Affiliations of authors: Cancer Epidemiology Program, Dana-Farber/Harvard Cancer Center, and Channing Laboratory, Brigham and Women's Hospital, and Harvard Medical School, Boston, MA.
Correspondence to: Graham Colditz, MD, DrPH, Channing Laboratory, Brigham and Women's Hospital and Harvard Medical School, 181 Longwood Ave., 3rd Fl., Boston, MA 021155899 (e-mail: graham.colditz{at}channing.harvard.edu)
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ABSTRACT |
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INTRODUCTION |
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Biomathematical models that relate epidemiologic risk factors to cancer incidence can provide a context in which to study the process of carcinogenesis. These types of models can also summarize the impact of multiple variables and can provide a means to identify areas of research that require more study (23). In more recent clinical applications (24,25) of these models, patients at high risk for breast cancer have been identified so that they can be recruited to prevention trials. The classical models of carcinogenesis proposed by Armitage and Doll (26) and by Moolgavkar and Knudson (27) are the most well known. In addition, Pike et al. (2) reviewed the epidemiologic evidence for breast cancer in the early 1980s and proposed a model of tissue aging to account for the relationship between reproductive risk factors and breast cancer incidence. The work of Rosner et al. (4,5), and similar work by Moolgavkar et al. (1,27) and Pathak et al. (3,28), extended the analytic approach proposed by Pike et al. (2) by relating the timing of reproductive events, which are established risk factors for breast cancer, to the incidence of disease.
In the original Pike model of breast cancer incidence (2), breast tissue age increased at a constant rate c from menarche through first birth. At the time of first birth, there was an immediate increase in breast tissue age (of magnitude k1) and a corresponding decrease in the rate of breast tissue aging (after first birth) to a rate of c - d1. Breast tissue age then increased at the same rate from first birth through age 40 years, after which time the rate of increase in breast tissue aging diminished linearly until, at menopause, the rate of increase in breast tissue age was d3 units lower than the rate at age 40 years.
Early versions of the Pike model did not accommodate terms for the spacing of pregnancies, for premenopausal women (who, by definition, have no age at menopause), or for pregnancies after age 40 years. Such problems led Rosner and Colditz (5) to consider an alternative class of models (i.e., log-incidence models) in which the natural log of breast cancer incidence is a linear function of time [as compared with the Pike models (2), in which log breast cancer incidence is a linear function of log time or log breast tissue age].
Results from fitting this modified Pike model to breast cancer incidence in the Nurses' Health Study cohort have been reported by Rosner and Colditz (5). Briefly, among nulliparous women, breast cancer incidence was found to increase 8.5% per year before menopause and 5.1% per year after menopause. Depending on the relative magnitude of age at first birth minus age at menarche versus the birth index (defined as the sum of [minimum (age, age at menopause) minus age at ith birth]) over all births, parous women may be at either an increased or a decreased risk of breast cancer compared with nulliparous women. The net effect of pregnancy is a short-term increase in breast cancer incidence followed by a subsequent long-term decrease in breast cancer incidence. The magnitude of such changes in incidence for parous women is primarily a function of age at first birth and, to a lesser extent, age at each subsequent birth. Specifically, before menopause, the incidence of breast cancer increases 1.7% for each 1-year increase in age at first birth and 0.4% for each 1-year increase in age at each subsequent birth. This modified model was then further extended to include additional terms for benign breast disease, body mass index (BMI), height, alcohol use, and use of postmenopausal hormones (6).
In this article, we build on our previous work in the modeling of breast cancer incidence to evaluate risk factors for ER+/- and PR+/- tumors using breast cancer modeling approaches that account for the timing of exposure to lifestyle factors. We extend follow-up in the Nurses' Health Study cohort through June 1, 2000, and evaluate established breast cancer risk factors (e.g., age at menarche, parity, age at each birth, age at menopause and type of menopause, use of postmenopausal hormones, alcohol use, history of benign breast disease, and family history of breast cancer) and their association with incident cases of breast cancer according to ER and PR status.
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PARTICIPANTS AND METHODS |
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The Nurses' Health Study cohort was established in 1976, when 121 701 female, U.S. registered nurses between the ages of 30 and 55 years responded to a mailed questionnaire that inquired about risk factors for cancer and heart disease, with a specific focus on reproductive history, menopausal status, contraceptive practices, hormone use, cigarette smoking, and use of permanent hair dyes. The details of the establishment of this cohort have been previously reported (29). Briefly, in 1976, women reported their age at first full-term pregnancy and the number of pregnancies lasting 6 months or more. In 1978 this information was updated, and the women were asked to record the ages of their living children. Every 2 years thereafter, follow-up questionnaires have been mailed to the women to bring the information about risk factors up to date and to ascertain whether major medical events have occurred. Reproductive history has been updated through 1984, and other breast cancer risk factors have been updated through 1998. Deaths in the cohort have been reported by family members or identified through the postal service or by a search of the National Death Index. It is estimated that mortality ascertainment in this cohort of women is 98% complete (30,31). This study was approved by the Brigham and Women's Hospital institutional review board for the protection of human subjects.
Identification of Breast Cancer Cases
On each questionnaire, the woman was asked whether breast cancer had been diagnosed and, if so, the date of diagnosis. All women who reported having breast cancer (or the next of kin for decedents) were contacted for permission to review their relevant medical records to confirm the diagnosis. Pathology reports were also reviewed to obtain information on ER and PR status. Cases of invasive breast cancer for which we had a pathology report were included in this analysis. Receptor status was determined by either biochemical or immunoperoxidase assay, with the immunoperoxidase assay more commonly used than the biochemical assay on the more recent breast cancer cases. We excluded 750 breast cancer cases from the analysis because of missing ER and/or PR status. We also excluded cases of in situ tumors from the analysis. A total of 2096 incident cases of breast cancer1281 ER+/PR+ tumors, 417 ER-/PR- tumors, 318 ER+/PR- tumors, and 80 ER-/PR+ tumorswere identified among women for whom complete information on breast cancer risk factors was available.
Population for Analysis
The endpoint for the analysis was incident invasive breast cancer with reported ER and PR status. We excluded from the analysis all women (n = 2270) who reported breast or other cancer (excluding nonmelanoma skin cancer) on the 1976 questionnaire. This left a total of 119 431 women eligible for follow-up. A total of 105 450 women returned the 1978 questionnaire in which age at each pregnancy was first ascertained. A total of 4204 women were excluded from this cohort because their number of pregnancies reported in 1976 differed by two or more children from the estimated number of pregnancies in 1976 based on reported ages of children in 1978. We also excluded 6993 women whose number of living children, as derived from the reported ages of their children, differed from their parity in 1978 and 2756 women whose number of children in 1978 was less than their reported number of children in 1976. In addition, we excluded 765 women whose age at first birth (estimated from the reported ages of children in 1978) was greater than 3 years plus the age at first birth reported in 1976. Another 763 women whose age at menarche was less than or equal to 8 years of age or greater than or equal to 22 years of age were excluded from the analysis. Reasons for further exclusions included having unknown parity (n = 83), having an age at any birth greater than the age at menopause (n = 671), having an unknown age at menopause (n = 23), being male or an invalid participant in 1976 (n = 73), and having no follow-up beyond 1978 (n = 17). These exclusions left a cohort of 89 102 women eligible for follow-up. From this follow-up cohort, we further excluded women who first became eligible in 1994 or beyond (n = 9), women with unknown duration or type of postmenopausal hormone use (n = 3776), women with unknown weight at age 18 years, women with unknown weight or height in 1976 (n = 8871), and women who had a hysterectomy with either one or no ovaries removed (n = 10 301), because these women do not have a precise age at menopause.
After all exclusions, a total of 66 145 women were followed for 1 029 414 person-years from 1980 through 2000, during which time 2846 cases of incident breast cancer occurred (as noted above, 750 women were omitted because of missing information on ER and/or PR status). Analysis began in 1980, because this is the year when weight at age 18 years and alcohol use were first reported. Compared with that of the population of women used in the model analysis, the breast cancer incidence rate ratio for the excluded subpopulation of women was 0.96 (95% confidence interval [CI] = 0.92 to 1.00), reflecting the fact that the women who were excluded from the analysis were mostly multiparous women with inconsistent pregnancy information (i.e., a low-risk population), women who had a hysterectomy (who generally have an earlier but unknown time of menopause; also considered a low-risk population), and women with unknown BMI at age 18 years.
Description of the Log-Incidence Model of Breast Cancer
We fit our log-incidence model of breast cancer to incident cases of invasive breast cancer that were identified during follow-up of the Nurses' Health Study cohort. The approach to model fitting was to assume that incidence at time t(It) is proportional to the number of cell divisions (Ct) accumulated throughout life up to age t, that is, It = kCt.
The cumulative number of breast cell divisions is calculated as follows:
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Thus, i = Ci+1/Ci represents the rate of increase in the number of breast cell divisions from age i to age i + 1. Log (
i) is assumed to be a linear function of risk factors that are relevant at age i. The set of relevant risk factors and their magnitude may vary according to the stage of reproductive life. The details of the representation of Ci are given in (6). The overall model is given by
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where t = age; to = age at menarche; tm = age at menopause; t* = minimum (age, age at menopause); mt = 1 (if postmenopausal at age t, 0 otherwise); st = parity at age t; ti = age at ith birth, i = 1,. . , st; b = birth index =
(t* - ti)bit; (bit = 1 if parity
i at age t, 0 otherwise); mA= 1 (if natural menopause, 0 otherwise); mB = 1 (if bilateral oophorectomy, 0 otherwise); bbd = 1 (if benign breast disease = yes, 0 otherwise); fhx = 1 (if family history of breast cancer in mother or sister = yes, 0 otherwise); pmhA = number of years on oral estrogen; pmhB = number of years on oral estrogen and progestin; pmhC = number of years on other types of postmenopausal hormones; pmhcur,t = 1 (if current user of postmenopausal hormones at age t, 0 otherwise); pmhpast,t = 1 (if past user of postmenopausal hormones at age t, 0 otherwise); BMIj = BMI at age j (kg/m2); alcj = alcohol use (grams) at age j; h = height (inches).
o represents the rate of increase in incidence before menopause among nulliparous women with no benign breast disease and no family history.
1 and
2 represent modifications to the rate of increase in incidence for parous women according to the number and precise spacing of births.
1 and
2 represent rates of increase in incidence after menopause according to type of menopause among women without benign breast disease not currently using postmenopausal hormones.
1,
2, and
3 represent modifications to the rate of increase in incidence after menopause among women currently using postmenopausal hormones according to the duration of the specific types of postmenopausal hormones used.
4 and
5 represent the immediate effect of starting and stopping postmenopausal hormone use on rates of increase in incidence after menopause.
represents the effect of family history of breast cancer on the number of breast cell divisions at birth (i.e., Co).
The terms for BMI, height, and alcohol use in relation to menopause and postmenopausal use of hormones are summarized below:
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3 (
4) represents the effect of BMI (height) either before menopause or after menopause on breast cancer incidence while currently using postmenopausal hormones.
*3 repre-sents the effect of BMI (height) after menopause on breast cancer incidence while not using postmenopausal hormones.
5,
5*, and
5** represent the effects of alcohol before menopause, after menopause while currently using postmenopausal hormones, and after menopause while not using postmenopausal hormones, respectively. The rationale for the separate terms is the finding in exploratory analyses driven by previous literature (32) that 1) the effects of BMI and possibly height and alcohol use on breast cancer incidence are different before and after menopause and 2) the effect of BMI on breast cancer incidence after menopause differs according to whether a woman is or is not currently using postmenopausal hormones (33).
1,
2,
3, and
4 represent modifications, among women with benign breast disease, to 1) the number of breast cell divisions at birth, 2) the rates of increase in the number of cell divisions after birth but before menarche, 3) the rates of increase in the number of cell divisions after menarche but before menopause, and 4) the rates of increase in the number of cell divisions after menopause. The rationale for the extra terms involving benign breast disease (
1, ...,
4) is that the relative risk for benign breast disease varies according to age, is strongest among younger women, and diminishes over time.
The general rationale for a log-incidence model of a specific cancer is that the number of precancerous cells increases multiplicatively with time, but that the risk factor profile from birth through current age differentially affects the rate of increase in incidence. Specifically, in the breast cancer incidence model described above the number of precancerous cells is assumed to increase annually at the rate of exp(0) before menopause for nulliparous women, at the rate of exp(
0 +
1s) before menopause for parous women with parity = s, and so forth. Finally, the number of precancerous cells increases immediately after the first birth by exp[
2(t1 - t0)]. The incidence rate of breast cancer is assumed to be approximately proportional to the number of precancerous cells.
Model Fit and Analyses
The log-incidence model was fit using iteratively reweighted least squares, with PROC NLIN in SAS, version 6.12 (34). The parameters of the model are readily interpretable in a relative risk (RR) context. For example, exp(-0) = RR for a 1-year increase in age at menarche among nulliparous women, exp[-(
0 +
2)] = RR for a 1-year increase in age at menarche among parous women, and so forth.
To evaluate the consistency of risk estimates among the four tumor receptor categories (i.e., ER+/PR+, ER+/PR-, ER-/PR+, and ER-/PR- breast cancers), we ran a model that allowed estimates to vary for all exposure variables using polychotomous logistic regression (35). If 1++ (i.e., the effect of the duration of premenopause on ER+/PR+ tumors),
1+- (i.e., the effect of the duration of premenopause on ER+/PR- tumors),
1-+,
1-- are defined similarly, then we tested the null hypothesis (H0):
1++ =
1+- =
1-+ =
1-- versus H1: the effect of the duration of premenopause is different on at least two tumor receptor types; the effects of all other risk factors are also assumed to be different among the four tumor subtypes under either H0 or H1. A similar test was performed for all other risk factors (i.e., duration of menopause, pregnancy history, benign breast disease, postmenopausal hormone use, BMI, height, and alcohol use).
On the basis of log-likelihood analyses, we calculated a heterogeneity chi-square and P value for each risk factor (Table 1). In performing the heterogeneity analyses, some risk factors were tested as a group (e.g., natural menopause and bilateral oophorectomy) because they are interdependent. To test for differences in risk factor odds ratios based on the marginal ER and PR categories, we evaluated ER status while controlling for PR status and vice versa. Specifically, to test for the effect of ER status on risk factors while controlling for PR status, we calculated dER, which is the weighted average of the effect of ER status among women who are PR+ and PR-, respectively, with weights inversely proportional to the variance: dER = [(1++ -
1-+)w1 + (
1+- -
1--)w2]/(w1 + w2), where w1 = 1/[var(
1++) + var(
1-+)], w2 = 1/[var(
1+-) + var(
1--)], standard error (SE) (dER) = [1/(w1 + w2)]1/2, and the variances (var) were obtained from Table 1. The test statistic (i.e., ZER = dER/SEER) was compared with a standard normal distribution N(0,1) to obtain a P value. A similar approach was used to assess the marginal effect of PR status based on dPR.
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RESULTS |
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BMI after menopause was statistically significantly associated with the incidence of ER+/PR+ tumors but not with the incidence of ER-/PR- tumors (P = .016 for test of heterogeneity for BMI among categories of receptor status; Table 1). There was no statistically significant difference in breast cancer incidence among tumor subtypes for BMI before menopause. BMI after menopause was also statistically significantly associated with the incidence of ER-/PR+ tumors, whereas it was not associated with the incidence of ER+/PR- tumors. The difference in the association of BMI after menopause with breast cancer incidence according to PR status was statistically significant after controlling for ER status (P = .005; Table 2). Alcohol use before menopause had a stronger association with the incidence of ER+/PR+ tumors (P = .001) than with that of ER-/PR- tumors (P = .86) (Table 1), but the difference in the association of alcohol use with incidence was not statistically significant (P = .70; Table 1).
Benign breast disease, family history, and height were each consistently associated with the incidence of ER+/PR+ and ER-/PR- tumors. Additional analyses were performed in which a term for calendar year was added to the model to control for possible secular trends in breast cancer incidence. There was an approximately 7% decrease in breast cancer incidence over 20 years after controlling for risk factors that were included in the model (see Table 1). After adjusting for secular trends, the results for breast cancer incidence according to risk factors were similar to those given in Table 1 (data not shown).
Model Fit
To evaluate the performance of the log-incidence model in predicting breast cancer incidence, we conducted goodness-of-fit and area under the receiver operator characteristic (ROC) curve analysis. We calculated the observed and expected number of ER+/PR+ and ER-/PR- breast cancer cases in 5-year age strata by using deciles of predicted age-specific breast cancer risk. The observed and expected number of cases for specific deciles of age-specific risk were then summed over all age strata and compared with a goodness-of-fit test. For prediction of the number of ER+/PR+ breast cancer cases, the overall chi-square (with 9 df) was 7.87 (P = .55), indicating an adequate fit. The log-incidence model provided a good spread in risk for ER+/PR+, with an observed relative risk, comparing the top decile to the bottom decile, of 7.2 (95% CI = 5.2 to 9.9) and an expected relative risk of 5.6 (95% CI = 4.1 to 7.5). For ER-/PR- breast cancer cases, the overall chi-square (with 9 df) was 2.99 (P = .97), with an observed relative risk, comparing the top decile to the bottom decile, of 3.9 (95% CI = 2.4 to 6.3) and an expected relative risk of 4.2 (95% CI = 2.6 to 6.9).
The predictive ability of our log-incidence model to discriminate between women who would develop ER+/PR+ breast cancer and those who would not was also evaluated using ROC curve analysis. First, we calculated the predicted absolute risk of breast cancer for each woman and stratified the data by 5-year age groups. Within each age group, we then calculated the Mann-Whitney U statistic, which compares the predicted risk of the case patients with the predicted risk of the control subjects (i.e., women who remained free from breast cancer). Thus, we obtained the area under the ROC curve for our predictive model for women in a specific age group; this value can be interpreted as the probability that, within a specific 5-year age group, a random case patient will have a higher predicted risk than a random control subject. We then calculated a weighted average of the age-specific Mann-Whitney U statistics with weights equal to the inverse variance of the age-specific statistics. Overall, the area under the ROC curve adjusted for age was 0.64 (95% CI = 0.63 to 0.66) for ER+/PR+ tumors and 0.61 (95% CI = 0.58 to 0.64) for ER-/PR- tumors, indicating adequate discriminatory accuracy.
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DISCUSSION |
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The distribution of the receptor status of the tumors in this study is comparable to that reported in other studies (14,15,18,22) using cross-classification of both ER and PR status. Furthermore, consistent with other studies (14,15,18,22), information on ER/PR status was available for about 70% of cancer cases. Women diagnosed with breast cancer early in follow-up were less likely than women diagnosed late in follow-up to have their tumor ER/PR status measured and their medical records obtained. Our results, similar to the results of the Surveillance, Epidemiology, and End Results (SEER) Program1, are based on reports from individual institutions without centralized quality control (36); however, the prevalence of ER+/PR+ tumors in this study is consistent with the prevalence of ER+/PR+ tumors in non-Hispanic white women in the SEER database (36).
Our results for breast cancer incidence according to age are consistent with previous literature (7,8). Findings for reproductive variables are somewhat difficult to interpret in previous studies because data on ER and PR status have been presented separately. However, several studies (10,12,18) have shown that, among postmenopausal women, nulliparity is inversely associated with risk for developing ER-/PR- tumors, whereas other studies (12,1416) have shown that parity is inversely associated with ER+ tumors but not with ER- tumors, suggesting that there are differing influences of parity on incidence, according to ER status of tumors. In general, previous studies have had low statistical power to evaluate the relationship between incidence and reproductive variables and have often not cross-classified ER and PR status.
Interestingly, Potter et al. (18), in analyzing the prospective Iowa Women's Health Study, noted that ER+/PR- tumors had a risk profile somewhat different than that of the other three ER/PR categories. In particular, they noted that family history was not associated with risk of ER+/PR- tumors. In our larger study, the association of family history with ER/PR status was consistent across all tumor receptor categories. Furthermore, Potter et al. (18) proposed that breast tumors be classified into three receptor groups; PR+, ER-/PR-, and ER+/PR-. Our results, which had more statistical power than those from the study by Potter et al., do not support the collapsing of the PR+ tumor category across ER status because both ER and PR status were associated independently with different risk factors, as summarized in Table 2.
Similar to the findings of Potter et al. (18), our findings show that epidemiologic risk factors vary by the hormone receptor expression of the breast cancer, supporting the hypothesis that these receptor expression categories represent distinct stable phenotypes in human breast cancer (37) rather than a single disease with a single biologic pathway. Anderson et al. (38) showed that among lymph node-negative women in the SEER database, each of the four ER/PR tumor subtypes was associated with separate age frequency-density plots, again suggesting that breast cancer does not represent a single disease. Treatment of breast cancer has already been divided by hormone receptor status in that hormonal agents are only used in receptor-positive cancers, and the same division of cancer cases according to receptor status should be considered for etiologic investigations.
Qualitatively comparing relative risks for breast cancer without a statistical evaluation, as reported in many of the earlier studies [e.g., (13)], can suggest differences in these risks but can also be problematic. Furthermore, a comparison of statistical significance between outcomes is limited by the dependence of statistical significance levels on the numbers of events for each component of the outcome. For example, small numbers of cancer cases in some of our subgroup analyses limited our ability to evaluate differences in breast cancer risk among categories defined by receptor status. In particular, the small number of ER-/PR+ cancer cases limited our ability to detect associations between this tumor receptor subtype and breast cancer risk.
The results of this study offer a rigorous comparison of risk factors for breast cancer categorized according to ER and PR status and provide flexibility in terms of allowing some risk estimates to be the same and others to be different, based on likelihood ratio methods. The Marshall and Chisholm method (35), which we used to compute the polychotomous logistic regression models, has advantages over other approaches such as PROC CATMOD in SAS (SAS Institute, Cary, NC), which forces all variables to differ in the outcome categories. Moreover, if some variables have similar risks for the polychotomous outcome categories, the estimates for all exposure variables will be less accurate if estimated separately (39). Because of this problem, we believe our estimates for all risk factors are more precise than estimates using PROC CATMOD.
There are also several advantages of the log-incidence model of cancer risk over conventional logistic models. First, the log-incidence model readily allows for the interaction among variables. For example, the model used in this study allowed for the interactions among age, age at first birth, and parity, which have been observed in various epidemiologic studies (3,28). Second, this model allows for a more precise timing of exposures in relation to subsequent risk of breast cancer than other models that do not account for the varying effects of risk factors with age. We note that several variables including BMI have different effects on risk before and after menopause.
We recently fit the breast cancer incidence model, derived using data from 1980 through 1994, to an independent series of cases (diagnosed from 1994 through 1998) from the Nurses' Health Study and observed a goodness of fit that was consistent across age strata and a fourfold increase in the risk of breast cancer comparing the top and bottom deciles of risk. Furthermore, an age-adjusted concordance statistic gave an area under the ROC curve of 0.62. Thus, this incidence model, when fit to an independent case series from the Nurses' Health Study, appears to be robust and to have good predictive value. When fitting the model for ER+/PR+ tumors, the age-adjusted concordance statistic value was higher (0.64) than that observed for the Gail model prediction of total breast cancer incidence (0.58) (24), suggesting a modest improvement in predictive ability for the most common breast cancer tumor subtype with our log-incidence model.
In conclusion, our data indicate that some important risk factors for breast cancer differ according to ER status (e.g., age and postmenopausal hormone use) and PR status (e.g., reproductive history and BMI after menopause). These data support the hypothesis that different patterns of receptor expression correspond to different types of breast tumor. Thus, we suggest that it would be prudent to divide breast cancer cases according to both the ER and PR status of the tumor. This categorization may also be useful in understanding differences in breast cancer risk profiles among ethnic groups (e.g., Caucasian versus African American), where the mix of ER/PR types may differ.
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NOTES |
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Supported by grant CA87969 (to G. A. Colditz) from the National Cancer Institute, National Institutes of Health, Department of Health and Human Services; by a Harvard Breast Cancer Specialized Projects of Oncology Research Excellence (SPORE) grant; and by the U.S. Army Center of Excellence in ER-Negative Breast Cancer. G. A. Colditz is an American Cancer Society Clinical Research Professor.
We thank Frank E. Speizer, Robert Glynn, and Walter C. Willett for critical input to the study. Marion McPhee, Barbara Egan, Gary Chase, and Karen Corsano provided technical assistance during this study.
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Manuscript received April 29, 2003; revised November 21, 2003; accepted December 5, 2003.
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