Correspondence
Bone Mass and the Risk of Breast Cancer
N Engl J Med 1997; 337:199-200July 17, 1997
- Article
To the Editor:
Zhang et al. (Feb. 27 issue)1 present data confirming the finding of the Study of Osteoporotic Fractures Research Group2 that increased bone mass in postmenopausal women is associated with an increased risk of subsequent breast cancer. However, I am concerned about the accuracy of the multivariate-adjusted rate ratios that Zhang et al. report.
The authors included 10 variables in addition to bone mass in their multivariate model. Since the number of observed events (i.e., cases of breast cancer) was only 91, the ratio of the number of events to the number of variables is less than 10. As a rule of thumb, this ratio should be at least 10 in order to prevent overfitting.3 Models that are overfitted may give results that are numerically unstable and too dependent on the observed data.4 This may be evidenced by overly large coefficients or standard errors. Can the authors allay this concern by indicating the estimated coefficients and standard errors or perhaps by repeating the analysis after omitting some of the less important variables? In addition, perhaps the authors could indicate whether they checked their model for goodness of fit and for conformity to the assumption of proportional hazards.
4 ReferencesCarl D. Atkins, M.D.
242 Merrick Rd., Rockville Centre, NY 115701
Zhang Y ,Kiel DP ,Kreger BE , et al. Bone mass and the risk of breast cancer among postmenopausal women. N Engl J Med 1997;336:611-617
Full Text | Web of Science | Medline2
Cauley JA ,Lucas FL ,Kuller LH ,Vogt MT ,Browner WS ,Cummings SR . Bone mineral density and risk of breast cancer in older women: the study of osteoporotic fractures. JAMA 1996;276:1404-1408
CrossRef | Web of Science | Medline3
Concato J ,Feinstein AR ,Holford TR . The risk of determining risk with multivariable models. Ann Intern Med 1993;118:201-210
Web of Science | Medline4
Model-building strategies for logistic regression. In: Hosmer D, Lemeshow S. Applied logistic regression. New York: Wiley, 1989:82-134.
To the Editor:
Zhang et al. report that the risk of breast cancer among women in the highest quartile of metacarpal bone mass was 3.5 times the risk among those in the lowest quartile. Cumulative exposure to estrogen was believed to play a part. Yet to avoid hip fracture, postmenopausal women are being urged to maximize their bone mass by increasing their calcium intake and by using estrogen replacement.
What are the bone-mass and hormonal characteristics of women in a population at very low risk for breast cancer? Data from Baragwanath Hospital (3400 beds) in Soweto, South Africa (population, 3 to 4 million), indicate that black African women have a very low incidence of the disease1 -- about 7 cases per 100,000 world population. Many years ago, we investigated bone mass in black children and mothers.2 The dimensions of the second metacarpal were used, as in the present study, as well as those of the humerus. The mean values for cortical thickness were 7 to 13 percent lower in black mothers than in local white women in the case of the metacarpal but only 1 to 4 percent lower in the case of the humerus. Thus, in black African women, whose range of bone mass differs little from that of white women, the incidence of breast cancer is low; moreover, despite low calcium intake, the incidence of hip fracture is very low -- a 10th of that in white women.1
2 ReferencesAlexander R.P. Walker, D.Sc.
South African Institute for Medical Research, Johannesburg 2000, South AfricaHester M. Burger, B.Sc.
University of Potchefstroom, Potchefstroom 2520, South Africa1
Solomon L . Bone density in ageing Caucasian and African populations. Lancet 1979;2:1326-1330
CrossRef | Web of Science | Medline2
Walker AR ,Richardson B ,Walker F . The influence of numerous pregnancies and lactations on bone dimensions in South African Bantu and Caucasian mothers. Clin Sci 1972;42:189-196
Web of Science | Medline
To the Editor:
Zhang et al. implicated endogenous estrogen as the likely reason for the increased risk of breast cancer among postmenopausal women in the highest quartile of bone mineral density. However, we believe that longer survival among women with high bone mineral density may also account for the difference.1 Women with high bone mineral density may be at greater risk for breast cancer because they live longer, not because of estrogen. Disparate rates of mortality from all causes would be expected to result in different age distributions over time, with the women with high bone density becoming relatively older. If so, one would expect a higher rate of breast cancer in the group with high bone density. This potential bias might be accounted for by adjustment for age at the time of an event or by censorship in the proportional-hazards model.
1 ReferencesMichael Ballesteros, M.S.
Denis Nash, M.P.H.
Alan Fix, M.D.
Trudy Bush, Ph.D., M.H.S.
University of Maryland at Baltimore, Baltimore, MD 212011
Browner WS ,Seeley DG ,Vogt TM ,Cummings SR . Non-trauma mortality in elderly women with low bone mineral density. Lancet 1991;338:355-358
CrossRef | Web of Science | Medline
To the Editor:
In their discussion, Zhang et al. ignore their finding that women in the highest quartile of metacarpal cortical area were 2.25 times as likely to receive estrogen-replacement therapy for five or more years as women in the lowest quartile (their 2).
It would appear from their data that the main difference between the lowest and highest quartiles is the long-term use of estrogen. What is the incidence of cancer in women in the highest quartile who do not take estrogen? Of the 44 women with breast cancer in the highest quartile, how many had been taking estrogen for a long period?
C. Norman Shealy, M.D., Ph.D.
Shealy Institute, Springfield, MO 65803-4400Author/Editor Response
The authors reply:
To the Editor: Dr. Atkins is concerned that we may have overfitted our predictive model by including too many potentially confounding variables. However, with the exception of age, adjustment for additional potentially confounding variables did not affect the association. There is no good statistical method to test the goodness of fit for the Cox proportional-hazards model. However, when we examined the validity of the proportional-hazards assumption by including a time-dependent explanatory variable in the model, the P value was less than 0.2, suggesting that the proportional-hazards assumption was not violated.
Walker and Burger's comment does not necessarily contradict our findings. The mean age of the women in their study was about 36 to 39 years; therefore, almost all of them were premenopausal.1 The distribution of many other risk factors for breast cancer probably differed between the two racial groups; these risk factors may affect bone mass as well.
We agree with Ballesteros and colleagues that women with higher bone mass may live longer than those with lower bone mass. The mean (±SD) follow-up for the women in the first, second, third, and fourth quartiles of age-specific bone mass was 17.8±7.4, 18.5±6.3, 19.2±6.6, and 18.3±6.8 years, respectively. Thus, women in the lowest age-specific quartile of bone mass survived six months less than women in the highest quartile. This small difference is unlikely to have biased our results. In addition, age-adjusted incidence rates rose by about 1.2 percent per year from 1940 to the early 1980s, and they have recently increased more steeply.2 To include age at the time of an event or use censorship in the proportional-hazards model may create another problem -- that is, a birth-cohort effect. To account for these issues, we applied a ``risk-set'' method3 to a Cox proportional-hazards model to assess the relation of age-specific bone-mass categories to the risk of breast cancer. The results are the same as our previous findings -- that is, the relative risks of bone cancer in the first, second, third, and fourth quartiles of bone mass were 1.0, 1.3, 1.3, and 3.5, respectively.
We think that the results presented in 4 of our article should address Dr. Shealy's concern. Among women who did not receive any postmenopausal estrogen therapy, those in the highest age-specific quartile of bone mass had a risk of breast cancer that was 2.9 times the risk for those in the lowest quartile of bone mass.
3 ReferencesYuqing Zhang, D.Sc., M.B.
Boston University School of Medicine, Boston, MA 02118-2394Douglas P. Kiel, M.D., M.P.H.
Harvard Medical School, Boston, MA 02115David T. Felson, M.D., M.P.H.
Boston University School of Medicine, Boston, MA 02118-23941
Walker AR ,Richardson B ,Walker F . The influence of numerous pregnancies and lactations on bone dimensions in South African Bantu and Caucasian mothers. Clin Sci 1972;42:189-196
Web of Science | Medline2
Kelsey JL ,Horn-Ross PL . Breast cancer: magnitude of the problem and descriptive epidemiology. Epidemiol Rev 1993;15:7-16
Web of Science | Medline3
Breslow NE, Day NE. Statistical methods in cancer research. Vol. 2. The design and analysis of cohort studies. Lyon, France: International Agency for Research on Cancer, 1987:178-229. (IARC scientific publications no. 82.)
