Table 2.

Results of simulations for PM₁₀ setting: β₁ × 10 = 0.00509, [24] and β₂ × 10 = 0.0677, [23]

Correlation between “true” and modelled data (τ)	Ratio of variances: modelled vs “true” (λ)	Estimating the health effect of short-term exposure				Estimating the health effect of long-term exposure
		$\widehat{{\beta }_1}\times 10$ a $\left(\mathit{se}\left(\widehat{{\beta }_1}\right)\times 10\right)$ a	Biasb (%)	Coverage probability (%)	Powerc (%)	$\widehat{{\beta }_2}\times 10$ a $\left(\mathit{se}\left(\widehat{{\beta }_2}\right)\times 10\right)$ a	Biasb (%)	Coverage probability (%)	Powerc (%)
1	1	0.00531 (0.00351)	4.3	95.8	33.8	0.0621 (0.0975)	−8.3	93.0	13.0
0.5	2.0	0.00179 (0.00248)	−64.8	72.8	12.0	0.0229 (0.0725)	−66.2	87.8	6.4
	1.25	0.00233 (0.00314)	−54.2	85.4	10.4	0.0268 (0.0892)	−60.4	89.0	8.4
	1	0.00266 (0.00351)	−47.7	91.2	12.4	0.0424 (0.0977)	−37.4	90.0	11.0
	0.75	0.00285 (0.00405)	−44.0	90.8	10.2	0.0383 (0.1092)	−43.4	91.4	11.8
	0.5	0.00339 (0.00496)	−33.4	95.8	11.0	0.0592 (0.1271)	−12.6	84.6	15.2
0.6	2.0	0.00232 (0.00248)	−54.4	79.8	17.4	0.0305 (0.0725)	−54.9	90.4	8.6
	1.25	0.00301 (0.00314)	−40.9	90.6	16.4	0.0378(0.0884)	−44.2	89.2	11.6
	1	0.00289 (0.00352)	−43.2	90.0	13.8	0.0412 (0.0971)	−39.1	89.4	8.8
	0.75	0.00358 (0.00406)	−29.7	93.4	15.4	0.0531 (0.1097)	−21.6	90.4	14.2
	0.5	0.00422 (0.00496)	−17.1	95.6	14.8	0.0594 (0.1264)	−12.3	89.4	13.0
0.7	2.0	0.00262 (0.00248)	−48.5	82.6	17.4	0.0338 (0.0726)	−50.1	90.8	8.2
	1.25	0.00336 (0.00314)	−34.0	91.4	19.2	0.0415 (0.0884)	−38.7	90.8	9.4
	1	0.00369 (0.00351)	−27.5	92.0	19.6	0.0464 (0.0968)	−31.5	91.8	10.4
	0.75	0.00407 (0.00405)	−20.0	94.6	17.6	0.0591 (0.1083)	−12.7	91.0	12.4
	0.5	0.00511 (0.00496)	0.4	95.2	16.2	0.0578 (0.1261)	−14.6	89.4	14.0
0.8	2.0	0.00282 (0.00248)	−44.6	85.0	19.4	0.0363 (0.0727)	−46.4	91.8	10.2
	1.25	0.00378 (0.00314)	−25.7	94.0	23.4	0.0532 (0.0890)	−21.4	93.2	11.4
	1	0.00395 (0.00351)	−22.4	93.6	20.8	0.0633 (0.0973)	−6.5	90.4	13.6
	0.75	0.00459 (0.00406)	−9.8	94.0	19.2	0.0504 (0.1100)	−25.6	88.2	13.2
	0.5	0.00602 (0.00496)	18.3	93.8	22.6	0.0707 (0.1269)	4.4	89.0	15.0
0.9	2.0	0.00329 (0.00248)	−35.4	87.8	25.4	0.0458 (0.0726)	−32.3	91.4	10.2
	1.25	0.00418 (0.00314)	−17.9	93.0	29.0	0.0545 (0.0891)	−19.5	90.8	13.4
	1	0.00466 (0.00351)	−8.4	95.8	24.8	0.0557 (0.0970)	−17.7	92.2	13.4
	0.75	0.00516 (0.00405)	1.4	94.8	24.8	0.0759 (0.1096)	12.1	91.2	15.6
	0.5	0.00667 (0.00496)	31.0	95.4	27.6	0.0909 (0.1265)	34.3	89.8	16.4

^aCoefficients and standard errors are averages of their respective within-simulation estimates. ^bPercent bias is highlighted in bold when positive (i.e. away from the null). ^cThe percentage of effect estimates that were statistically significant (p < 0.05)