Estimation with vanishing baseline risk

Our plain-English summary of Estimation with vanishing baseline risk, by R.M. Park (Epidemiology, 2012).

The study

• Author: R.M. Park
• Journal: Epidemiology
• Published: 2012;23(6):937-8
• Type of article: Letter
• Cited by: 1 article, as counted by NIH iCite
• Read it: PubMed · Publisher · Free full text

In plain English

This was a short letter to the editor, by one author at the U.S. National Institute for Occupational Safety and Health, testing a statistical method with computer simulations, not real people. The letter noted that diseases associated with specific exposures, such as mesothelioma from environmental asbestos, may have little or no observable background rate without the exposure, which makes standard relative-rate models unstable. The author simulated hypothetical populations of 500 subjects and compared standard Poisson regression with two fixes: fixing the baseline term (the intercept) at a small value, or adding random background cases. With the standard model, the exposure-response coefficient varied widely across 1,000 populations (mean 13.4, SD 94.5, range 0.1 to 2834). With the fixed intercept, the mean was 5.9 (SD 0.76, range 3.7 to 8.8). The standard model underestimated the excess rate coefficient by 15%, while the fixed-intercept estimate was close to the true value. Bias was larger, 32%, in populations of 50 subjects. The author concluded that the two fixes gave equivalent results and that simply fixing the intercept is entirely adequate.

We wrote this plain-English summary from the full article with the help of AI, and a second AI model checked each sentence against the article. It is not the authors' wording; the abstract and the article are their own account.

What the study did and found

• Design: Methodological letter to the editor reporting a computer simulation study comparing Poisson regression approaches
• Who was studied: Hypothetical simulated populations of 500 subjects each (1,000 populations; also 100 populations each with 100 random baselines), plus smaller simulated populations of 50 subjects. No real people were studied.
• Exposure: A simulated exposure of random duration and level. Cases attributable to it were generated in proportion to cumulative exposure. Mesothelioma from environmental asbestos was given only as an example of a disease that may have little or no observable background rate.
• Main results:
  • With the standard model, the excess rate ratio coefficient across 1,000 simulated populations of 500 subjects had mean 13.4 (SD 94.5) and range 0.1 to 2834
  • With the intercept constrained (fixed), the excess rate ratio coefficient had mean 5.9 (SD 0.76) and range 3.7 to 8.8
  • Against a nominal value of 0.00006, the mean excess rate coefficient was 0.00005981 with fixed intercepts. It was 0.00005095 in standard models, biased downward by 15%.
  • The mean-squared deviation of the excess rate coefficient was 0.59 times 10 to the minus 10 with fixed intercepts versus 1.62 times 10 to the minus 10 with the standard model, a 63% reduction
  • With added random baseline cases (100 populations, each with 100 iterations), the mean excess rate coefficient was close to nominal with the fixed intercept (0.00005964) and without it (0.00006009)
  • Bias in the excess rate coefficient was 15% in populations of 500 subjects and 32% in populations of 50 subjects
• The authors' conclusion: The author concluded that the two treatments for vanishing baseline risk gave equivalent results, and that simply fixing the intercept is entirely adequate

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