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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, Empirical2strong, Empirical2moderate, and Empirical2minimal) 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 Empirical2strong a Empirical2moderate b Empirical2minimal 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%
  1. aPrior support: 70th -95th percentiles for scenarios 1 & 3, 40th – 65th percentiles for scenario 2, and 1st -10th percentiles for scenario 4
  2. bPrior support: 50th -99th percentiles for scenarios 1 & 3, 30th -80th percentiles for scenario 2, and 1st -50th percentiles for scenario 4
  3. cPrior support: 1st – 99th percentiles for all scenarios