. Author manuscript; available in PMC: 2011 May 10.

Published in final edited form as: Stat Biopharm Res. 2011 Feb 1;3(1):97–105. doi: 10.1198/sbr.2010.09044

Table 4.

Power of the proposed test (Q) to detect small and large differences^a between mean tumor rates for historical (π^h) and current (π^c) controls by tumor rate (π^h), 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.

π^h	γ₁	No extra variation^b				Extra variation^b
π^h	γ₁	k=1	k=2	k=5	k=10	k=2	k=5	k=10
		Small difference between π^c and π^h
0.01	1.5	18.1	24.0	26.4	33.1	25.3	30.0	38.7
	3.0	18.3	24.1	26.9	33.3	25.5	29.7	37.7
	6.0	18.0	23.0	25.9	32.9	24.1	27.8	35.5
0.05	1.5	7.3	25.6	35.6	39.5	27.7	39.1	43.9
	3.0	7.1	25.6	35.8	40.4	27.7	39.0	43.8
	6.0	7.1	25.4	35.7	40.3	27.3	38.1	43.2
0.15	1.5	9.9	27.0	36.7	39.8	29.0	38.7	43.1
	3.0	10.0	27.6	36.9	40.1	29.4	39.4	42.9
	6.0	10.3	27.6	36.6	40.4	28.9	38.9	42.2
0.30	1.5	17.5	24.2	31.7	34.5	25.5	33.0	36.0
	3.0	17.8	24.6	32.2	35.3	26.4	33.5	36.7
	6.0	18.4	25.6	32.7	35.6	26.4	33.8	36.6
		Large difference between π^c and π^h
0.01	1.5	55.5	78.0	87.7	91.9	81.9	91.9	96.1
	3.0	55.8	78.1	87.9	91.5	81.4	91.6	96.0
	6.0	54.7	76.9	86.7	91.3	79.6	90.2	94.8
0.05	1.5	24.3	88.0	95.9	97.4	90.8	97.6	98.8
	3.0	22.5	86.1	95.2	96.7	88.7	96.8	98.2
	6.0	23.7	86.3	95.3	96.9	88.7	96.7	98.0
0.15	1.5	69.4	86.5	95.1	96.7	89.2	96.7	97.9
	3.0	71.2	87.2	95.5	96.7	89.4	96.7	98.1
	6.0	72.7	87.4	95.6	97.2	88.9	96.6	97.9
0.30	1.5	70.5	80.0	91.2	93.8	82.6	92.7	95.0
	3.0	71.4	81.3	92.1	94.5	83.1	93.3	95.0
	6.0	74.1	82.7	93.1	94.7	83.0	93.8	95.3

Small (large) differences are values of π^c that are 25% (50%) larger than π^h on the log scale.

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.