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The hypothesis that exposure to magnetic fields (MFs) may increase the risk of breast cancer via interaction with melatonin levels was proposed more than a decade ago. 1 Several animal studies and experiments on human volunteers suggested that MF exposure reduces the pineal gland’s nocturnal production of the hormone melatonin. 2,3 In humans, melatonin concentrations follow a diurnal cycle, with the highest concentrations at night. These nightly increases in melatonin suppress estrogen concentrations. Although the results are not entirely consistent across studies, it appears biologically plausible that MF exposure may increase susceptibility to breast cancer by decreasing melatonin levels and increasing a women’s total exposure to estrogen.
Few epidemiologic studies have investigated this hypothesis. 4–8 The results of these studies are inconsistent, but several studies suggested that occupational exposure to higher levels of MFs (often determined by job titles) increased the rate of breast cancer. Although they were based on small numbers, studies by Coogan et al6 and Feychting et al7 suggested the risk may be higher in premenopausal women.
As part of a feasibility study to develop protocols for a case-control study of occupational MF exposures and female breast cancer, we needed to evaluate confounder data collection requirements. Evaluation of the potential association between MF exposure and breast cancer is particularly complex because of the variety and number of factors that may act as potential confounders, including presence of specific genes, family history of breast cancer, reproductive history (for example, age at menarche, parity, menopausal status), and alcohol consumption. Narrowing down this list of potential confounders to select those that may plausibly affect the study results has important design and cost implications.
The generally accepted rule regarding the properties required for a factor to explain completely an observed exposure-disease association states that the relative prevalence of a confounder C among persons exposed to factor X compared with the unexposed must be greater than the apparent relative risk associated with X. 9
In his recent work, Langholz 10 applied this approach to examine potential confounding in studies evaluating the association between power line configuration and childhood leukemia. Langholz concluded that many of the factors proposed as potential confounders are unlikely to explain the observed relative risk estimates. In this study, we expand Langholz’s method 10 to determine which breast cancer factors are capable of producing a substantial confounded odds ratio in a planned case-control study. This information will be used to optimize study design and data collection. These methods can be applied in the planning stage of epidemiologic studies that focus on environmental factors and cancer, when the specific cancer may have numerous reported risk factors.
Subjects and Methods
Breslow and Day 11 mathematically describe the effect of a confounder. Suppose the exposure of interest is measured by a dichotomous factor X and a causal confounder is measured by a dichotomous factor C. Then assuming a multiplicative model for the joint exposure-confounder association with disease,
Langholz 10 describes a situation in which factor C explains all of the apparent risk associated with factor X, which is to say ψx = 1. Then the equation describing the apparent risk reduces to:
A series of algebraic transformations allows us to calculate P1:
In this case, P1 represents the prevalence of the confounder among the exposed group required to explain the observed “confounded” relative risk estimate for exposure, and P0 is the prevalence of the confounder among the unexposed group. Because the prevalence of high exposure to MFs is low, one may approximate P0 from general population data. Then an estimate of P1 in the exposed study group is all that is needed to evaluate the possibility that all of the apparent risk associated with X is attributable to confounding.
It is possible to expand the equation to describe the impact of two or more factors. Consider a factor under study denoted as “X,” and two dichotomous confounders marked “A” and “B,” in which the two confounders are independent and act multiplicatively. In this case,
One could generalize this equation even further. Let i = 1 −K be a set of K dichotomous independent factors that act multiplicatively. Then,
P1i and P0i are the prevalences of factor i among study subjects exposed and unexposed to factor X, and ψi is the relative risk of disease associated with factor i alone.
We compiled a list of risk factors for female breast cancer using the 1993 and 1996 comprehensive reviews by Kelsey 12 and Kelsey and Bernstein, 13 supplemented with additional MEDLINE searches and secondary references. Data were extracted on each risk factor to describe the strength of association with breast cancer (ψc) and prevalence in the general population (P0). We assumed that each confounding factor was dichotomous and, by itself, could explain completely an association between MF exposure and breast cancer. When considering several potential confounders, we assumed that all were independent and that their relative risks were multiplicative. It is important to note that assumption of independence is questionable in many real world circumstances and may substantially affect the results under a multiplicative model.
For the purpose of our investigation, we will use the term “MF-exposed” to characterize women exposed to relatively high levels of occupational MFs. In most cases, this exposure is inferred from job titles. 4,6 Treatment of MF exposure as a dichotomous variable sufficiently simplifies the analysis for the purpose of our investigation.
Because risk factors may vary by age and because age is strongly related to disease frequency, we assumed that the MF-exposed and the MF-unexposed groups have the same age distribution. Furthermore, no study can be considered valid without controlling for age.
We used the data to calculate the prevalence of the risk factor in the study population that would explain odds ratios of 0.5, 1.5, and 2.0 (ψ*) between female breast cancer and MF exposure. Any resulting P1 > 100% or <0% was interpreted as evidence that this risk factor alone could not explain ψ*. Any P1 ≥0 % and ≤ 100% was interpreted as evidence that this factor alone was capable of explaining the ψ*. Further evaluation of P1 values (P1 ≥ 0% and ≤ 100%) determined whether P1 was plausible given previous research.
We calculated ψ* for all possible combinations of two confounding factors acting simultaneously, assuming three scenarios: (1) the prevalence of the risk factor in the MF-exposed women was twice that in the unexposed women (P1 =P0 × 2); (2) the prevalence of the risk factor in the MF-exposed women was four times higher than the prevalence in the unexposed women (P1 =P0 × 4); and (3) the prevalence of the risk factor in the MF-exposed women was half that in the unexposed women (P1 =P0 × 0.5). The calculations for two confounding factors were performed using the formula:
Those confounders capable of explaining an odds ratio of 1.5 (that is, 0% ≤P1 ≤ 100%) were included in further analyses of ψ* for three, four, and five confounding factors using the general formula:
The calculations for multiple factors were performed using the same P1/ P0 ratios as the two-factor calculations.
The relative strengths of breast cancer risk factors were grouped into categories of high relative risk (ψc > 4), moderate relative risk (ψc = 2–4), and low relative risk (ψc = 1–2) (Table 1). From this list, we selected 12 risk factors for inclusion in our analyses primarily on the basis of their strength of association (Table 2). With the exception of age, the strongest predictors of female breast cancer were continent of birth, family history of breast cancer in a first-degree relative, densities on the mammogram (types P2 and DY according to Wolfe’s classification 14), benign proliferative breast disease (BPBD), history of cancer in one breast, and consumption of at least two alcoholic drinks per day. The association of breast cancer with other factors, such as age at menopause and menarche, age at first full-term birth, second-degree relatives with breast cancer, and consumption of small amounts of alcohol, appeared less important.
We first present the results of the analyses for each factor separately, followed by the analyses for all two-factor combinations, and selected combinations of three, four, or more factors. Before showing the results of our analyses, we briefly summarize the literature, which served as a basis for our assumptions regarding the prevalence of each factor in the general population (P0) and the relative risk of breast cancer associated with each factor (ψc). Table 3 summarizes the results for each potential risk factor as the prevalence in the MF-exposed group (P1) needed to explain completely hypothetical confounded odds ratios of 0.5, 1.5, and 2.0.
Place of Birth
According to Broeders and Verbeek, 15 the risk of breast cancer among women born in North America and Europe is approximately five times higher than that among women born in Asia and Africa. Women born in Latin America have an intermediate risk. In 1997, approximately 8 million women 18–64 years of age who were born outside of Europe and North America were U.S. residents. 16 The total number of working-age women residing in the United States in March 1997 17 was estimated at 82.8 million. Given that the relative risk estimate for breast cancer associated with birth in North America/Europe (ψc) is 5.0, and that women born on these two continents make up approximately 90% of the working female population (P0), no prevalence among the exposed could possibly account for ψ* = 1.5. A lower proportion of women born in North America/Europe in the MF-exposed group relative to the unexposed might explain an apparent decreased risk of breast cancer. For instance, a prevalence of 33% among the exposed would explain a ψ* of 0.5. This prevalence might not be unreasonable in, for example, a potential study of garment workers, which could include a high percentage of Latin American or Asian women.
There was substantial discrepancy in the estimates of the risk associated with having both a mother and a sister diagnosed with breast cancer. According to the meta-analysis by Pharoah et al, 18 the relative risk is 3.6, whereas Sattin et al19 reported a relative risk of 14. Because general population data are not available on the proportion of women with breast cancer in two first-degree relatives, we used the control data from Sattin et al. 19 The authors ascertained nearly 5,000 controls from the general population by Waksberg’s method of random-digit dialing and reported that 0.063% of these women had breast cancer in two first-degree relatives. Our analyses found that for ψc = 14, the MF-exposed group would need to have at least 4% and 8% of women reporting breast cancer in both mothers and sisters to account completely for relative risk of 1.5 and 2.0, respectively. A far more conservative ψc estimate of 3.6 would require a prevalence of 19% among the MF-exposed group to explain an odds ratio of 1.5 and nearly 39% for a ψ* of 2.0. Given a population prevalence of familial breast cancer of less than 1%, the large prevalences in MF-exposed women that would be required to explain even moderate associations between MF exposure and breast cancer seem very unlikely.
In comparison with women with both mother and sister affected by breast cancer, those with only one first-degree relative have a lower but still substantial elevated risk of breast cancer. There appears to be a consensus that the relative risk associated with breast cancer in first-degree relatives is a little more than 2. 16,17 A recent study by Sellers et al20 examined the prevalence of family history of breast cancer among the 27,578 participants of the Iowa Women’s Health Study. The study reported that 14% of women had at least one first-degree relative affected by the disease. Although the Sellers et al20 study is limited to white postmenopausal women, its findings are generally in agreement with the 12% estimate reported by Parker et al, 21 which was based on a general population survey of women under 49 years of age. Assuming a prevalence of 12% among unexposed women, the prevalence of a family history of breast cancer would have to be at least 64% in the MF-exposed group to alone explain odds ratios of 1.5. Again, this is an unlikely value.
Past History of Breast Cancer
According to Chen et al, 22 women with a history of cancer in one breast have up to a sixfold higher risk of developing another primary breast neoplasm than women in the general population. In 1999, the National Cancer Institute estimated that the number of newly diagnosed and preexisting breast cancer cases among U.S. women was 2,043,610, including 1,198,939 cases among women 65 years of age or older. 23 No cases occurred among women less than 20 years of age. According to the U.S. Census Bureau, in 1999 there were approximately 85 million working-age women in the United States. Therefore, overall prevalence of breast cancer among working-age women in 1999 was approximately 1%. Assuming that the prevalence of a history of cancer in one breast in the general population is 1% and a ψc of 6.0, the prevalence of a history of cancer in one breast in the MF-exposed group would need to be 12% and 22% to explain ψ* of 1.5 and 2.0, respectively.
Exposure to Endogenous Estrogens
Several studies report that women who had a shorter period of exposure to endogenous estrogens appear to have a lower risk of developing breast cancer than women whose exposure to estrogens was relatively long. For example, women with the onset of menopause after they were 50 years of age have roughly a twofold increase in the risk of breast cancer over that of women whose menopause occurred when they were younger than 45 years of age. 24 According to Cooper and Sandler, 25 58% of U.S. women experience onset of menopause after 50 years of age. Our calculations show that, assuming a relative risk (ψc) of 2.0 for “late” age of menopause onset and the general population prevalence of 58%, the differences in the age at menopause will not be able to account for ψ* of 1.5 or 2.0. The analysis for the early age at menarche (ψ = 1.3) 26 and late age at first full-term birth (ψ = 1.7) 27 showed similar results.
Density on Mammogram
Case-control studies by Carlile et al27 and Byrne et al28 reported that U.S. women whose mammography showed parenchymal patterns classified as P2 and DY had a twofold increase in risk of breast cancer compared with women possessing parenchymal patterns of P1 and N1. A more recent study by Atkinson et al29 reported that British women with the P2 and DY patterns had a 3.6-fold increase in risk. Carlile et al27 and Byrne et al28 estimated the prevalence of P2 and DY patterns in the general population on the basis of random controls drawn from 40,000 and 280,000 participants, respectively, in the Breast Cancer Detection Demonstration Project. The prevalence of P2 and DY patterns was 53% in the Carlile et al27 study and 54% in the Byrne et al28 study. The 188 controls for the Atkinson et al29 study were selected from cancer-free women who participated in the Medical Research Council tamoxifen screening trial; 42% of women showed P2 and DY patterns. If we assume the most extreme relative risk of 3.6 as reported by Atkinson et al29 and the general population prevalence of 54% as reported by Byrne et al, 28 then parenchymal density will not be able to account for ψ* of 1.5 or 2.0. It might, however, explain a ψ* of 0.5 if the prevalence of P2 and DY in the MF-exposed group was as low as 7.8%.
Benign Proliferative Breast Disease
A review by Vogel 30 reports that the prevalence of BPBD in the general population is approximately 2.3%. The breast cancer risk associated with BPBD depends on histologic type. According to Kelsey and Bernstein, 13 the highest risks (up to 5.0) are found for BPBD with atypical hyperplasia, whereas BPBD without atypia is associated with a twofold increase in risk. Assuming that the relative risk of all BPBD is 5.0, the prevalence of BPBD would need to be 16% and 30% among MF-exposed women to account for the ψ* of 1.5 and 2.0.
The World Health Organization has defined obesity as a body mass index (BMI) of >30 kg/m2 for women. 31 According to Williamson, 32 up to 37% of all postmenopausal women are overweight (BMI of >27.3), and 14% are severely overweight (BMI of >32.3). Obesity is associated with a twofold increase in risk of breast cancer for postmenopausal women. 33,34 Among premenopausal women, increased BMI has a small protective effect or no effect. Assuming that the prevalence of obesity in all unexposed postmenopausal women is 30% and ψc is 2.0, almost all women in the MF-exposed group (P1 = 95%) would have to be obese to account for a ψ* of 1.5.
According to Longnecker et al, 35 women who consume at least two drinks per day have roughly a 1.5- to 2.0-fold increase in risk of developing breast cancer. A 1992 National Longitudinal Alcohol Epidemiologic Survey reported that the prevalence of current drinkers among women is 33.7%. Among current drinkers, 9.9% consumed two or more drinks per day. 36 We estimated a population prevalence of drinking two or more alcoholic beverages per day as approximately 3%. Assuming the general population prevalence of 3% and a ψc of 2.0, the prevalence of having two or more drinks per day among MF-exposed women would have to be 55% to explain an odds ratio of 1.5. Similar analysis for the ψ* of 2.0 yielded an impossible prevalence in MF-exposed of 106%.
Summary of Univariate Analyses
In summary, of the 12 factors we examined in univariate analyses, only national origin and alcohol consumption appeared capable of explaining an association between MF exposure and breast cancer. Alcohol consumption among the MF-exposed group, however, would have to be an extreme departure (almost 20-fold) from general population estimates.
Table 4 shows the anticipated ψ* values for all possible combinations of two factors. For example, a twofold difference in the prevalence of obesity (P1 = 2 × 30%) and history of cancer in one breast (P1 = 2 × 1%) among the MF-exposed compared with the unexposed group could result in a confounded odds ratio of 1.26. If the MF-exposed group included 4% of women with a history of cancer in one breast (P1 = 4 ×P0), and all of the MF-exposed women are obese (P1 = 100%), this situation could result in a confounded odds ratio of 1.63. Similarly, a twofold increase in obesity and consumption of at least two alcoholic beverages per day could produce a confounded odds ratio of 1.25. A fourfold increase could result in an odds ratio of 1.59. If all MF-exposed women were born outside of North America and Europe, the effect of a fourfold increase in alcohol consumption could be offset, resulting in a ψ* of 1.11.
The results of the analyses taking into consideration several factors simultaneously show that a twofold increase in prevalence (P1 = 2 ×P0) of (1) history of breast cancer in a first-degree relative, (2) BPBD, and (3) obesity could result in a confounded odds ratio of 1.34 (Table 5). A fourfold increase in prevalence of these factors could result in a ψ* value of 1.90. A twofold and a fourfold increase in prevalence of history of cancer in one breast, obesity, and consumption of two or more drinks per day could result in confounded odds ratios of 1.28 and 1.68, respectively. Similar analyses for four-factor combinations generated comparable results.
A twofold increase in prevalence of five factors—(1) history of breast cancer in a first-degree relative, (2) history of cancer in one breast, (3) BPBD, (4) obesity, and (5) consumption of two or more drinks per day—could result in a confounded odds ratio of 1.38. If all five factors demonstrated a fourfold difference between MF-exposed and unexposed women, the confounded odds ratio could reach 2.00.
The Cornfield rule 9 states that a confounder C may explain an exposure-disease association with factor X only if the relative prevalence of C among persons exposed to X compared with the unexposed is greater than the apparent relative risk associated with C. We applied this rule to determine which, if any, known breast cancer risk factors could explain various hypothetical associations between occupational MF exposure and female breast cancer. Our results suggest that factors associated with a high risk of breast cancer, such as history of two affected first-degree relatives, are rare, and therefore require unrealistically high prevalence in the exposed population to account for an observed association between MF exposure and breast cancer. Relatively common factors (for example, obesity) have a weaker association with breast cancer and appear unable to explain a substantial increase in risk by themselves.
Although some factors may appear to be numerically capable of confounding, realistically we would not expect any one of them to cause much distortion of study results by itself. For example, to explain completely a confounded odds ratio of 1.5, 12% of the MF-exposed women would have to have a history of cancer in one breast, an unrealistic tenfold increase in prevalence compared with the general population.
These methods allowed us to estimate the degree to which uncontrolled breast cancer risk factors could distort an observed relative risk, subject to our simplifying assumptions. Before collecting data on these potential confounders, other information about the intended study group should be reviewed to determine whether there are characteristics of the study population that would suggest a higher or lower prevalence of the confounder in the exposed group compared with the general population. For example, behaviors common in a particular group (for example, delayed childbearing) could lead to the decision to collect the relevant data. For the occupational study under consideration, data should at least be collected on place of birth, past history of cancer, obesity, and alcohol consumption, as these factors may be associated with occupation. By contrast, BPBD, density on mammograms, and family history are probably unrelated to occupation and are therefore unlikely to produce a confounded odds ratio.
All of the analyses were based on the assumption that the apparent risk associated with MF exposure was due entirely to the presence of confounding, which is to say that ψx equals 1. The discussion can be extended to the situation in which ψx is not 1. By analogy, the prevalence of a confounder that could explain all of an apparent risk of 1.5 in the MF-exposed study group is the same as the prevalence required to increase the apparent risk by 50% (for example, from 1.5 to 2.25). Similarly, the percentage increases in apparent risk due to multiple confounders can be determined from Tables 4 and 5.
For simplicity, we assumed that all risk factors are dichotomous. If the assumption of dichotomy is unacceptable, however, an alternative analysis could rely on a multinomial or continuous distribution. If the risk of a factor can be described by a linear model or by a stratified distribution and the prevalence of each stratum in the general population is known, then it can be determined what hypothetical shift in the distribution of prevalence within the exposed group would produce a spurious apparent risk.
Our approach considers the potential impact of uncontrolled confounders on the relative risk of exposure to MFs. Although beyond the scope of this study, another important issue is misclassification of confounders. A considerable body of literature shows that nondifferential misclassification of potential confounders may produce an effect comparable with that of uncontrolled confounding. Greenland and Robins 37 provided a series of examples when the presence of confounder C is detected with variable sensitivity and specificity. Proceeding along the same lines, Ahlbom and Steineck 38 showed that a serious misclassification of confounders (for example, sensitivity = 0.5 and specificity = 0.75) may result in a distortion of both ψc and ψ*. Although misclassification of “established” confounders is an important study design issue, it was not the emphasis of this analysis. Rather, our objective was to determine whether a factor is a potentially important confounder, thus requiring data collection and analytical control.
We conclude that uncontrolled confounders, either alone or in combination, are unlikely to produce a spurious odds ratio of more than 1.5 between MF exposure and breast cancer. Uncontrolled confounders, however, could account for a relative risk in the 1.2–1.3 range. Conversely, a spurious negative association between MF exposure and breast cancer could occur if the study group included a large number of immigrants from Asia and Africa.
Although the goal of this study was to evaluate the potential impact of confounding on the association between MF and breast cancer, we propose using this approach for evaluation of numerous exposure-disease associations in which the disease is known to have many potential risk factors. The approach can be applied both in the planning stage of an epidemiologic study and in the evaluation of existing literature.
We thank Sander Greenland for his review and comment of an earlier draft of this work.
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