Table 2.

Type I error rates for the unadjusted (R) and survival-adjusted (R*) range-based tests 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 based on a sample size of n=50 per group, with 70% of the animals (on average) surviving to the terminal sacrifice.

πa	γ1	No extra variationb			Extra variationb
		k=2	k=5	k=10	k=2	k=5	k=10
		Unadjusted range-based test (R)
0.01	1.5	27.9	9.0	4.4	30.2	9.6	4.6
	3.0	27.9	9.0	4.3	30.1	9.4	4.8
	6.0	28.6	8.8	5.1	31.0	9.7	4.6
0.05	1.5	48.7	20.9	11.0	49.6	22.0	11.5
	3.0	48.4	21.0	11.0	49.6	21.7	11.7
	6.0	49.2	20.8	11.2	50.0	21.5	11.4
0.15	1.5	55.9	26.0	13.1	56.1	25.8	13.6
	3.0	56.1	26.3	13.1	56.3	26.1	13.4
	6.0	56.1	26.2	13.0	56.1	26.5	13.6
0.30	1.5	57.7	26.5	14.0	58.1	26.7	14.1
	3.0	58.1	27.2	14.0	58.7	27.1	14.1
	6.0	58.7	26.7	13.8	58.5	26.9	14.5
		Poly-3 survival-adjusted range-based test (R*)
0.01	1.5	36.9	16.4	9.1	40.4	16.8	8.8
	3.0	37.0	16.4	9.1	39.9	16.7	9.2
	6.0	38.0	16.3	9.9	41.4	17.3	9.1
0.05	1.5	65.6	31.5	17.1	66.2	32.6	18.4
	3.0	65.8	31.8	17.4	66.1	32.3	18.5
	6.0	65.9	31.9	17.2	66.2	32.4	17.8
0.15	1.5	67.0	34.0	18.2	66.3	33.7	18.2
	3.0	67.0	34.0	17.9	66.6	33.8	18.1
	6.0	66.7	33.8	17.9	66.6	33.8	18.4
0.30	1.5	65.9	33.2	18.2	66.1	32.6	17.8
	3.0	66.2	32.9	17.9	66.5	33.3	17.7
	6.0	66.5	32.9	17.5	66.8	33.2	18.3

^aThe mean tumor rate among the historical control groups (π^h) equals the mean tumor rate in the current control group (π^c) under the null hypothesis (H₀: π^h = π^c = π).

^bThe 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.