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Modelling complex mixtures in epidemiologic analysis: additive versus relative measures for differential effectiveness
  1. Ghassan Badri Hamra1,
  2. Richard MacLehose2,
  3. David Richardson3,
  4. Stephen Bertke4,
  5. Robert D Daniels4
  1. 1Section of Environment and Radiation, International Agency for Research on Cancer, Lyon, France
  2. 2Division of Epidemiology and Community Health, University of Minnesota, Minneapolis, Minnesota, USA
  3. 3Department of Epidemiology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA
  4. 4National Institute for Occupational Safety and Health (NIOSH), Division of Surveillance, Hazard Evaluations, and Field Studies (DSHEFS), Industrywide Studies Branch (IWSB), Cincinnati, Ohio, USA
  1. Correspondence to Dr Ghassan Hamra, Section of Environment and Radiation, International Agency for Research on Cancer, 150 Cours Albert Thomas, Lyon 69006, France; hamrag{at}


Objectives Mixed exposures are often combined into single exposure measures using weighting factors. This occurs for many complex mixtures in environmental and occupational epidemiology including multiple congeners, air pollutants and unique forms of ionising radiation, among others.

Methods The weights used for combining exposures are most often determined from experimental animal and cellular research. However, evidence from observational research is necessary to support their use in risk analyses, since results from experimental research do not directly translate to observational epidemiology.

Results Using simulated data, we show that ratio-based relative weights cannot be reliably estimated from observational research. As a solution to this problem, we propose an approach for estimating differences in effectiveness of distinct exposures based on their excess effectiveness compared with a reference exposure.

Conclusions This alternative is easy to calculate and provides reliable estimates of differences in effectiveness of distinct exposures. This is important to regulatory bodies using relative measures for policy decisions, as well as practicing epidemiologists conducting risk analyses.

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