title: Avoiding bias from aggregate measures of exposure.
abstract: BACKGROUND
  Sometimes in descriptive epidemiology or in the evaluation of a health intervention policy change, proportions exposed to a risk factor or to an intervention are used as explanatory variables in log-linear regressions for disease incidence or mortality.
  
  
  OBJECTIVE
  To demonstrate how estimates from such models can be substantially inaccurate as estimates of the effect of the risk factor or intervention at individual level. To show how the individual level effect can be correctly estimated by excess relative risk models.
  
  
  METHODS
  The problem and solution are demonstrated using data on prostate-specific antigen testing and prostate cancer incidence.
authors: Cancer Research UK Centre for Epidemiology, Mathematics and Statistics, Wolfson Institute of Preventive Medicine, Charterhouse Square, London EC1M 6BQ, UK.
authors: Stephen W
authors: SW
authors: Duffy
authors: Håkan
authors: H
authors: Jonsson
authors: Olorunsola F
authors: OF
authors: Agbaje
authors: Nora
authors: N
authors: Pashayan
authors: Rhian
authors: R
authors: Gabe
mesh_terms: D015982:Bias; D006801:Humans; D016015:Logistic Models; D012306:Risk; D018570:Risk Assessment