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J Natl Cancer Inst. 2011 January 19; 103(2): 82–83.
PMCID: PMC3022621

Inference From a Multiplicative Model of Joint Genetic Effects or Ovarian Cancer Risk

Ramus et al. (1) in this issue of the Journal report that a genetic marker at 9p22.2 protects against ovarian cancer in a population of BRCA1 or BRCA2 mutation carriers. The hazard ratios (HRs) in BRCA1 mutation carriers (HR = 0.78) and in BRCA2 mutation carriers (HR = 0.80) (1) are remarkably similar to those from a genome-wide association study in populations with very low frequencies of mutation carriers (HR = 0.82) (2), given random variation, population differences in linkage disequilibrium patterns affecting the attenuation from use of a marker instead of the causal single-nucleotide polymorphism, challenges of achieving unbiased and consistent case ascertainment and control selection (especially for BRCA1 and/or BRCA2 [BRCA1/2] mutation carriers), and disease diagnosis.

The similarity of the three hazard ratios for the 9p22.2 marker suggests that the joint effects of a BRCA1 or BRCA2 mutation and the marker are multiplicative. In a multiplicative model involving two dichotomous risk factors A and B, the relative risk (or relative hazard) of those exposed to A and B is the product of 1) the relative risk of those exposed to A and not B and 2) the relative risk of those exposed to B but not A, all compared with those exposed to neither. The estimated 30- to 50-fold increase in ovarian cancer risk conferred by carrying either a BRCA1 or a BRCA2 mutation (35) implies that the absolute reduction in risk for those with the genetic variant at 9p22.2 is far greater in BRCA1 and BRCA2 mutation carriers than in noncarriers. Consequently, the observed data are inconsistent with an additive model.

The multiplicative model has received a great deal of attention in the literature. It is the primary null hypothesis in power calculations that justify major efforts to study, for example, gene–environment interactions, by screening for departures from the multiplicative joint effects. Can we learn anything from the fact that the joint effects of genetic variation at 9p22.2 and carrying a BRCA1 or BRCA2 mutation are strongly consistent with a multiplicative model?

Interaction is the antithesis of independence. Different meanings of independence, particularly regarding disease mechanism, imply different conceptions of interaction and, therefore, suggest different statistical approaches. Exposure to tobacco may influence the pathway by which human papillomavirus (HPV) infections cause cervical cancer; if so, the effect of HPV exposure depends on smoking, and smoking interacts with infection to cause disease. Response to a therapeutic agent may depend on disease characteristics; for example, the effectiveness of hormone-based therapies like tamoxifen is greater in breast cancer patients whose tumor is estrogen receptor positive. Furthermore, it is difficult to conceptualize interaction, given the challenges in applying statistical tools to complex and dynamic, but poorly understood, biological phenomena. Weinberg (6) showed that “simple independent action,” as used in toxicology, provides a framework for an additive model of joint effects of two factors. In the additive model, the increase in risk (or excess hazard to be more precise and to avoid the need to invoke a rare disease assumption) for those exposed to both A and B is the sum of the respective excess risks of those exposed to either factor, where excess risk is the difference between the risks in the exposed group and in the referent group (ie, those exposed to neither A nor B). Under a model of simple independent action, no mechanism leading to disease requires both A and B. Furthermore, any other set of causes of disease act separately from exposures A and B. This construct implies that the excess risk of a rare disease in those exposed to A will be unaffected by presence or absence of B, and vice versa.

Simple independent action requires that A and B actively contribute to carcinogenesis (or pathogenesis for diseases other than cancer), as do smoking or infection with HPV or Helicobacter pylori. A different concept of independence is needed when exposure A or B inhibits carcinogenesis involving one or more causal agent (6). For example, the rapid acetylation type of the NAT2 enzyme reduces the risk of bladder cancer among individuals who have been exposed to tobacco smoke (7), and HPV vaccine prevents future infection and thereby reduces risk of cervical cancer.

We propose that a useful model of independence for a preventive agent A is that its mechanism is unrelated to the disease pathway. Under the multiplicative model, the relative risk reduction due to A is the same regardless of the carcinogenic pathway or, in particular, the presence of any other factor B. For example, under a multiplicative model, an independently acting chemopreventive agent will lead to a similar percentage reduction in lung cancer risk regardless of whether the underlying causal pathway involves smoking, radon, asbestos, polycyclic aromatic hydrocarbons, air pollution, a genetic variant, DNA methylation, or a combination of various factors. For example, if an agent reduces lung cancer risk by 50%, those who are not exposed to the agent will have double the risk of those exposed to the agent, and this effect would be essentially the same among both smokers and nonsmokers. Alternatively, a preventive intervention, such as tamoxifen chemoprevention therapy, may reduce risk of breast cancer by the same percentage in both African American and white women or in both BRCA1/2 mutation carriers and noncarriers. However, not all preventive agents will be so impartial and conform to this sort of independent action. For example, the rapid acetylation type of NAT2 protein likely protects individuals against bladder cancer but only those who have been exposed to tobacco smoke or another carcinogen that contains aromatic amines, which are detoxified by the NAT2 enzyme (7,8).

Other forms of independence can also yield a multiplicative model of joint effects. Previous studies (9,10) have reported that factors that act separately on different steps of multistep pathogenesis will appear to act multiplicatively.

What can we infer from the data on BRCA1/2, genetic variation at 9p22.2, and ovarian cancer risk? BRCA1 and BRCA2 appear to be involved in the maintenance of genome stability and suppression of tumors. The apparent multiplicative model may indicate that the effectiveness of nonmutated BRCA1/2 proteins is the same regardless of the DNA-damaging exposure. The data indicate that any preventive effect of 9p22.2 variation is the same regardless of other risk factors. We cannot, however, even be sure whether the variation is causal or preventive.

As the authors (1) note, the effect of variation of 9p22.2 on absolute risk is far greater in BRCA1 and BRCA2 mutation carriers than in noncarriers. The combination of multiplicative model of joint effects and high baseline risk in carriers means that even common variants with weak associations of the magnitude seen in genome-wide association studies in unselected populations can have a major effect on risk prediction. By contrast, the impact of 9p22.2 on risk estimation in carriers would be far less if baseline risk were low, or if the additive model holds, so the differences in the risks, rather than ratio of risks, would be the same in BRCA1 or BRCA2 mutation carriers and noncarriers.

This example of risk patterns following the multiplicative model shows both the opportunity and the danger in studying joint effects of two or more factors. The null hypothesis is far more complicated when testing interaction than when testing whether a single factor is causal, which is challenging enough. Nonetheless, the concept of multiplicative interaction is still useful, contrary to discussion in an epidemiology textbook (11). Further consideration of the meaning of the additive and multiplicative models may improve design, analysis, and interpretation of studies of interactions among genetic and environmental factors and their effect on ovarian and other cancers.


Intramural Research Program of the National Institutes of Health (NIH), National Cancer Institute, Division of Cancer Epidemiology and Genetics under project ZIA CP010181 and National Institute of Environmental Health Sciences under project Z01 ES040007.


This article may be the work product of an employee or group of employees of the National Institute of Environmental Health Sciences (NIEHS), NIH; however, the statements, opinions or conclusions contained therein do not necessarily represent the statements, opinions or conclusions of NIEHS, NIH or the United States government.


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