title: Attenuation of exposure-response rate ratios at higher exposures: a simulation study focusing on frailty and measurement error.
abstract: BACKGROUND
  Positive exposure-response trends for rate ratios (RRs) often diminish at higher exposures. Depletion of susceptibles with higher exposure and increased measurement error at higher exposures are possible reasons.
  
  
  METHODS
  We conducted simulations to investigate attenuation under various assumptions about susceptibility to exposure effects and measurement error, considering a hypothetical occupational cohort, using an excess relative risk model. We simulated an occupational cohort in which entry occurred over time. The metric of interest was cumulative exposure, which had a strong linear effect (RR = 4 for mean exposure), maximizing potential depletion. Measurement error of both classical and Berkson types was also simulated, increasing with increasing exposure. We conducted 100 simulations per scenario, each with 25,000 subjects enrolled from years 1940 to 2010, followed through 2010.
  
  
  RESULTS
  With less than 100% susceptibility to exposure (a requirement for depletion), there was only modest evidence of depletion of susceptibles with increasing cumulative exposure distributed normally. There was correspondingly little attenuation of RRs, and linear exposure-response models fit well. Adding classical measurement error to cumulative exposure, increasing with increasing exposure, resulted in some modest attenuation. Using log normal instead of normally distributed cumulative exposure also resulted in some attenuation.
  
  
  CONCLUSIONS
  Strong attenuation of relatively strong linear exposure-response trends using cumulative exposure, with relatively common disease and heterogeneous susceptibility, does not appear likely due to depletion of susceptibles. Strong attenuation seems more likely to be due to other mechanisms.
authors: From the Departments of aEnvironmental Health and bEpidemiology, Rollins School of Public Health, Emory University, Atlanta, GA.
authors: Kyle
authors: K
authors: Steenland
authors: Conny
authors: C
authors: Karnes
authors: Lyndsey
authors: L
authors: Darrow
authors: Vaughn
authors: V
authors: Barry
mesh_terms: D000367:Age Factors; D003430:Cross-Sectional Studies; D000068598:Data Accuracy; D004198:Disease Susceptibility / Q000453:epidemiology; D004813:Epidemiology; D006801:Humans; D016273:Occupational Exposure / Q000009:adverse effects / Q000592:standards / Q000706:statistics & numerical data*; D012306:Risk