Journal of the National Cancer Institute Advance Access originally published online on April 29, 2008
JNCI Journal of the National Cancer Institute 2008 100(9):684; doi:10.1093/jnci/djn110
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Published by Oxford University Press 2008.
CORRESPONDENCE |
Response:Re: Projecting Individualized Absolute Invasive Breast Cancer Risk in African American Women
Affiliations of authors: Division of Cancer Epidemiology and Genetics, National Cancer Institute, Bethesda, MD (MHG); Beckman Research Institute and Department of Cancer Etiology, City of Hope Comprehensive Cancer Center, Duarte, CA (LB); Department of Biostatistics, Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA (JPC); Information Management Services, Rockville, MD (DP); Department of Preventive Medicine, Keck School of Medicine and Norris Comprehensive Cancer Center, University of Southern California, Los Angeles, CA (GU)
Correspondence to: Mitchell H. Gail, MD, PhD, Division of Cancer Epidemiology and Genetics, National Cancer Institute, Executive Plaza South, Rm 8032, Bethesda, MD 20892-7244 (e-mail: gailm{at}mail.nih.gov).
We wrote (1) that the area under the curve (AUC) is inherently a retrospective quantity because it can be estimated from a random sample of case patients and of control subjects. Arguably better criteria for assessing risk models (2–4), such as positive and negative predictive value, misclassification rate, calibration, and expected loss in a decision problem, cannot be estimated from case patients and control subjects; follow-up data on the probability of disease are needed.
A model that is based solely on age-specific incidence rates can be useful, even though it has an age-specific AUC of 0.5. If a 62-year-old white woman knows, on the basis of her age alone, that her chance of developing breast cancer is 1.7% in the next 5 years, she should carefully consider whether to take tamoxifen to prevent breast cancer, because the tamoxifen-induced increases in the risks of stroke and endometrial cancer exceed the decrease in breast cancer risk, as shown in table 10 of Gail et al. (5).
We stated (1): "A limitation of the CARE model is that it has low age-specific discriminatory accuracy as measured by the concordance or AUC...," where the Women's CARE Study is the Women's Contraceptive and Reproductive Experiences Study. Levine points to the AUC of 0.507 for African American women who are aged 60–64 years. The average age-specific AUC, 0.555 (95% confidence interval [CI] = 0.535 to 0.575), measures the discriminatory ability of the risk factors for women in a given age group. If, as is common in the cardiovascular literature, one also credits age when computing the AUC, the CARE model AUC (1) increases to 0.636 (95% CI = 0.617 to 0.655).
Levine states: "Gail et al. imply a key question in their Discussion: might it be better, overall, to tell all women in the general population they will not get breast cancer in the next 5 years and be wrong only a small percentage of the time?" We certainly did not mean to imply this question. Indeed, we disagree with the idea that one should use an estimated 5-year risk to decide whether a woman will or will not develop breast cancer. Rather, that estimate should provide perspective on the level of risk and allow the woman to compare that risk with other risks that she might face. A formal analysis of losses from misclassification (3) indicates that high discriminatory accuracy is needed to reliably screen the general population to identify women for whom special diagnostic or other measures are indicated. However, well-calibrated models with modest discriminatory accuracy can be useful for deciding whether an intervention, such as tamoxifen, that has offsetting risks and benefits should be used.
Levine asserts that it is possible to "increase entropy" by "attempting to segregate individuals ...into ...high- and low-risk" groups. Suppose r(X) is a well-calibrated (3) risk model for a person with risk factors X. The average risk is 
where F is the distribution of X. The entropy, given X, is 
Because H is concave, Jensen's (6) inequality implies that 
. This result is true for any set of risk factors and joint distribution F. Thus, a well-calibrated model, such as the CARE model, will never increase entropy above that which results from assigning all women the average risk. Likewise, a well-calibrated model that partitions the population into high- and low-risk groups cannot increase entropy, contrary to Levine's assertion.
REFERENCES
1. Gail MH, Costantino JP, Pee D, et al. Projecting individualized absolute invasive breast cancer risk in African American women. J Natl Cancer Inst (2007) 99(23):1782–1792.
2. Cook NR. Use and misuse of the receiver operating characteristic curve in risk prediction. Circulation (2007) 115(7):928–935.
3. Gail MH, Pfeiffer RM. On criteria for evaluating models of absolute risk. Biostatistics (2005) 6(2):227–239.[Abstract]
4. Pepe MS. The Statistical Evaluation of Medical Tests for Classification and Prediction (2003) New York, NY: Oxford University Press.
5. Gail MH, Costantino JP, Bryant J, et al. Weighing the risks and benefits of tamoxifen treatment for preventing breast cancer. J Natl Cancer Inst (1999) 91(21):1829–1846.
6. Jensen JLWV. Sur les fonctions convexes et les inégalités entre les valeurs moyenne. Acta Mathematica (1906) 30(1):175–193.[CrossRef][Web of Science]
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J Natl Cancer Inst 2008 100: 683-684.
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