BMC Medical Research Methodology

Table 2 Mean Bias (Bias) and root mean squared error (RMSE) for the point estimate and the coverage probability (%CP) of the interval estimate in estimating the cold- and heat-related relative risk (RR) by six different methods (Argmin1, Argmin2, Empirical1, Empirical2_strong, Empirical2_moderate, and Empirical2_minimal) for each of the 4 scenarios; U-shape (Scenario 1), reverse J-shape (Scenario 2), rotated S-shape (Scenario 3) and sector shape (Scenario 4)

From: Monte Carlo simulation-based estimation for the minimum mortality temperature in temperature-mortality association study

			Methods
			Argmin1	Argmin2	Empirical1	Empirical2_strong ^a	Empirical2_moderate ^b	Empirical2_minimal ^c
Cold-related RR	Scenario 1 (True RR = 1.094)	Bias	-0.0002	0.0001	-0.0009	-0.0008	-0.0003	-0.0006
		RMSE	0.0093	0.0090	0.0094	0.0092	0.0090	0.0090
		% CP	94.2%	95.6%	94.9%	96.7%	95.2%	95.0%
	Scenario 2 (True RR = 1.023)	Bias	-0.001	-0.0004	-0.004	-0.006	-0.0038	-0.0030
		RMSE	0.0069	0.0067	0.0073	0.0069	0.0056	0.0061
		% CP	95.4%	94.0%	95.7%	96.2%	96.7%	95.4%
	Scenario 3 (True RR = 1.070)	Bias	-0.030	-0.005	-0.046	-0.022	-0.280	-0.0221
		RMSE	0.0548	0.0287	0.0548	0.0250	0.0325	0.0275
		% CP	94.6%	93.5%	86.8%	99.7%	96.0%	98.0%
	Scenario 4 (True RR = 1.000)	Bias	-0.008	-0.002	-0.013	-0.005	-0.0059	-0.0061
		RMSE	0.0126	0.0036	0.0155	0.0055	0.0061	0.0063
		% CP	95.8%	58.4%	70.3%	93.2%	76.5%	75.6%
Heat-related RR	Scenario 1 (True RR = 1.079)	Bias	-0.0005	-0.0005	-0.0006	-0.001	-0.0007	-0.0011
		RMSE	0.0062	0.0064	0.0062	0.0062	0.0063	0.0061
		% CP	96.0%	95.4%	95.5%	93.5%	93.9%	95.8%
	Scenario 2 (True RR = 1.118)	Bias	-0.002	0.0001	-0.004	0.0005	0.0003	-0.0005
		RMSE	0.0100	0.0084	0.0114	0.0050	0.0068	0.0075
		% CP	95.6%	95.0%	94.3%	99.9%	99.5%	98.8%
	Scenario 3 (True RR = 1.015)	Bias	-0.027	-0.003	-0.044	-0.019	-0.0122	-0.121
		RMSE	0.0548	0.0144	0.0632	0.0192	0.0145	0.0144
		% CP	95.6%	85.8%	89.2%	98.1%	99.0%	98.8%
	Scenario 4 (True RR = 1.185)	Bias	-0.010	-0.0016	-0.016	-0.006	-0.0023	-0.0019
		RMSE	0.0205	0.0111	0.0232	0.0085	0.0079	0.0073
		% CP	96.2%	95.1%	90.0%	99.4%	99.6%	100%

^aPrior support: 70th -95th percentiles for scenarios 1 & 3, 40th – 65th percentiles for scenario 2, and 1st -10th percentiles for scenario 4
^bPrior support: 50th -99th percentiles for scenarios 1 & 3, 30th -80th percentiles for scenario 2, and 1st -50th percentiles for scenario 4
^cPrior support: 1st – 99th percentiles for all scenarios

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