Power estimation using simulations for air pollution time-series studies

Winquist, Andrea; Klein, Mitchel; Tolbert, Paige; Sarnat, Stefanie Ebelt

doi:10.1186/1476-069X-11-68

Environmental Health

Table 2 Power estimates for time-series models of air pollution under various scenarios

From: Power estimation using simulations for air pollution time-series studies

	Outcome	Pollutant(s) in model	Specified Risk Ratio	Series Length	Mean daily visits	Power from simulations	G*Power Estimates†
Scenario Set 1	CVD	PM_2.5	1.024 per 10 μg/m³	1 year	21.5	0.17	0.16
					42.9	0.29	0.28
					85.8	0.53	0.49
					128.7	0.70	0.66
					171.6	0.81	0.78
					214.5	0.88	0.86
				2 years	21.5	0.28	0.28
					42.9	0.50	0.49
					85.8	0.82	0.78
					128.7	0.94	0.92
					171.6	0.98	0.97
					214.5	0.99	0.99
				3 years	21.5	0.41	0.39
					42.9	0.70	0.66
					85.8	0.93	0.92
					128.7	0.99	0.98
					171.6	1.00	1.00
					214.5	1.00	1.00
				4 years	21.5	0.52	0.50
					42.9	0.81	0.79
					85.8	0.98	0.97
					128.7	1.00	1.00
					171.6	1.00	1.00
					214.5	1.00	1.00
	Dysrhythmia	PM_2.5	1.026 per 10 μg/m³	1 year	5.4	0.07	0.08
					10.7	0.11	0.11
					21.4	0.19	0.18
					32.1	0.25	0.25
					42.8	0.31	0.31
					53.5	0.38	0.38
				2 years	5.4	0.11	0.12
					10.7	0.19	0.18
					21.4	0.32	0.32
					32.1	0.43	0.45
					42.8	0.54	0.56
					53.5	0.63	0.65
				3 years	5.4	0.13	0.15
					10.7	0.25	0.25
					21.4	0.44	0.45
					32.1	0.60	0.61
					42.8	0.73	0.73
					53.5	0.82	0.82
				4 years	5.4	0.16	0.19
					10.7	0.31	0.32
					21.4	0.56	0.56
					32.1	0.72	0.73
					42.8	0.83	0.85
					53.5	0.91	0.92
	Cardiac Arrest	PM_2.5	1.104 per 10 μg/m³	1 year	1.6	0.18	0.22
					3.1	0.32	0.38
					6.2	0.58	0.64
					9.3	0.75	0.81
					12.4	0.87	0.91
					15.5	0.93	0.96
				2 years	1.6	0.32	0.39
					3.1	0.57	0.65
					6.2	0.85	0.91
					9.3	0.96	0.98
					12.4	1.00	1.00
					15.5	1.00	1.00
				3 years	1.6	0.45	0.54
					3.1	0.75	0.82
					6.2	0.96	0.98
					9.3	1.00	1.00
12.4					1.00	1.00
15.5					1.00	1.00
4 years				1.6	0.56	0.67
				3.1	0.86	0.91
				6.2	0.99	1.00
				9.3	1.00	1.00
				12.4	1.00	1.00
				15.5	1.00	1.00
Scenario Set 2	CVD	Total water- soluble PM_2.5 metals	1.03 per 0.03 μg/m³	1 year	85.8	0.77	0.72
			1.05 per 0.03 μg/m³			0.99	0.99
			1.07 per 0.03 μg/m³			1.00	1.00
			1.03 per 0.03 μg/m³	2 years		0.97	0.95
			1.05 per 0.03 μg/m³			1.00	1.00
			1.07 per 0.03 μg/m³			1.00	1.00
	Dysrhythmia		1.03 per 0.03 μg/m³	1 year	21.4	0.28	0.24
			1.05 per 0.03 μg/m³			0.62	0.55
			1.07 per 0.03 μg/m³			0.90	0.83
			1.03 per 0.03 μg/m³	2 years		0.50	0.44
			1.05 per 0.03 μg/m³			0.89	0.85
			1.07 per 0.03 μg/m³			1.00	0.99
Scenario Set 3	CVD	Elemental carbon (EC) (single pollutant model)§	EC: 1.052 per 2 μg/m³	1 year	85.8	EC: 0.98	0.99
			EC: 1.052 per 2 μg/m³	2 years		EC: 1.00	1.00
			EC: 1.052 per 2 μg/m³	3 years		EC: 1.00	1.00
			EC: 1.052 per 2 μg/m³	4 years		EC: 1.00	1.00
		Carbon monoxide (CO) (single pollutant model)§	CO: 1.039 per 1 ppmV	1 year		CO: 1.00	1.00
			CO: 1.039 per 1 ppmV	2 years		CO: 1.00	1.00
			CO: 1.039 per 1 ppmV	3 years		CO: 1.00	1.00
			CO: 1.039 per 1 ppmV	4 years		CO: 1.00	1.00
		Elemental carbon (EC) and Carbon monoxide (CO) in two- pollutant model	EC: 1.022 per 2 μg/m³	1 year		EC: 0.32	0.35
			CO: 1.032 per 1 ppmV	1 year		CO: 0.94	0.95
			EC: 1.022 per 2 μg/m³	2 years		EC: 0.54	0.61
			CO: 1.032 per 1 ppmV	2 years		CO: 1.00	1.00
			EC: 1.022 per 2 μg/m³	3 years		EC: 0.73	0.78
			CO: 1.032 per 1 ppmV	3 years		CO: 1.00	1.00
			EC: 1.022 per 2 μg/m³	4 years		EC: 0.83	0.89
			CO: 1.032 per 1 ppmV	4 years		CO: 1.00	1.00
	Dysrhythmia	Elemental carbon (EC) (single pollutant model)	EC: 1.106 per 2 μg/m³	1 year	21.4	EC: 0.98	0.99
			EC: 1.106 per 2 μg/m³	2 years		EC: 1.00	1.00
			EC: 1.106 per 2 μg/m³	3 years		EC: 1.00	1.00
			EC: 1.106 per 2 μg/m³	4 years		EC: 1.00	1.00
		Carbon monoxide (CO) (single pollutant model)	CO: 1.067 per 1 ppmV	1 year		CO: 0.99	0.99
			CO: 1.067 per 1 ppmV	2 years		CO: 1.00	1.00
			CO: 1.067 per 1 ppmV	3 years		CO: 1.00	1.00
			CO: 1.067 per 1 ppmV	4 years		CO: 1.00	1.00
		Elemental carbon (EC) and Carbon monoxide (CO) in two- pollutant model	EC: 1.058 per 2 μg/m³	1 year		EC: 0.49	0.55
			CO: 1.049 per 1 ppmV	1 year		CO: 0.81	0.79
			EC: 1.058 per 2 μg/m³	2 years		EC: 0.78	0.84
			CO: 1.049 per 1 ppmV	2 years		CO: 0.98	0.97
			EC: 1.058 per 2 μg/m³	3 years		EC: 0.92	0.95
			CO: 1.049 per 1 ppmV	3 years		CO: 1.00	1.00
			EC: 1.058 per 2 μg/m³	4 years		EC: 0.97	0.99
			CO: 1.049 per 1 ppmV	4 years		CO: 1.00	1.00

All models controlled for temperature (cubic splines with knots at 12.22°C and 23.89°C, for the moving average of daily average temperature (lags 0–2 days)), dew point (cubic splines with knots at 4.33°C and 18.28°C, for the moving average of daily average dew point (lags 0–2 days)), weekday, hospital participation periods, and underlying time trends (cubic spline for time with seasonal knots for four seasons).
† G*Power estimates were generated using the Lyles Enumeration Procedure. Power estimates obtained using PASS were very similar (all within 2 percentage points of the G* Power results) and are not shown. G*Power estimates use the mean daily count as expβ0 and account for days with missing pollutant values.
§Single pollutant models have missing values on the same days as the two-pollutant models.

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ISSN: 1476-069X

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