epidemiol 21(Suppl) 2007, in

recurrence of pregnancy-related conditions is no exception.

press

Optimizing study design using the best available data, appro-

9. Wilcox AJ, Skjaerven R, Irgens LM: Harsh social conditions and peri-

priately adjusting for confounding and other biases, choosing

natal survival: an age-period-cohort analysis of the World War II occu-

appropriate statistical models and, most importantly, careful pation of Norway. Am J Public Health 84:1463-1467, 1994

10. Ananth CV, Wilcox AJ, Savitz DA, et al: Effect of maternal age and

interpretation of findings are extremely important. Given the

parity on the risk of uteroplacental bleeding disorders in pregnancy.

complexities in all these facets in studies of recurrence, the

Obstet Gynecol 88:511-516, 1996

challenges are quite daunting. It is clear that as recurrence

11. Basso O, Olsen J, Knudsen LB, et al: Low birth weight and preterm birth

research becomes more common and as the methodology

after short interpregnancy intervals. Am J Obstet Gynecol 178:259-

matures, active collaborations will be necessary among epi- 263, 1998

12. Smith GC, Pell JP, Dobbie R: Interpregnancy interval and risk of pre-

demiologists, biostatisticians, and the clinical community to

term birth and neonatal death: retrospective cohort study. Br Med J

get the most out of our efforts.

Observational studies of recurrent pregnancy complica-

13. Zhu BP, Rolfs RT, Nangle BE, et al: Effect of the interval between

tions are difficult to perform well, and cohort studies that

pregnancies on perinatal outcomes. N Engl J Med 340:589-594, 1999

entail a recurrence component are much more complicated. 14. Conde-Agudelo A, Rosas-Bermudez A, Kafury-Goeta AC: Birth spacing

and risk of adverse perinatal outcomes: a meta-analysis. J Am Med

In addition to the limitations afforded in following prospec-

Assoc 295:1809-1823, 2006

tive cohorts (including resources, time and personnel ef-

15. Resnik R: Intrauterine growth restriction. Obstet Gynecol 99:490-496,

forts), studies of recurrence need to carefully consider the

issues highlighted in this review. Such studies require atten-

16. Maclure M: The case-crossover design: a method for studying transient

tion to inherent biases (eg, selective fertility, selective man- effects on the risk of acute events. Am J Epidemiol 133:144-153, 1991

17. Maclure M, Mittleman MA: Should we use a case-crossover design?

agement), and failure to recognize and account for such lim-

Annu Rev Public Health 21:193-221, 2000

itations will invariably result in distorted findings of

18. Greenland S, Rothman KJ: Measures of effect and measures of associa-

Studying recurrent events in pregnancy 201

tion, in Rothman KJ, Greenland S (eds): Modern Epidemiology (ed 2). 25. Kinzler WL, Kaminsky L: Fetal growth restriction and subsequent preg- Philadelphia, PA, Lippincott Williams & Wilkins, 1998, pp 47-64

nancy risks. Semin Perinatol 2007, in press 19. Warner L, Macaluso M, Austin HD, et al: Application of the case-

26. Liang KY, Zeger SL: Regression analysis for correlated data. Annu Rev crossover design to reduce unmeasured confounding in studies of con-

Public Health 14:43-68, 1993

dom effectiveness. Am J Epidemiol 161:765-773, 2005 27. Zeger SL, Liang KY: Longitudinal data analysis for discrete and contin- 20. Bodnar LM, Davidian M, Siega-Riz AM, et al: Marginal structural mod-

uous outcomes. Biometrics 42:121-130, 1986 els for analyzing causal effects of time-dependent treatments: an appli-

28. Liang K-Y, Zeger SL: Longitudinal data analysis using generalized linear cation in perinatal epidemiology. Am J Epidemiol 159:926-934, 2004

models. Biometrika 73:13-22, 1986

21. Robins JM, Hernan MA, Brumback B: Marginal structural models and causal inference in epidemiology. Epidemiology 11:550-560, 2000

29. Louis GB, Dukic V, Heagerty PJ, et al: Analysis of repeated pregnancy 22. Wilcox AJ, Gladen BC: Spontaneous abortion: the role of heteroge-

outcomes. Stat Methods Med Res 15:103-126, 2006 neous risk and selective fertility. Early Hum Dev 7:165-178, 1982

30. Zeger SL, Liang KY: An overview of methods for the analysis of longi- 23. Skjaerven R, Wilcox AJ, Lie RT, et al: Selective fertility and the distor-

tudinal data. Stat Med 11:1825-1839, 1992 tion of perinatal mortality. Am J Epidemiol 128:1352-1363, 1988

31. Zeger SL, Liang KY, Albert PS: Models for longitudinal data: a general- 24. Lydon-Rochelle M, Holt VL, Easterling TR, et al: Risk of uterine rupture

ized estimating equation approach. Biometrics 44:1049-1060, 1988 during labor among women with a prior cesarean delivery. N Engl

32. Smulian JC: Research on recurrent pregnancy complications: a clini- J Med 345:3-8, 2001

cian’s perspective. Paediatr Perinat Epidemiol Suppl 2007, in press