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 |