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Table 1 Empirical results from 10,000 simulations of weighted sums of Poisson parameters. (EU = distribution of sample population is same as European standard population)

From: Evaluation of stability of directly standardized rates for sparse data using simulation methods

  Normal approximation Dobson method Tiwari method
Expected events Population ratio youngest vs. oldest Incidence ratio oldest vs. youngest 95% LCL 95% UCL Coverage (%) 95% LCL 95% UCL Coverage (%) 95% LCL 95% UCL Coverage (%)
5 1 1 0.05 1.9 89.9 0.27 2.3 96.4 0.28 2.3 97.0
5 1 5000 0.02 1.9 87.6 0.25 2.4 94.6 0.26 2.4 96.9
5 50 1 0.03 1.9 87.0 0.24 2.4 94.0 0.26 2.6 97.9
5 50 5000 0.06 1.8 89.2 0.27 2.3 95.5 0.28 2.4 97.9
5 EU 1 0.12 1.9 86.9 0.32 2.3 98.0 0.32 2.3 98.0
5 EU 5000 0.12 1.9 87.0 0.32 2.3 97.9 0.32 2.3 97.9
10 1 1 0.34 1.6 92.2 0.44 1.9 96.3 0.45 1.9 96.4
10 1 5000 0.30 1.7 92.2 0.41 1.9 96.1 0.43 1.9 96.6
10 50 1 0.30 1.6 91.2 0.41 1.9 95.4 0.42 2.0 97.7
10 50 5000 0.33 1.6 92.0 0.43 1.9 95.8 0.44 1.9 96.6
10 EU 1 0.38 1.6 92.7 0.48 1.8 97.5 0.48 1.8 97.5
10 EU 5000 0.38 1.6 92.6 0.48 1.8 97.6 0.48 1.8 97.6
15 1 1 0.46 1.5 93.2 0.53 1.7 96.1 0.53 1.7 96.2
15 1 5000 0.43 1.5 93.3 0.51 1.7 96.0 0.51 1.7 96.3
15 50 1 0.43 1.5 92.1 0.50 1.7 95.6 0.51 1.8 97.0
15 50 5000 0.45 1.5 92.5 0.52 1.7 96.2 0.52 1.7 96.6
15 EU 1 0.49 1.5 91.8 0.56 1.6 96.3 0.56 1.6 96.3
15 EU 5000 0.49 1.5 92.0 0.56 1.6 96.3 0.56 1.6 96.3
25 1 1 0.58 1.4 93.9 0.62 1.5 95.9 0.62 1.5 96.0
25 1 5000 0.56 1.4 93.9 0.61 1.5 96.0 0.61 1.5 96.1
25 50 1 0.56 1.4 93.4 0.60 1.5 95.5 0.61 1.5 96.4
25 50 5000 0.57 1.4 93.5 0.62 1.5 95.6 0.62 1.5 95.9
25 EU 1 0.61 1.4 94.7 0.65 1.5 95.5 0.65 1.5 95.5
25 EU 5000 0.61 1.4 94.8 0.65 1.5 95.5 0.65 1.5 95.5
100 1 1 0.79 1.2 94.9 0.80 1.2 95.6 0.80 1.2 95.6
100 1 5000 0.78 1.2 95.0 0.79 1.2 95.8 0.79 1.2 95.8
100 50 1 0.78 1.2 94.5 0.79 1.2 95.4 0.79 1.2 95.7
100 50 5000 0.79 1.2 94.9 0.80 1.2 95.8 0.80 1.2 95.8
100 EU 1 0.80 1.2 94.6 0.81 1.2 95.5 0.81 1.2 95.5
100 EU 5000 0.80 1.2 94.5 0.81 1.2 95.4 0.81 1.2 95.4