Measurement error in time-series analysis: a simulation study comparing modelled and monitored data

Table 4 Summarising the analysis of 1000 simulated data sets: nitrogen dioxide concentrations with proportional error

Description of simulated data	No. of grids per region containing a monitor	Urban background Nitrogen Dioxideβ × 10 = 0.00399		Rural background Nitrogen Dioxide β × 10 = 0.00399
		$\hat{β} \times 10$	Coverage probability;	$\hat{β} \times 10$	Coverage probability;
		$SE (\hat{β}) \times 10$	Power	$SE (\hat{β}) \times 10$	Power
*Monitor data:* regional average used for each 5 km × 5km grid within region (instrument and monitor-site location error included)	1	0.00262 (0.00191)	86%; 28%	0.00201 (0.00319)	86%; 10%
	2	0.00313 (0.00207)	91%; 32%	0.00252 (0.00350)	92%; 11%
	3	0.00333 (0.00213)	93%; 35%	0.00279 (0.00365)	93%; 12%
	5	0.00353 (0.00219)	94%; 37%	0.00306 (0.00381)	93%; 13%
	10	0.00372 (0.00224)	95%; 38%	0.00335 (0.00396)	94%; 14%
*“true” data:* grid-specific monitor data (no instrument or monitor-site location error)	25	0.00394 (0.00225)	95%; 43%	0.00393 (0.00403)	95%; 17%
*Model data:* grid-specific model data	-	0.00231 (0.00182)	85%; 25%	0.00185 (0.00222)	83%; 14%

The table presents estimated regression coefficients $(\hat{β})$ , standard errors $(SE (\hat{β}))$ , coverage probabilities and power, each based on the analysis of 1000 sets of simulated time-series data. The “true” value of the regression coefficient β for NO₂ (i.e. β × 10 = 0.00399) equates to a 0.4% increase in mortality per 10 μg/m³ increase in NO₂.

ISSN: 1471-2288