Skip to main content

Table 2 Summary of the true and error-prone regression coefficients, their standard errors (SE) x 10-4 and relative bias from 144,000 simulated datasets on the impact of three error models (classical, Berkson and mixture) on 2-pollutant Poisson regression by area of study. Results presented for all scenarios (N = 48,000 in each row)

From: Quantifying the short-term effects of air pollution on health in the presence of exposure measurement error: a simulation study of multi-pollutant model results

Exposure CRFsa: PM2.5: β1 = 5.4a NO2: β2 = 6a
Area \( {\hat{\boldsymbol{\beta}}}_{\mathbf{1}} \) (SEW)/(SEB)b Bias (%)c Coverage Probability (%) Power (%) \( {\hat{\boldsymbol{\beta}}}_{\mathbf{2}} \) (SEW)/(SEB)b Bias (%)c Coverage Probability (%) Power (%)
True Europe 5.37 (1.48)/(3.46) 6.00 (1.79)/(4.20)
East NA 5.42 (1.88)/(4.41 5.98 (1.39)/(3.25)
West NA 5.40 (1.95)/(4.58) 5.99 (1.48)/(3.45)
Classical Europe 4.86 (1.36)/(3.27) −10.0 55.3 76.0 4.49 (1.52)/(3.82) −25.1 51.1 67.6
East NA 4.58 (1.67)/(4.02) −15.1 54.6 65.2 4.97 (1.25)/(3.09) −17.2 53.9 80.4
West NA 4.52 (1.72)/(4.17) −16.3 54.3 63.7 4.85 (1.30)/(3.24) −19.2 52.8 77.2
Berkson Europe 5.84 (1.70)/(4.02) + 8.2 59.3 75.4 5.53 (2.46)/(5.89) −7.9 58.8 62.2
East NA 5.78 (2.73)/(6.43) + 7.1 59.3 62.2 6.17 (1.95)/(4.58) + 2.8 59.7 75.6
West NA 5.62 (3.29)/(7.88) + 4.1 59.3 60.2 6.09 (2.50)/(5.87) + 1.5 59.2 71.1
Mixtured Europe 5.33 (1.49)/(3.57) −1.3 57.9 76.1 4.36 (2.00)/(5.10) −27.4 55.0 60.8
East NA 4.91 (1.91)/(4.61) −9.1 57.1 63.2 5.37 (1.48)/(3.58) −10.6 58.0 76.9
West NA 4.84 (1.99)/(4.81) −10.3 57.2 61.5 5.20 (1.58)/(3.85) −13.3 57.1 72.8
  1. aConcentration-response functions for generation of the health outcome
  2. b SEW:Within-simulations (or model-based) standard error, SEB:Between-simulations (or empirical) standard error
  3. c Relative bias = \( \frac{\left({\hat{\boldsymbol{\beta}}}_{\boldsymbol{\iota}}-{\boldsymbol{\beta}}_{\boldsymbol{\iota}}\right)}{{\boldsymbol{\beta}}_{\boldsymbol{\iota}}} \)
  4. d (Classical,Berkson) percentages: (43,57%) for PM2.5, (33,67%) for NO2