Affiliations of authors: A. Decarli, Dipartimento di Scienze Biomediche e Biotecnologie, Sezione di Statistica Medica e Biometria, Università degli Studi di Brescia, Italy; M. Mezzetti, Department of Biostatistics, Harvard School of Public Health, Boston, MA, and Dipartimento di Metodi Quantitativi, Università Bocconi, Milan, Italy; C. La Vecchia, Istituto di Biometria e Statistica Medica, Università degli Studi di Milano, and Istituto di Richerche Farmacologiche Mario Negri, Milan, Italy.
Correspondence to: Maura Mezzetti, Ph.D., Department of Biostatistics, Harvard School of Public Health, 655 Huntington Ave., Boston, MA 02115 (e-mail: mezzetti{at}hsph.harvard.edu).
We thank Dr. Eide and co-workers for their interest in PARs and in our study in particular. Estimation of adjusted PARs for combination of several variables is not computationally possible because of the small number of subjects in the various strata. This fact makes it impossible to obtain PARs and, more importantly, to estimate their variances on which confidence intervals are based. The same line of reasoning applies to subgroup analyses, including those restricted to nulliparous women (402 case patients and 383 control subjects). It is clear, in any case, that the combined effect of various factors does not lead to a PAR that is the sum of each single factor, due to the intercorrelations between various factors. In most cases, as shown in Table 3 of our article, the combination of various factors leads to a PAR that is less than the sum of the PARs of each single factor, although, in rare cases, such a combination may lead to a PAR that is greater than the sum (1). To estimate PAR for the combination of several factors, it is possible to obtain odds ratio estimates for each stratum with the use of a multiplicative logistic model in the absence of controls in one or more strata. This model does not allow us, however, to estimate the corresponding variance (2).
Finally, we thank Dr. Eide and colleagues for noting a mistake in the first footnote to our Table 3, which should read: "For ß-carotene, this meant more than 5053.2 µg/day; for vitamin E, more than 11.7 mg/day; for alcohol, nondrinkers; for physical activity, high levels."
REFERENCES
1 Benichou J, Gail MH. Variance calculations and confidence intervals for estimates of the attributable risk based on logistic models. Biometrics 1990;46:9911003.[Medline]
2 Negri E, La Vecchia C, Franceschi S, Decarli A, Bruzzi P. Attributable risks for oesophageal cancer in Northern Italy. Eur J Cancer 1992;28:116771.
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