Estimation with vanishing baseline risk.
Epidemiology 2012 Nov; 23(6):937-938
Diseases associated with specific exposures may have little or no observable background rate in the absence of the exposure. Examples include mesothelioma (environmental asbestos), aplastic anemia (benzene), bronchiolitis obliterans (artificial butter flavorings), Reye's syndrome (aspirin in children), and angiosarcoma of the liver (vinyl chloride). Relative-rate models of exposure-response produce unstable near-zero baseline risk and unbounded coefficients, especially when age confounding requires baseline age dependence. The same problem arises in a proportional-hazards context. Baseline risk volatility also threatens meta-analyses, a procedure that assumes uniformity. Using Poisson regression, we investigated two methods: (1) fixing the intercept at a small value corresponding to 1% of attributable cases and (2) generating random sets of new cases across observation time independent of any predictor, possibly preempting true cases. Although models can be reliably fit using randomly generated cases, repetition would reduce variability in parameter estimates. The two treatments for vanishing baseline yield equivalent results demonstrating that simply fixing the intercept is entirely adequate.
Risk-analysis; Risk-factors; Mathematical-models; Statistical-analysis; Statistical-quality-control; Exposure-assessment; Diseases; Analytical-processes
Robert M. Park, Centers for Disease Control and Prevention, National Institute for Occupational Safety and Health, Education and Information Division, 4676 Columbia Parkway, Cincinnati, OH 45226