Table 3.
Type I error rates for the proposed test (Q) by tumor rate (π), shape of the incidence curve (γ1), number of historical control groups (k), and absence/presence of extra variation. All tests were performed at the nominal 5% level, with a sample size of n=50 per group and with 70% of the animals (on average) surviving to the terminal sacrifice.
| πa | γ1 | No extra variationb |
Extra variationb |
|||||
|---|---|---|---|---|---|---|---|---|
| k=1 | k=2 | k=5 | k=10 | k=2 | k=5 | k=10 | ||
| 0.01 | 1.5 | 2.3 | 5.5 | 4.6 | 5.0 | 5.5 | 4.4 | 4.5 |
| 3.0 | 2.2 | 5.5 | 4.5 | 5.0 | 5.5 | 4.4 | 5.1 | |
| 6.0 | 2.4 | 5.5 | 4.3 | 5.7 | 5.8 | 4.1 | 4.8 | |
| 0.05 | 1.5 | 5.4 | 5.1 | 3.9 | 4.1 | 5.1 | 4.4 | 4.6 |
| 3.0 | 5.3 | 5.0 | 3.7 | 4.3 | 5.1 | 4.3 | 4.7 | |
| 6.0 | 5.3 | 5.0 | 3.8 | 4.2 | 5.0 | 4.1 | 4.4 | |
| 0.15 | 1.5 | 4.8 | 5.1 | 4.8 | 4.8 | 4.9 | 4.8 | 4.8 |
| 3.0 | 4.7 | 5.0 | 4.7 | 4.9 | 5.1 | 4.7 | 4.8 | |
| 6.0 | 4.4 | 4.9 | 4.9 | 4.8 | 4.8 | 4.9 | 4.9 | |
| 0.30 | 1.5 | 5.3 | 5.0 | 5.1 | 5.0 | 4.8 | 5.0 | 5.0 |
| 3.0 | 5.2 | 5.0 | 5.2 | 4.8 | 4.9 | 5.1 | 5.2 | |
| 6.0 | 5.2 | 5.0 | 5.1 | 5.1 | 5.0 | 5.0 | 5.3 | |
a
The mean tumor rate among the historical control groups (πh) equals the mean tumor rate in the current control group (πc) under the null hypothesis (H0: πh = πc = π).
b
The variance of the tumor rates among the historical control groups in the presence of extra variation is 20% larger than in the absence of extra variation.