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

Table 3 Summarising the analysis of 1000 simulated data sets: rural pollution concentrations with additive error

Description of simulated data	No. of grids per region containing a monitor	Ozoneβ × 10 = 0.00399		log_e(Nitrogen Dioxide)β = 0.0419
		$\hat{β} \times 10$	Coverage probability;	$\hat{β}$	Coverage probability;
		$SE (\hat{β}) \times 10$	Power	$SE (\hat{β})$	Power
*Monitor data:* regional average used for each 5 km × 5km grid within region (instrument and monitor-site location error included)	1	0.00346 (0.00244)	95%; 30%	0.0258 (0.0072)	39%; 96%
	2	0.00371 (0.00254)	95%; 31%	0.0319 (0.0080)	76%; 98%
	3	0.00381 (0.00258)	95%; 31%	0.0347 (0.0083)	86%; 98%
	5	0.00389 (0.00261)	95%; 32%	0.0372 (0.0087)	93%; 99%
	10	0.00397 (0.00263)	96%; 31%	0.0395 (0.0089)	95%; 99%
*“true” data:* grid-specific monitor data (no instrument or monitor-site location error)	25	0.00392 (0.00264)	95%; 33%	0.0418 (0.0091)	94%; 100%
*Model data:* grid-specific model data	-	0.00310 (0.00257)	94%; 22%	0.0233 (0.0058)	11%; 99%

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 ozone (i.e. β × 10 = 0.00399) equates to a 0.4% increase in mortality per 10 μg/m³ increase in ozone and the “true” value of the regression coefficient for log_e(NO₂) (i.e. β = 0.0419) equates to a 0.4% increase in mortality per 10% increase in NO₂.

ISSN: 1471-2288