Can We Interpret Analyses of Etiologic Heterogeneity When Molecular Markers Are Used to Classify Tumors?

Abstract

Background:

Analyses of etiologic heterogeneity use molecular markers to subtype cancers (e.g., breast cancer) and test whether an exposure is more strongly associated with one tumor subtype as opposed to other subtypes. However, these molecular markers (e.g., a mutated oncogene) may best be conceptualized as mediators of exposure–disease relationships.

Methods:

Seven model causal scenarios, based on data from the literature on postmenopausal breast cancer, were created with varying relationships between an exposure, a mediating or non-mediating molecular marker, and a disease status, with molecular marker used to subtype the disease. Using numerical examples, we assessed how well the analyses of etiologic heterogeneity identify the distinct etiologic pathways in these seven scenarios.

Results:

Etiologic heterogeneity analyses of the data from the four causal mediation models produced similar results despite the mediating role of molecular marker differing across scenarios, with heterogeneity effect sizes ranging from 1.47 to 1.60. Analyses of data from the two scenarios, in which molecular marker did not affect the risk of disease, also produced evidence of etiologic heterogeneity, with heterogeneity effect sizes of 1.53 and 2.66. The smallest heterogeneity effect size (1.33) was observed in the scenario in which molecular marker was a sufficient cause of disease.

Conclusions:

This methodologic research indicates that analyses of etiologic heterogeneity cannot distinguish between the modeled causal scenarios when a mediating or non-mediating molecular marker is used to subtype tumors.

Impact:

We discuss these results in the context of the literature on obesity and etiologic heterogeneity in breast tumors subtyped by sex hormone receptor status.

Introduction

A premise of molecular cancer epidemiology is that mechanistic hypotheses connecting exposures to cancers can be tested by incorporating data on molecular markers (biomarkers) into epidemiologic studies (1). For example, a study exploring vinyl chloride carcinogenesis might include a marker of TP53 mutation to test whether the loss of TP53 function was implicated in vinyl chloride–induced angiosarcoma (2). One analytic approach leveraging such biomarker data is the etiologic heterogeneity design described by Begg and colleagues (3–5). Etiologic heterogeneity analyses use data on tumor characteristics to subdivide cancer defined by a site (e.g., breast cancer) into subgroups (e.g., pathologic subtype or subtypes defined by hormone receptor status) that are thought to be more homogeneous in regards to a putative causal factor (e.g., obesity; refs. 3–8).

Although early etiologic heterogeneity studies subdivided tumors by histology (e.g., adeno vs. squamous cancers of the lung) or location (e.g., ascending vs. descending colon cancers), more recent studies typically use molecular markers, such as overexpression of hormone receptors and oncogenes and mutations in tumor suppressor genes, to subgroup cases (6–14). Analyses showing etiologic heterogeneity between obesity and postmenopausal breast cancer subgrouped by hormone receptor status have been interpreted as evidence for obesity causing breast cancer through a hormone-related pathway (11). Likewise, analyses of environmental carcinogens and tumors subtyped by TP53 mutation/expression status have been used to construct theories for how these carcinogens cause cancer (5, 15, 16).

However, both evidence and theory suggest that the molecular markers often used in studies to define tumor subtypes are steps along carcinogenesis and do not define the ultimate disease subtype entity (1, 17, 18). The observation of overexpression of estrogen receptors (ER) in ductal carcinoma in situ of the breast suggests that overexpression can begin in the earliest stages of breast carcinogenesis (19, 20). Likewise, the overexpression of HER2/neu, cyclin D1, and Ras and mutation of TP53, markers used in prior studies of etiologic heterogeneity, have been observed in precursor lesions of breast, colon, and prostate cancers (21–30). Oncoproteins, mutated TP53 DNA, and auto-antibodies to p53 have been detected in blood samples from populations exposed to known carcinogens and in controls from case–control studies, suggesting that these abnormal markers are being expressed in some healthy individuals (2, 31–35). In other words, the overexpression of hormone receptors and overexpression and/or mutation of oncogenes and tumor suppressor genes can occur as steps or events in tumorigenesis but need not be sufficient to cause disease; in a causal analysis framework, these markers can be conceptualized as mediators between exposure and disease (1, 18).

If the measured molecular markers function causally as mediators, then treating their associations with exposures in etiologic heterogeneity studies as evidence of causation may lead to incorrect conclusions about etiology. Suppose, for instance, that obesity-related breast cancer can develop through either of two pathways—an ER expression–mediated pathway and another possible pathway via alterations in circulating insulin-like growth factor-1, the latter of which is not measured in a study—resulting in the causal directed acyclic graphs (DAG) displayed in Fig. 1 (36). A study participant might develop breast cancer through the insulin-like growth factor-1–mediated pathway (i.e., follow paths B and C) but also develop overexpression of ERs without developing cancer through this pathway (i.e., follow path A but not D). An etiologic heterogeneity analysis that classifies this participant’s tumor as ER+ could correctly identify an association between obesity and the presence of an ER+ tumor, but the study would overestimate the proportion of tumors generated through the ER-mediated pathway.

Figure 1.

An example causal model in which overexpression of ERs is a partial mediator between obesity and breast cancer risk and a second pathway exists that connects obesity to breast cancer risk via obesity-related changes in the level of circulating insulin-like growth factor-1 (IGF-1).

Here, we consider the extent to which analyses of etiologic heterogeneity provide causal or biological evidence when the molecular markers used to classify subtypes of disease are mediators between exposure and final disease status. Conceptually, we ask whether analyses of etiologic heterogeneity by molecular marker status represent an analysis of mediation with missing data on the mediator in the non-diseased? We develop a model system of a cohort study that includes an exposure, a molecular marker, and a disease outcome, and from this system, we develop a series of numerical examples. We analyze data generated by this model system under a series of different scenarios, including scenarios in which the marker is a causal mediator and scenarios in which it is not. We discuss the results in the context of the literature on obesity and breast cancers classified by hormone receptor status.

Materials and Methods

We created seven causal scenarios and created numerical examples of a cohort study for each scenario. In four of the scenarios, the effect of exposure on disease was mediated by the molecular marker with varying causal models for mediation. In three of the examples, the molecular marker was not a mediator for the effect of exposure on disease. Each individual in the cohort has variable for exposure status (E; coded as yes/no), a variable for disease status (D; coded as yes/no), and a variable for molecular marker status (M; coded as positive/negative). Each of the causal scenario examples was implemented in Excel spreadsheets to calculate case counts by marker positive and negative status.

We sought to place these numerical examples within the context of studies of obesity and postmenopausal breast cancer (11). Each cohort was conceptualized as being comprised of 50-year-old women with a 2.4% 10-year risk of developing breast cancer. The molecular marker was modeled after ER+/progesterone receptor (PR)+ status in breast cancer, with a prevalence of marker positivity between 60% and 70% among cases. As reported in a meta-analysis by Munsell and colleagues, the overall obesity to postmenopausal breast cancer RR was 1.20 [95% confidence interval (CI), 1.19–1.31] for cohort studies, and the RR for ER+/PR+ tumors was 1.39 (95% CI, 1.14–1.70) and the RR for ER−/PR− tumors was 0.98 (95% CI, 0.78–1.22; ref. 11). We sought to create numerical examples in which the overall E-to-D RR was 1.20, or within the 95% CI reported by Munsell, the M+ prevalence among cases was between 60% and 69%, the overall 10-year risk for disease was 2.4%, and the RR for M+ tumors was 1.39, or within the 95% CI reported by Munsell. We implemented the seven causal models and manipulated (1) the prevalence of M+ among E−, (2) the association between E and M, (3) the association between M and D, and (4) the interaction between E and M to generate numerical examples that met the constraints described above. There are minimal data on the background rate of breast tissue ER+/PR+ status in normal breast tissue, with estimates for ER+ status ranging from 40% to 55% for fibroadenomas and from 25% to 30% for fibrocystic conditions, 70% or 79% for ductal carcinoma in situ, 57%, 64%, or 68% for benign breast disease controls in case–control studies, and 70% for normal tissue adjacent to tumor tissue (19, 20, 37–42). Based on these data from the literature, the numerical examples began with a 25% prevalence of M+ among E−. Each causal scenario, and its numerical example, is available in the Online Supplementary Table S1 Excel spreadsheet, and the parameters can be changed to create new numerical examples.

The mediation scenarios were that

• 1) M is a full mediator: E+ increases risk for M+ (RR = 1.39) and M+ increases risk for D+ (RR = 5.0), but not everyone who is M+ becomes D+. E has no other effect on D except through M+.

• 2) M is partial mediator: E affects D through M and through an additional pathway that does not involve M. As in scenario 1, E+ increases the risk of M+ 1.39 fold compared with E−. Note, however, that because this scenario includes an additional pathway from E to D (through M−), the RR for the M+ to D+ is lower and the prevalence of M+ among E− had to be increased to 0.40, for the overall risk ratio to hold numerically.

• 3) Exposure–mediator interaction: scenario 3 builds on scenario 1 by adding an E × M interaction. Note that in this scenario, the prevalence of M+ among E− is even higher to allow the other effects to remain within the defined ranges.

• 4) M is a partial mediator and there is an exposure–mediator interaction: This scenario increases the number of ways that E+ increases risk for D+. E+ increases the risk of M+, M+ increases the risk of D+, there is an interaction between E and M, and E+ can raise the risk of D+ among those who are M−. Thus, to achieve an overall E-to-D RR of 1.20, some of the causal effects are smaller compared with scenarios 1 to 3 and the prevalence of M+ among E− had to be raised to 0.525. The E+ to M+ RR was 1.16; the M+ to D+ RR among E− was 1.15; the E × M interaction effect was 1.20; and the M+ to D+ RR, among E−, was 1.25.

The non-mediation scenarios were

• 5) No effect of exposure on disease: E causes M (RR = 1.39), but E does not cause D, and M does not cause D.

• 6) M is a passenger variable: E causes M (RR = 1.16) and D (RR = 1.20), but M does not cause D (43).

• 7) M+ equals D+: in this scenario, M+ is a sufficient cause of disease. M+ is the final step in the causal pathway from E to D, so everyone who is M+ is also D+. E+ causes M+ (RR = 1.32), and 100% of M are D+. Because everyone who is M+ is also D+, the prevalence of M+ among E− had to be lowered to 0.0135.

Figure 2 shows a causal diagram for each scenario.

Figure 2.

Causal models for the tested scenarios with varying relationships between an exposure, a mediating or non-mediating molecular marker, and a disease status (D, disease; E, exposure; M, marker). In each scenario, the molecular marker is used to subtype the disease for analyses of etiologic heterogeneity. In scenario 7, everyone who is positive for the mediator has the disease, so M+ = D+ in the scenario.

We analyzed the data produced by each numerical example of a causal scenario as a cohort study with a polytomous outcome: (1) M+ disease, (2) M– disease, and (3) healthy, no disease. The data were also analyzed as a cumulative incidence-sampled case–control study nested in the cohort with a polytomous outcome and using a case-only design (5). Because of the relationship between the case-only OR and the ratio of ORs from case–control analyses, we also calculated the ratio of ORs from the case–control study (5). The extent of etiologic heterogeneity can be assessed as the ratio of the RR (or OR) for E to M+ disease and the RR (or OR) for E to M– disease or via the case-only OR. The online Supplementary Table S1 provides an Excel spreadsheet that implements the scenarios and generates case counts by M+ and M− status and that can be modified to create additional causal scenarios.

Results

Analyses of the numerical examples for each of the causal scenarios, including the scenario in which E does not cause D, generate results indicative of etiologic heterogeneity, with the extent of etiologic heterogeneity ranging from 1.33 to 2.66 (see Table 1). Although each of the seven scenarios implemented different causal models for the relationships between E, M, and D, it was possible to build numerical examples that would be interpretable as providing evidence of etiologic heterogeneity under a conventional etiologic heterogeneity design. More formally, all scenarios included an overall E+ to D+ RR of 1.20 and an RR for E+ to M+ cases of 1.39. However, numerical examples for the “Full Mediator,” “Partial Mediator,” “Full Mediator and E × M Interaction,” “Partial Mediator and E × M Interaction,” and “M is a Passenger Variable” scenarios all produced similar results for analyses of etiologic heterogeneity (range of 1.47–1.60 for the etiologic heterogeneity effect; Table 1). It follows that the analyses of etiologic heterogeneity, particularly when estimated from a case-only analysis in which an estimate of the overall E to D relationship is not available, cannot reliably distinguish between these causal scenarios.

Table 1.

Results of analyses of etiologic heterogeneity for cohort, case–control, and case-only analyses of data generated by each scenario.

​	Cohort analyses	Cohort analyses of etiologic heterogeneity		Case–control analyses of etiologic heterogeneity			Case-only analyses
	Overall RR for E+ to D	RR for M+ cases	RR for M– cases	OR for M+ cases	OR for M– cases	Ratio OR	Case-only OR
Mediator scenarios	​	​	​	​	​	​	​
1) Full mediator	1.20	1.39	0.87	1.39	0.87	1.60	1.60
2) Partial mediator	1.20	1.39	0.89	1.39	0.89	1.57	1.57
3) Full mediator and E × M interaction	1.20	1.39	0.88	1.39	0.88	1.58	1.58
4) Partial mediator and E × M interaction	1.20	1.39	0.95	1.39	0.95	1.47	1.47
Non-mediator scenarios	​	​	​	​	​	​	​
5) No effect of E on D	1	1.39	0.52	1.39	0.52	2.66	2.66
6) M is a passenger variable	1.20	1.39	0.92	1.40	0.92	1.53	1.53
7) M is a sufficient cause of D (M+ = D+)	1.20	1.32	1.00	1.33	1.00	1.33	1.33

In the two scenarios in which M does not have a causal relationship with D (“No effect of E on D” and “M is a Passenger Variable”) analyses of etiologic heterogeneity suggest that the effect of E on D differs for subtypes of disease characterized by the presence or absence of M. That is, the results of analyses are consistent with those expected if etiologic heterogeneity by M were present, even though M does not affect risk of D. The largest etiologic heterogeneity effect size across the presented scenarios was observed in the scenario in which E caused M, but E did not cause D. These results seem to be contrary to the underlying premise of analyses of etiologic heterogeneity (5, 6, 8).

Of the presented scenarios, the “M is a Sufficient Cause of D (M+ = D+)” scenario has the closest alignment to prior discussions of the underlying premise for analyses of etiologic heterogeneity (5, 6, 8). Although this scenario has the most direct link between M and D, this is the scenario in which the smallest etiologic heterogeneity effect size was observed (effect size = 1.33). That is, analyses of etiologic heterogeneity did not yield a large effect size in a scenario that most closely mimics the premise for conducting these analyses.

Discussion

We used numerical examples of various causal scenarios to explore the results of etiologic heterogeneity analyses when the variable used to define subtypes of disease is a molecular marker that acts as a mediator or as a non-mediator. Across several mediation scenarios, when M is a causal mediator and is used to subtype the disease outcome, the concept of analyses of etiologic heterogeneity seems to align with a mediation model. That is, the results of an analysis of etiologic heterogeneity are consistent with the idea that M can be used to define subgroups of the disease that vary in their association with E, because, as in a traditional mediation model, E+ causes M+ and M+ causes D+. However, our illustrations show that, across various differing assumptions for the role of that mediator in the exposure–disease relationship, analyses of etiologic heterogeneity can produce very similar results, suggesting that this design cannot reliably distinguish between these causal scenarios. Furthermore, in two scenarios in which the marker has no causal relationship with disease, analyses of etiologic heterogeneity suggest that there are different associations between exposure and disease subtypes defined by the presence or absence of the marker. Overall, we find that analyses of etiologic heterogeneity produce ambiguous results, especially when implemented as a case-only design in which the overall effect of E on D cannot be estimated.

Our findings challenge the interpretation of etiology heterogeneity analyses as distinguishing biological pathways and further challenge this design’s use as a screening tool for identifying subtypes of disease associated with exposures. Specifically, we found that in scenarios in which the exposure causes both the marker and the disease, analyses of etiologic heterogeneity produce a similar pattern of results in polytomous analyses and the similar case-only OR regardless of whether the marker causes the disease. That is, even in circumstances in which the underlying causal model does not conform to Begg’s (and others’) conceptualization of etiologic heterogeneity, analyses can produce results that indicate the presence of etiologic heterogeneity (6, 7). This is concerning because it has been argued that etiologic heterogeneity designs are necessary for identifying subtype-specific risk factors. That is, when a particular risk factor is strongly associated only with a low-prevalence subtype of a given outcome, the overall association between the risk factor and the outcome, when all subtypes are combined, may be close to null (7). It has been argued that, in such a scenario, risk factors for disease may remain undiscovered when etiologic heterogeneity is not tested for (7). However, we observe that in the scenario in which E has no effect on D (i.e., RR = 1), but E causes M, that appreciable apparent etiologic heterogeneity can be observed when disease is subtyped by M. This suggests that when the overall association between a risk factor and disease is null, screening for associations between the risk factor and disease subtypes using analyses of etiologic heterogeneity can produce spurious results. Furthermore, for the scenario “M is a sufficient cause of D (M+ = D+),” in which M had the most direct link to D, the analyses of the numerical example showed the smallest etiologic heterogeneity effect size. This suggests that screening for associations between an exposure and subtypes of tumors based on the magnitude of the etiologic heterogeneity effect size may miss instances in which M has the strongest association with D.

Studies of obesity and postmenopausal breast cancer subtyped by receptor status produce a pattern of results in which (1) obesity is modestly associated with breast cancer overall, (2) obesity is most strongly associated with receptor-positive breast cancer, and (3) ORs and RRs for the association between obesity and receptor-negative breast cancer are close to one (11, 44). A proposed mechanism for the link between obesity and postmenopausal breast cancer is that after menopause, adipose tissue is an important source of sex hormones and these higher sex hormone levels drive hormone receptor–positive tumors to grow (11). However, the pattern of results observed in the literature is compatible with our scenarios that hormone receptor expression in breast tissue is a mediator between obesity and breast cancer, with the possibility of hormone receptor expression being only a partial mediator or that there is an interaction between obesity and receptor expression. Thus, our numerical examples suggest that there could be additional biological processes beyond obesity-related increases in sex hormone levels binding to hormone receptors that underlie the apparent etiologic heterogeneity observed with postmenopausal breast cancer risk.

More broadly, our results fit into a larger scholarly discussion of appropriate analytic approaches to identify mediation. When a molecular marker used to subtype cases reflects an event on a multistep biological pathway to a final diagnosed disease state, an analysis of mediation is an appropriate analytic framework. Because these markers are often available only in samples taken from individuals with the disease, data on the marker are typically missing from the non-diseased. As such, analyses of etiologic heterogeneity can be understood to be a pragmatic alternative to conventional mediation analyses, using available data to provide information about the underlying disease process. For rare tumors for which the precursor lesion that might express the molecular marker is also rare, the distinction between analyses of etiologic heterogeneity and mediation analyses is likely to be modest. However, for tumors of the breast, colon, and prostate, for which the precursor lesions are more prevalent, it is likely that in any cohort, a portion of the non-diseased will be harboring a precursor lesion expressing the tumor marker being used to subtype tumors in the cases. In these examples, the missing data on a marker that is conceptually a mediator can make the interpretation of analyses of etiologic heterogeneity, particularly case-only analyses, fraught.

We highlight that biology plays a role in which analyses are possible: if a molecular marker expressed in tissues undergoing tumorigenesis is shed into circulation and can be measured in blood samples at baseline in a cohort or in cases and controls, and in tumor tissue from the cases, full mediation analyses may be possible (45, 46). Furthermore, with such data, Begg’s concept of analyses of etiologic heterogeneity could be combined with mediation analyses in a single study and would likely allow for improved interpretation of analytic results to support or refute hypotheses about disease pathways.

The work presented here is limited in that we simulated only a single-model cohort system based on data for breast cancer in which the prevalence of exposure is not varied. However, the spreadsheets provided with this article (Supplementary Table S1 Content) are designed to allow a user to alter the assumptions and generate additional scenarios and analyses. As we experienced in generating these numerical examples, there are many possible combinations of RR that can be created, even when applying the constraints used here. Although as the casual model scenarios become more complex, the possible combinations are reduced. We tried to limit the number of possible numerical examples that could possibly be generated by focusing on published marker prevalences and overall effect sizes and building each successive mediator scenario on the prior scenario. The scenarios presented here use a single marker to subgroup disease, but more recent work has considered using panels of markers to subset tumors (47, 48). We hypothesize that the greater complexity of using multiple tumor markers, especially if several of them are mediators, will not alleviate difficulties of distinguishing between causal models using analyses of etiologic heterogeneity. However, further work is required to test our hypothesis. We show here in single-marker examples, the simplest case that analyses of etiologic heterogeneity do not strongly distinguish between very different underlying casual scenarios. Furthermore, although we contextualized this work in the field of molecular epidemiology, analyses of etiologic heterogeneity are used in other fields, with injury epidemiology frequently using case-only analyses of etiologic heterogeneity (49). Whether or not the variables used to subtype cases series in other fields is conceptually a mediator between E and D deserves further consideration.

In conclusion, we argue that analyses of etiologic heterogeneity with biomarker-defined case subgroups produce ambiguous results when the marker represents an intermediate step (mediator) on a causal pathway. This ambiguity is increased because the scenario in which exposure does not cause disease and the scenario in which the marker does not influence disease risk also produce analytic results consistent with those expected under etiologic heterogeneity. Researchers might prefer alternate analytic approaches, including conventional mediation analyses that require gathering data on the mediator among the non-diseased as well, as these analyses may provide less biased estimates about the proportion of cases arising through the hypothesized mediating pathways.

Supplementary Material

Supplementary Table 1

Excel spreadsheet showing the implementation of each the numerical examples in the paper.

Data Availability

The data for the seven numerical examples are available online as Supplementary Table S1, an Excel spreadsheet that also enables a user to create additional numerical examples.

Authors’ Disclosures

No disclosures were reported.

Authors’ Contributions

S.J. Mooney: Conceptualization, validation, writing–review and editing. A.G. Rundle: Conceptualization, resources, data curation, formal analysis, investigation, methodology, writing–original draft.