Methodological Issues in Population-Based Studies of Multigenerational Associations

Abstract

Laboratory-based animal research has revealed a number of exposures with multigenerational effects—ones that affect the children and grandchildren of those directly exposed. An important task for epidemiology is to investigate these relationships in human populations. Without the relative control achieved in laboratory settings, however, population-based studies of multigenerational associations have had to use a broader range of study designs. Current strategies to obtain multigenerational data include exploiting birth registries and existing cohort studies, ascertaining exposures within them, and measuring outcomes across multiple generations. In this paper, we describe the methodological challenges inherent to multigenerational studies in human populations. After outlining standard taxonomy to facilitate discussion of study designs and target exposure associations, we highlight the methodological issues, focusing on the interplay between study design, analysis strategy, and the fact that outcomes may be related to family size. In a simulation study, we show that different multigenerational designs lead to estimates of different exposure associations with distinct scientific interpretations. Nevertheless, target associations can be recovered by incorporating (possibly) auxiliary information, and we provide insights into choosing an appropriate target association. Finally, we identify areas requiring further methodological development.

Abbreviations

ADHD

attention-deficit/hyperactivity disorder

CPP

Collaborative Perinatal Project

DES

diethylstilbestrol

GEE

generalized estimating equations

IEE

independence estimating equations

WEE

weighted estimating equations

Epidemiologists have recently shown interest in studying multigenerational associations—where exposures are related to not only persons directly exposed but also their progeny (1–29). Despite a rich body of epidemiologic methods, however, multigenerational studies exhibit a number of distinct features that require special methodological consideration.

One hypothesized mechanism by which multigenerational effects arise is through modifications of the epigenome of germline cells, such as methylation patterns, which are inherited by subsequent generations (7, 30). Much of the evidence for this has been gathered via laboratory-based animal studies (1, 7, 31–41). Given the degree of control that laboratories provide, these studies have typically been conducted by exposing members of an initial generation (and leaving some unexposed) and prospectively ascertaining outcomes among future generations of the exposed and unexposed groups (1, 7, 8, 31–34, 37).

Whether interest lies in the epigenetic action of environmental pollutants (3–7) or in the downstream consequences of social determinants of health (19–28), the practical and ethical limitations of population-based multigenerational studies seldom allow for the straightforward study designs of animal studies or randomized controlled trials. Instead, researchers have exploited birth registries and existing cohort studies, ascertaining exposures within them (sometimes retrospectively) and measuring outcomes across multiple generations (2–6, 9–15, 30). Typically, however, such registries/cohorts have not been constructed specifically for investigation of multigenerational associations, and the data structure available has varied substantially, raising a number of methodological issues unique to population-based studies of multigenerational associations. In Nurses’ Health Study II (NHS II), for example, children’s outcomes were not just cluster-correlated within families but also varied by family size (6). In addition, with multiple generations of people on which to make observations, selecting a study design and analysis strategy that permits estimation of the association of interest is an important task. These issues—and their interrelationships—warrant careful consideration even in studies tailored to investigating multigenerational associations.

In this paper, we illustrate these methodological issues in detail. We first introduce 2 motivating cohorts and, with these as a guide, outline key terms for describing multigenerational study designs and associations. We then explore via simulation how the interplay between study design, variation in cluster sizes, and the approach to analysis affects the scope of scientific inquiry.

MOTIVATING EXAMPLES

Studies of multigenerational associations require measurements across multiple generations. One such example of a study that has been used to investigate multigenerational associations is the Collaborative Perinatal Project (CPP) (16–18, 42), which recruited 48,197 pregnant women between 1959 and 1964. In addition to outcomes pertaining to the pregnancy at recruitment, the CPP ascertained outcomes retrospectively for prior pregnancies and prospectively for subsequent pregnancies in the same mothers. Using these data, Huang et al. (14) investigated the association between mother’s prepregnancy obesity and the neurodevelopment of her children, while Nelson and Ellenberg (15) studied the association between mother’s smoking history and febrile seizures in her children. In 1992–1994, a follow-up study called CPP Pathways to Adulthood investigated the health, cognitive development, and educational achievement of the grandchildren of mothers at the Baltimore, Maryland, CPP site (12, 13, 27).

As a second example, NHS II incorporated both retrospective and prospective observations to capture information about 3 successive generations. The NHS II investigators recruited 116,686 female nurses aged 25–42 years in 1989, who responded to multiple questionnaires over several years of follow-up, reporting health outcomes and exposures about not only themselves but also their families (43, 44). In 1993, for example, nurses retrospectively reported whether their mothers had taken any hormones while pregnant with them; in 2005, nurses reported neurodevelopmental outcomes among their children. In this way, Kioumourtzoglou et al. (6) were able to investigate the association between in-utero maternal diethylstilbestrol (DES) exposure and third-generation diagnosis of attention-deficit/hyperactivity disorder (ADHD).

While these examples highlight different study designs, many variations exist. Some other examples of multigenerational studies include the Dutch Famine Birth Cohort Study (9, 10, 45), the National Longitudinal Study of Adolescent to Adult Health (19, 29), and studies of birth cohorts from northern Finland (26), Sweden (23, 24), and Hong Kong (28).

KEY TERMS

Investigating multigenerational associations requires at least 2 successive generations. By convention, we label the first generation, the one that is directly exposed, the F0 generation (1, 7, 31–33, 46). In the CPP, the F0’s consisted of the pregnant women recruited into the study. In contrast, the F0’s in NHS II consisted of the mothers of the nurses/individuals who were recruited. Subsequent generations are indexed sequentially: The children of the F0’s belong to the F1 generation; the grandchildren of the F0’s belong to the F2 generation (12, 13).

Many different study designs may be employed to estimate multigenerational associations, as shown in Figure 1. Ideally, we would prospectively obtain data on the full population of F0’s and all associated F1’s (Figure 1A), but this is often infeasible. Researchers have instead implemented a range of subsampling strategies, which vary according to 1) the primary sampling generation—the generation to which the individuals recruited into the study belong—and 2) the completeness of the family structure—whether all or some offspring are observed. For example, investigators may recruit F0’s and then obtain information on all of their F1 children (Figure 1B) or on a single F1 child (e.g., the child from the current pregnancy; Figure 1C). Alternatively, researchers may initially recruit F1’s and obtain exposure information on the corresponding F0’s (Figure 1D). We explore the implications of these design considerations below.

Figure 1.

Example data structures for multigenerational studies. A) Full population; B) design I: sampling entire F0 families; C) design II: sampling single F1’s within F0 families; D) design III: sampling F1’s directly. Gray circles indicate people not observed in the sample. Asterisks (*) indicate the primary sampling units in designs I–III.

SIMULATION STUDY

Here we present a simulation study exploring the interplay between sampling designs and analysis considerations, specifically in terms of what exposure associations are estimable from the resulting data. We consider a hypothetical study spanning 2 generations, where the goal is to estimate the risk ratio characterizing the association between a binary F0-level exposure, , and a binary F1-level outcome, . We anchor select details of the simulated populations, specifically the distribution of family sizes and the outcome prevalence, to the study of DES exposure and ADHD reported by Kioumourtzoglou et al. (6) (see also McGee et al. (47)). The question we aim to answer is, Does each design estimate the same risk ratio?

Generating full cohorts

We generated R = 1,000 full cohorts, each consisting of K = 40,000 families (i.e., a single member from the F0 generation and their F1 children). Within each family, 25% of the F0’s (mothers) were “exposed” . A major consideration in multigenerational studies is the interplay between F0 exposure, family size, and F1 outcomes; as such, we simulate the F1 generation via a joint model for family size and F1 child outcomes (47, 48). Technical details are given in the Web Appendix (available at https://academic.oup.com/aje). Briefly, in our simulation study, both family size and F1 outcomes depended on the exposure status of the F0 mother as well as a shared (unobserved) random effect. Each family had at least 1 child in the F1 generation; we discuss the implications of families with no children below.

Under this data-generating mechanism, family sizes varied around the mode of 2 children, with 15% of the families having singletons and 6% having 5 or more children (Table 1). Average family size among the unexposed F0’s was 2.6, while that among the exposed F0’s was 2.3. Overall, the outcome was rare (1.5%) and more common among children of exposed mothers than children of unexposed mothers (2.5% vs. 1.3%). Moreover, outcomes were related to family size, with higher incidence in smaller families, ranging from 4.7% among single-child families to 0.2% in families of 5 or more (Table 1).

Table 1.

Characteristics (%) of a Simulated Full Population by Family Size (Number of F1’s), Computed on the Basis of a Single Population of Size K = 1,000,000^a

	All F0’s			Unexposed F0’s (X 1k = 0)		Exposed F0’s (X 1k = 1)
No. of F1’s	Proportion of F0’s	Exposure Prevalence	Outcome Prevalence	Proportion of F0’s	Outcome Prevalence	Proportion of F0’s	Outcome Prevalence
1	14.7	30.2	4.7	13.7	4.5	17.7	5.0
2	47.2	27.9	2.4	45.4	2.1	52.6	3.1
3	16.4	23.8	1.1	16.7	0.9	15.6	1.8
4	15.7	18.7	0.6	17.0	0.4	11.7	1.2
≥5	6.0	9.8	0.2	7.2	0.1	2.3	0.6

^a  K, number of clusters; X_1k, exposure for the kth cluster.

Analyses of the full cohorts

To estimate the risk ratio for the association between and , we assume the following working (marginal) model:

where is the exposure of the mother in the kth family and is the outcome of the ith child in the kth family. In a standard cluster-correlated data setting, one can estimate using generalized estimating equations (GEE), for which the analyst specifies a working covariance structure (49). Typically, even if this structure is incorrectly specified, the resulting estimate of β is consistent for the true value, and valid inference can be obtained by using the robust sandwich form of the variance. Here, however, the choice has important consequences because the family (or cluster) size is informative; that is, the outcomes among the individuals in the F1 generation are conditionally associated with the size of the family (i.e., associated not only though exposure/covariates) (48, 50, 51). This might occur if, say, some unaccounted-for factor such as toxicity or a shared genetic frailty affected both fertility and the offspring’s health outcomes.

A number of statistical methods have been proposed to acknowledge informative cluster sizes (48). Prominent among these is the use of working independence GEE coupled with either no further weighting (referred to as independence estimating equations (IEE)) or inverse cluster-size weights, (weighted estimating equations (WEE)) (51). Applying these to the simulated cohorts, the average estimated log risk ratio from IEE is log(1.9), while that from WEE is log(1.6) (Table 2). Rather than one estimator’s being biased for an unambiguous true value of the risk ratio, this difference is instead analogous to the role that noncollapsibility has in changing the “true” value of the odds ratio in logistic regression (52). The choice of weighting scheme thus has implications for the parameter being estimated when cluster size is informative. We elaborate on this below. In the remainder of this section, we consider the interplay between study design and analysis and their impact on the parameter being estimated.

Table 2.

Mean Log Risk Ratio Estimates of the Exposure-Outcome Association for Various Study Design–Analysis Pairs Across 1,000 Simulated Data Sets, Exponentiated to the Risk Ratio Scale (Simulation Results)^a

Data Structure	Weighting Scheme (Analysis)
	1 (IEE)	(WEE)
Full population	1.9	1.6
Design I	1.9	1.6
Design II	1.6		1.9
Design III	1.9	1.6

Abbreviations: IEE, independence estimating equations; WEE, weighted estimating equations.

^a  N_k, size of the kth cluster.

THE ROLE OF THE SAMPLING SCHEME

Motivated by the CPP and NHS II, described above, suppose it is not possible to observe the full cohorts. We consider 3 subsampling designs that vary according to the primary sampling generation and the completeness of the family structure. For each of the R = 1,000 simulated full cohorts, we obtained subsamples based on each design.

Design I: sampling F0 families

A natural subsample could be generated by recruiting F0’s and then obtaining information on all of their F1’s. The observed data would consist of a random sample of complete families (Figure 1B).

To implement this design, we randomly selected 8,000 F0’s (20%) and their families in each of the 1,000 full cohorts. Because of the variation in family sizes, , the number of F1’s included in the rth subsample—denoted —varied across data sets. (, where is 1 if the kth F0 is selected in the design I sample and 0 otherwise, and is the kth F0’s number of children).

Design II: sampling F1’s within F0-indexed families

Suppose again that we collect a random sample of F0’s (the primary sampling generation) but resources are only available for ascertaining outcomes on a single birth (Figure 1C). Regardless of the ultimate size of the family, , the family structure is incomplete, with observed data in the form of parent-child dyads. With only 1 child per family, methods such as GEE would likely be seen as “unnecessary,” so one might naturally proceed by means of a standard regression analysis without robust variance estimation. Note that the resulting estimator is the same as the IEE estimator.

To implement this, we randomly selected individuals in the F0 generation in the rth cohort, and we then randomly drew 1 F1 per selected F0.

Design III: sampling F1’s directly

Taking the F0 generation as the primary sampling generation, as done by designs I and II, may not always be feasible. Emanuel et al. (2), for example, studied birth weight in a sample of babies born between March 3 and 9, 1958, in the United Kingdom, with a range of exposures measured retrospectively on their parents. Thus, the primary sampling generation was the F1 generation. NHS II similarly sampled F1’s directly (43). Depending on the time frame and mode of recruiting, one may or may not observe siblings within families (Figure 1D). Either way, family structures are generally incomplete. As a consequence, analysis may or may not require consideration of within-cluster correlation.

To implement design III, we randomly selected individuals in the F1 generation in the rth cohort.

Simulation results

We applied IEE (weights of 1) and WEE (inverse cluster size weights, 1/N_k) to each subsample and report average log risk ratios across the 1,000 simulated cohorts in Table 2. Perhaps not surprisingly, design I behaved like the full cohort analyses: IEE and WEE yielded average log risk ratios of log(1.9) and log(1.6), respectively. By contrast, IEE applied to design II yielded log(1.6), whereas WEE recovered neither of the full-cohort risk ratio estimates. Interestingly, however, weighting by cluster size—that is, , as opposed to the inverse cluster size weights of WEE—yielded log(1.9). Design III performed similarly to design I: IEE and WEE recovered the full-cohort risk ratio estimates of log(1.9) and log(1.6).

A key takeaway is that each design was able to recover the full-cohort IEE and WEE risk ratios with appropriate weighting schemes. In practice, however, the weighted analyses rely on knowledge of the full cluster size, which may not be readily available in design II or III. We emphasize that auxiliary information on full cluster sizes may be necessary to recover the full-cohort IEE and WEE estimates.

TOWARD A MORE PRECISE SCIENTIFIC QUESTION

The simulation study suggested that when cluster size is informative, analyses based on different weighting schemes estimate different parameters. It is thus tempting to conclude that one is biased, but this is not so. Consider the mean value and the median value: While the two have different interpretations, both summarize the center of a distribution. In certain settings, they are numerically equal (i.e., symmetrical distributions), despite having different interpretations. Elsewhere they differ—yet neither represents the “correct” measure of the center of a distribution.

Table 2 shows an analogous phenomenon: 1.6 and 1.9 correspond to different parameters that offer distinct representations of the relationship between exposure and outcome; each carries a distinct interpretation and thus answers a subtly different scientific question (48, 51). As with the mean and median, the key to deciding which to pursue rests with careful consideration of how to interpret the 2 parameters—and pairing an interpretation to the scientific question of interest.

Toward this, consider 2 hypothetical randomized trials. In the first, we obtain a random sample of individuals from the F0 generation and randomly assign them to treatment or control status. Outcomes are then prospectively ascertained on all of their children, and we compare the outcomes of all children with mothers in the treatment arm to those of all children with mothers in the control arm. Thus, the comparison corresponds to the exposure association among all F1’s across all F0’s. We refer to this as the all F1 association.

In the second trial, we again obtain a random sample of individuals from the F0 generation and assign them to treatment or control status. At this point, however, the outcomes from 1 randomly selected child from each family are ascertained and form the basis of the comparison. In this sense, the contrast is not among all F1’s but rather corresponds to the exposure association for a typical F1 from a typical F0. We refer to this as the typical F1 association.

The all F1 association captures the exposure-outcome relationship in a way that acknowledges and, as such, varies with the outcome–cluster size relationship. Figure 2 illustrates this: Repeating the simulations described above with different outcome–cluster size relationships (within exposure groups), the all F1 association increases as cluster sizes and outcomes become more negatively correlated. As suggested by the first hypothetical trial, the all F1 association reflects what might occur in an entire population of F1’s; in this way, it balances the contributions of all existing F1’s. Put differently, it answers the question, What are the downstream consequences for the next generation if we introduce an exposure to a population? This implicitly incorporates the outcome-size association, which may or may not reflect some underlying biological mechanism—for example, if the burden of raising children with health issues leads to having fewer children. Consider investigating DES and ADHD: If the goal is to characterize the impact on public health that would result from exposing a population to DES—for example, to assess the overall burden it induces, or for planning purposes—the all F1 association may be an appropriate target of inference.

Figure 2.

Comparison of “all F1” effects and “typical F1” effects for multigenerational studies, by informativeness. The y-axis shows the mean estimate of the log odds ratio (OR) for the exposure effect, fitted via independence estimating equations (all F1 effect) and weighted estimating equations WEE (typical F1 effect), in R = 1,000 simulated populations. The x-axis shows the strength of the association between outcome risk and cluster size, conditional on exposure—intuitively, the informative cluster size relationship—quantified by the risk difference comparing exposed families with 3 children to exposed families with 1 child, computed in 1 population of K = 1,000,000 F0’s. Note that at x = 0, outcome risk is still related to cluster size, but only through the exposure (i.e., cluster size is noninformative). See the Web Appendix for details on the data-generating mechanism.

In contrast, the typical F1 association isolates the exposure-outcome relationship in that it remains constant under different outcome-size associations (Figure 2). It, too, averages over a population, albeit a hypothetical one that is free of the outcome–cluster size relationship; in this way, it balances the contributions of all existing F0’s. As such, the typical F1 association may be viewed as speaking less to some impact on public health writ large and more to studies of risk factors for diseases or of specific biological relationships. Returning to the DES-ADHD example, the fact that ADHD is more common in smaller families may, for example, be irrelevant to the goal of understanding the role of maternal DES exposure in brain development. In such a case, the typical F1 association may be a suitable target of inference.

Notably, if cluster size is noninformative—that is, related to outcomes only through the exposure/covariates—then the all F1 and typical F1 associations coincide numerically (Figure 2; x = 0). Their precise interpretations in this case may not be crucial, and analysts can proceed with the usual population-averaged interpretation that accompanies results from a GEE analysis.

OTHER METHODOLOGICAL CONSIDERATIONS

Above, we explored the interplay between study design, analysis, and the parameter being estimated in multigenerational studies. Here we briefly outline other methodological considerations, highlight recent developments, and indicate where new methods are needed.

Empty clusters

In multigenerational studies, the exposure is directly applied to members of the F0 generation, while outcomes are measured in their progeny. With this in mind, we have so far assumed that each individual in the F0 generation has at least 1 child, which may not be the case. That is, the observed F1 outcome data for an individual in the F0 generation may constitute an empty cluster. This presents unique challenges, both conceptually and analytically. If whether or not a woman bears children is unrelated to their potential health outcomes (given covariates), we say that clusters are noninformatively empty and no adjustments are needed; otherwise, clusters are informatively empty and the analysis requires more care (47).

Informative emptiness is a natural extension of informative cluster size. Recall that the all F1 association can be viewed through the lens of having balanced the contributions across the individuals in the F1 population. Since nonexistent F1’s play no role in this population, estimates of the all F1 association remain valid under informative emptiness. By contrast, the typical F1 association can be viewed as balancing the contributions of all F0’s. As such, F0’s with no children—as all F0’s—should contribute equally; and yet such empty clusters, containing no outcomes to report, are excluded from standard analyses. To resolve this, in settings where the full cohort is available or data are available through design I described above (sampling F0 families) and information is available on the empty clusters, one can adopt a joint marginalized model of outcomes and cluster sizes, a parametric analysis that can directly incorporate empty clusters into a likelihood framework (47, 48).

More generally, the interplay between design and informative emptiness needs to be characterized. Retrospective approaches like design III (sampling F1’s directly) are probably susceptible to selection bias, since they may never register information on empty clusters. Further research is needed to determine how—and whether—both exposure associations described here could be recovered from different designs under informative emptiness.

Misclassification

Given the practical limitations of following a population over the course of multiple generations, exposure data may only be available retrospectively, making them vulnerable to misclassification and recall bias (53–55). The circumstances of data collection may exacerbate the problem even more—for example, in NHS II, F1’s reported whether or not they had been exposed to DES in utero (6).

While misclassification and measurement error are commonplace in epidemiology (53, 54), multigenerational studies present new challenges. Take DES, for example, an exposure related to both family size and neurodevelopmental outcomes in NHS II. McGee et al. (56) showed that misclassification in such an exposure actually induces informative cluster size when cluster size would otherwise be noninformative. Moreover, the extent of misclassification itself varied by cluster size, with larger families exhibiting more severe misclassification (56). In particular, misclassification that depends on informative cluster size induces differential misclassification, leading to complex bias structures (56). Researchers might incorporate bias analyses to assess the impact of different misclassification patterns.

Volume-outcome studies (family size as a covariate)

We have thus far assumed that the goal of analysis is to estimate an exposure-outcome association and that the outcome–family size association is a nuisance. When the outcome–family size relationship is itself of interest, family size (or some function of it) can be incorporated into the model as a covariate (48). This intuitively “adjusts away” the outcome–family size relationship, such that cluster size would no longer be informative. As such, this represents an alternative method for handling informative cluster size, although it changes the scientific interpretation of the exposure association. It remains population-averaged, but it compares populations only of families of the same size. This is often inadvisable—for example, when cluster size is a mediator (see Seaman et al. (48) for a discussion).

DISCUSSION

As multigenerational cohorts mature and proliferate, so do opportunities to answer new epidemiologic questions. We have identified a number of methodological challenges inherent to these studies and summarized existing methods for analysis. Importantly, we have summarized when to consider informative cluster size, how this might affect design decisions, how the choice of analysis intersects with the design to determine what is being estimated, and how to differentiate the 2 target associations. Yet new challenges will surely emerge. For instance, we considered only 2 generations, which will generally be insufficient to isolate transgenerational associations—a subset of multigenerational associations that manifest through pathways distinct from the one through which direct exposure influences outcomes, for example, via epigenetic inheritance. Typically F2 outcomes are needed to identify an association as transgenerational, but F3 outcomes may even be necessary if F0 women pregnant with a female fetus are exposed (see Skinner et al. (46)). A next step is therefore to explore how the same basic building blocks as those summarized in Table 3—primary sampling generations, family completeness, cluster correlation, informative cluster size, empty clusters, weighting schemes—interact in studies spanning 3 or more generations. Nevertheless, the issues discussed here apply broadly to F0-F1 settings, including many studies of maternal exposures and child development (57–61).

Table 3.

Select Methodological Considerations Relevant to Population-Based F0-F1 Studies of Multigenerational Effects^a

Notation	Significance
Cluster correlation	Health outcomes are often correlated within families (clusters).
Empty clusters	Unlike many cluster-correlated settings, clusters may be of size zero () since F0’s may have no children.
Informative cluster size	If some latent factor is related to outcomes and number of children (i.e., cluster size), the typical F1 effect differs from the all F1 effect.
Informatively empty clusters	Informative emptiness occurs when an informative cluster-size mechanism causes clusters of size zero (i.e., some F0’s with no children). Empty clusters must be incorporated into the analysis to recover the typical F1 effect. Informatively empty clusters may interact with study designs (e.g., cause selection bias).
Primary sampling generation	The generation initially recruited (e.g., F0 or F1) is a key component of multigenerational study designs that affects the interpretation of exposure effects estimated from an unweighted analysis. may be unobservable if F1 is the primary sampling generation.
Family completeness	Whether all children or a random subset of children are sampled for each recruited F0 is another component of study designs that affects the interpretation of exposure effects estimated from an unweighted analysis. Family size may be unobservable when families are incomplete.
Weighting schemes	Unweighted analyses (GEE with working independence) recover an exposure effect implied by the study design. Weighting by cluster size () or its inverse () can recover the alternative effect. Both require that the design permit complete family size to be observed.
Misclassification	Retrospective multigenerational designs are particularly susceptible to exposure misclassification. Misclassification bias manifests in complex ways when the degree of misclassification is related to number of children.

Abbreviation: GEE, generalized estimating equations.

^a  , number of children born to the kth F0 (family size).

When a population exhibits informative cluster size, subsamples inherit its limitations on the scope of scientific inquiry—even when they do not exhibit cluster correlation (see “Simulation study: designs II and III”). By default, they estimate either an “all F1” association or the “typical F1” association. (While the simulation study produced results for risk ratios, we observe analogous results on the odds ratio and risk difference scales; see Tables 4 and 5). These differ in subtle ways, and choosing between them is a difficult task, requiring investigators to make explicit their scientific aims beyond simply estimating an exposure-outcome association. By analogy to 2 hypothetical clinical trials, we highlighted their differences and argued that the “all F1” association better suits studies assessing overall impacts on public health, while the “typical F1” association better suits studies of risk factors for disease and underlying biological relationships. Nevertheless, the two can often be estimated in the same sample, and one might ultimately report both.

Table 4.

Mean Log Odds Ratio Estimates of the Exposure-Outcome Association for Various Study Design–Analysis Pairs Across 1,000 Simulated Data Sets, Exponentiated to the Odds Ratio Scale (Simulation Results)^a

Data Structure	Weighting Scheme (Analysis)
	1 (IEE)	(WEE)
Full population	2.0	1.6
Design I	2.0	1.6
Design II	1.6		2.0
Design III	2.0	1.6

Abbreviations: IEE, independence estimating equations; WEE, weighted estimating equations.

^a  , size of the kth cluster.

Table 5.

Mean Risk Difference Estimates (%) of the Exposure-Outcome Association for Various Study Design–Analysis Pairs Across 1,000 Simulated Data Sets (Simulation Results)^a

Data Structure	Weighting Scheme (Analysis)
	1 (IEE)	(WEE)
Full population	1.2	1.1
Design I	1.2	1.1
Design II	1.1		1.2
Design III	1.2	1.1

Abbreviations: IEE, independence estimating equations; WEE, weighted estimating equations.

^a  , size of the kth cluster.

Designing multigenerational studies requires careful consideration. For example, one may need to collect auxiliary information—such as cluster size in design II or III or empty clusters—to recover an association of interest. Moreover, practical constraints on prospective studies spanning multiple generations motivate adapting outcome-dependent designs to this setting (62–68). These and other design challenges will likely play an important role in future research.