Beverly Rockhill

Use and misuse of population attributable fractions. B Rockhill, B Newman, and C WeinbergCopyRight https://doi.org/10.2105/AJPH.88.1.15 Published Online: October 07, 2011

BACKGROUND: Women and their clinicians are increasingly encouraged to use risk estimates derived from statistical models, primarily that of Gail et al., to aid decision making regarding potential prevention options for breast cancer, including chemoprevention with tamoxifen. METHODS: We evaluated both the goodness of fit of the Gail et al. model 2 that predicts the risk of developing invasive breast cancer specifically and its discriminatory accuracy at the individual level in the Nurses' Health Study. We began with a cohort of 82 109 white women aged 45-71 years in 1992 and applied the model of Gail et al. to these women over a 5-year follow-up period to estimate a 5-year risk of invasive breast cancer. All statistical tests were two-sided. RESULTS: The model fit well in the total sample (ratio of expected [E] to observed [O] numbers of cases = 0.94; 95% confidence interval [CI] = 0.89 to 0.99). Underprediction was slightly greater for younger women (<60 years), but in most age and risk factor strata, E/O ratios were close to 1.0. The model fit equally well (E/O ratio = 0.93; 95% CI = 0.87 to 0.99) in a subset of women reporting recent screening (i.e., within 1 year before the baseline); among women with an estimated 5-year risk of developing invasive breast cancer of 1.67% or greater, the E/O ratio was 1.04 (95% CI = 0.96 to 1.12). The concordance statistic, which indicates discriminatory accuracy, for the Gail et al. model 2 when used to estimate 5-year risk was 0.58 (95% CI = 0.56 to 0.60). Only 3.3% of the 1354 cases of breast cancer observed in the cohort arose among women who fell into age-risk strata expected to have statistically significant net health benefits from prophylactic tamoxifen use. CONCLUSIONS: The Gail et al. model 2 fit well in this sample in terms of predicting numbers of breast cancer cases in specific risk factor strata but had modest discriminatory accuracy at the individual level. This finding has implications for use of the model in clinical counseling of individual women.

BACKGROUND: Increased physical activity has been hypothesized to prevent breast cancer, largely by reducing cumulative lifetime exposure to circulating ovarian hormones. However, epidemiologic findings are inconsistent, and there is no consensus on the best way to quantify physical activity. We thus examined this issue in a large cohort of women, using several different measures of adult physical activity. METHODS: We analyzed data from the Nurses' Health Study, a prospective study of women aged 30 to 55 years in 1976. In 1980 and on subsequent surveys, women were asked about the average number of hours per week spent in various moderate and vigorous recreational physical activity during the past year. We computed a "baseline-only" (1980) measure of hours per week of physical activity, as well as a cumulative average measure that used updated reports on physical activity. During 16 years of follow-up, we identified 3137 cases of invasive breast cancer (1036 premenopausal and 2101 postmenopausal women). Data were analyzed by use of multivariate pooled logistic regression to produce relative risks of breast cancer, and the associated confidence intervals. RESULTS: Women who were more physically active in adulthood had a lower risk of breast cancer than those who were less physically active. Comparing those who reported engaging in moderate or vigorous physical activity for 7 or more hours per week with those who engaged in such physical activity for less than 1 hour per week, the relative risk was 0.82 (95% confidence interval, 0.70-0.97), using the cumulative average updating. The dose-response trend was statistically significant (P = .004). Using the baseline-only measure of physical activity produced slightly weaker relative risks. CONCLUSION: These results contribute to the body of evidence suggesting that higher levels of adult physical activity afford modest protection against breast cancer.

Survival-time studies sometimes do not yield distinct failure times. Several methods have been proposed to handle the resulting ties. The goal of this paper is to compare these methods. Simulations were conducted, in which failure times were generated for a two-sample problem with an exponential hazard, a constant hazard ratio, and no censoring. Failure times were grouped to produce heavy, moderate, and light ties, corresponding to a mean of 10.0, 5.0, and 2.5 failures per interval. Cox proportional hazards models were fit using each of three approximations for handling ties with each interval size for sample sizes of n = 25, 50, 250, and 500 in each group. The Breslow (1974, Biometrics 30, 89-99) approximation tends to underestimate the true beta, while the Kalbfleisch-Prentice (1973, Biometrika 60, 267-279) approximation tends to overestimate beta. As the ties become heavier, the bias of these approximations increases. The Efron (1977, Journal of the American Statistical Association 72, 557-565) approximation performs far better than the other two, particularly with moderate or heavy ties; even with n = 25 in each group, the bias is under 2%, and for sample sizes larger than 50 per group, it is less than 1%. Except for the heaviest ties in the smallest sample, confidence interval coverage for all three estimators fell in the range of 94-96%. However, the tail probabilities were asymmetric with the Breslow and Kalbfleisch-Prentice formulas; using the Efron approximation, they were closer to the nominal 2.5%. Although the Breslow approximation is the default in many standard software packages, the Efron method for handling ties is to be preferred, particularly when the sample size is small either from the outset or due to heavy censoring.

To examine the effects of smoking and N-acetylation genetics on breast cancer risk, we analyzed data from an ongoing, population-based, case-control study of invasive breast cancer in North Carolina. The study population consisted of 498 cases and 473 controls, with approximately equal numbers of African-American and white women, and women under the age of 50 and age 50 years or older. Among premenopausal women, there was no association between current smoking [odds ratio (OR), 0.9; 95% confidence interval (CI), 0.5-1.5] or past smoking (OR, 1.0; 95% CI, 0.6-1.6) and breast cancer risk. Among postmenopausal women, there was also no association with current smoking (OR, 1.2; 95% CI, 0.7-2.0); however, a small increase in risk was observed for past smoking (OR, 1.5; 95% CI, 1.0-2.4). For postmenopausal women who smoked in the past, ORs and 95% CIs were 3.4 (1.4-8.1) for smoking within the past 3 years, 3.0 (1.3-6.7) for smoking 4-9 years ago, and 0.6 (0.3-1.4) for smoking 10-19 years ago. Neither N-acetyltransferase 1 (NAT1) nor N-acetyltransferase 2 (NAT2) genotype alone was associated with increased breast cancer risk. There was little evidence for modification of smoking effects according to genotype, except among postmenopausal women. Among postmenopausal women, ORs for smoking within the past 3 years were greater for women with the NAT1*10 genotype (OR, 9.0; 95% CI, 1.9-41.8) than NAT1-non*10 (OR, 2.5; 95% CI, 0.9-7.2) and greater for NAT2-rapid genotype (OR, 7.4; 95% CI, 1.6-32.6) than NAT2-slow (OR, 2.8; 95% CI, 0.4-8.0). Future studies of NAT genotypes and breast cancer should investigate the effects of environmental tobacco smoke, diet, and other exposures.