Risk scores from logistic regression: unbiased estimates of relative and attributable risk

Abstract

In epidemiology, the risk of disease in terms of a set of covariates is often modelled by logistic regression. The resulting linear predictor can be used to define the extent of risk between extremes, and to calculate an attributable risk for the covariates taken together. As is well known, straightforward use of the linear predictor, on the sample from which it was derived, to obtain estimates the relative and attributable risk will be biased, often seriously. Use of the jack-knife technique is extended to produce asymptotically unbiased estimates of relative and attributable risks. The asymptotic variances associated with these estimates are derived by using the formulae of conditional variances. They are applied to the results of a case-control study of stomach cancer.