The effect of measurement error on the dose-response curve

Environ Health Perspect. 1990 Jul;87:173-8. doi: 10.1289/ehp.9087173.


In epidemiological studies for an environmental risk assessment, doses are often observed with errors. However, they have received little attention in data analysis. This paper studies the effect of measurement errors on the observed dose-response curve. Under the assumptions of the monotone likelihood ratio on errors and a monotone increasing dose-response curve, it is verified that the slope of the observed dose-response curve is likely to be gentler than the true one. The observed variance of responses are not so homogeneous as to be expected under models without errors. The estimation of parameters in a hockey-stick type dose-response curve with a threshold is considered on line of the maximum likelihood method for a functional relationship model. Numerical examples adaptable to the data in a 1986 study of the effect of air pollution that was conducted in Japan are also presented. The proposed model is proved to be suitable to the data in the example cited in this paper.

MeSH terms

  • Air Pollutants / adverse effects
  • Air Pollutants / analysis
  • Bias*
  • Cough / chemically induced
  • Cough / epidemiology
  • Cross-Sectional Studies
  • Dose-Response Relationship, Drug*
  • Dose-Response Relationship, Radiation*
  • Humans
  • Japan / epidemiology
  • Likelihood Functions
  • Male
  • Nitrogen Dioxide / adverse effects
  • Nitrogen Dioxide / analysis


  • Air Pollutants
  • Nitrogen Dioxide