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)
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 | |