Number of Patients per Cohort and Sample Size Considerations Using Dose Escalation with Overdose Control

Table 1

Estimated proportions of patients given doses in an 𝜀-neighborhood of the true MTD under designs ¹𝑃 and ³𝑃 and differences between these proportions for small values of 𝛾 and selected values of 𝜌₀.

	Sample size
	12			18			24			30
	^1𝑃	^3𝑃	Diff.	^1𝑃	^3𝑃	Diff.	^1𝑃	^3𝑃	Diff.	^1𝑃	^3𝑃	Diff.
(𝛾,𝜌0) = (0.2,0.075)
𝜀=0.20	0.9768	0.9829	−0.0061	0.9826	0.9854	−0.0028	0.9864	0.9890	−0.0026	0.9897	0.9910	−0.0013
𝜀=0.15	0.9065	0.9352	−0.0287	0.9290	0.9465	−0.0175	0.9433	0.9598	−0.0165	0.9542	0.9661	−0.0119
𝜀=0.10	0.7525	0.7004	0.0521	0.7958	0.7440	0.0518	0.8261	0.7897	0.0364	0.8569	0.8210	0.0359
𝜀=0.05	0.3634	0.2521	0.1114	0.4306	0.3309	0.0997	0.4747	0.3997	0.0750	0.5265	0.4444	0.0821
(𝛾,𝜌0) = (0.2,0.15)
𝜀=0.20	0.9340	0.9603	−0.0262	0.9430	0.9492	−0.0062	0.9517	0.9571	−0.0054	0.9592	0.9629	−0.0037
𝜀=0.15	0.8153	0.8839	−0.0687	0.8378	0.8760	−0.0382	0.8610	0.8896	−0.0287	0.8784	0.8958	−0.0174
𝜀=0.10	0.6297	0.6729	−0.0431	0.6507	0.6643	−0.0136	0.6831	0.6924	−0.0092	0.7032	0.7105	−0.0074
𝜀=0.05	0.2752	0.2298	0.0454	0.3142	0.2659	0.0483	0.3478	0.3152	0.0327	0.3713	0.3477	0.0236
(𝛾,𝜌0) = (0.2,0.225)
𝜀=0.20	0.8658	0.9351	−0.0693	0.8659	0.9032	−0.0373	0.8772	0.8926	−0.0155	0.8838	0.8984	−0.0146
𝜀=0.15	0.7122	0.8463	−0.1341	0.7190	0.8036	−0.0846	0.7359	0.7900	−0.0541	0.7438	0.7931	−0.0493
𝜀=0.10	0.5256	0.6533	−0.1277	0.5219	0.6063	−0.0845	0.5390	0.5865	−0.0475	0.5448	0.5915	−0.0467
𝜀=0.05	0.2154	0.2102	0.0052	0.2279	0.2276	0.0003	0.2549	0.2371	0.0178	0.2626	0.2604	0.0022
(𝛾,𝜌0) = (0.4,0.075)
𝜀=0.20	0.7855	0.7121	0.0734	0.8272	0.7762	0.0510	0.8542	0.8180	0.0362	0.8784	0.8504	0.0280
𝜀=0.15	0.6939	0.5833	0.1106	0.7269	0.6541	0.0728	0.7477	0.6968	0.0509	0.7825	0.7376	0.0449
𝜀=0.10	0.4885	0.5258	−0.0373	0.5267	0.5478	−0.0211	0.5474	0.5647	−0.0173	0.5874	0.5906	−0.0032
𝜀=0.05	0.2773	0.1144	0.1629	0.2956	0.1759	0.1197	0.3050	0.2165	0.0885	0.3282	0.2506	0.0776
(𝛾,𝜌0) = (0.4,0.15)
𝜀=0.20	0.7038	0.6680	0.0358	0.7433	0.7201	0.0231	0.7587	0.7541	0.0046	0.7748	0.7814	−0.0066
𝜀=0.15	0.6031	0.5135	0.0897	0.6247	0.5757	0.0490	0.6348	0.6103	0.0246	0.6489	0.6417	0.0072
𝜀=0.10	0.4129	0.4371	−0.0242	0.4348	0.4531	−0.0184	0.4458	0.4722	−0.0264	0.4580	0.4903	−0.0323
𝜀=0.05	0.2332	0.1125	0.1207	0.2388	0.1648	0.0740	0.2416	0.1835	0.0581	0.2489	0.2100	0.0389
(𝛾,𝜌0) = (0.4,0.225)
𝜀=0.20	0.6383	0.6107	0.0276	0.6484	0.6550	−0.0066	0.6573	0.6826	−0.0252	0.6608	0.6859	−0.0251
𝜀=0.15	0.5377	0.4446	0.0932	0.5364	0.5042	0.0322	0.5389	0.5313	0.0076	0.5322	0.5349	−0.0027
𝜀=0.10	0.3605	0.3556	0.0049	0.3651	0.3819	−0.0168	0.3680	0.3921	−0.0241	0.3627	0.3912	−0.0286
𝜀=0.05	0.2008	0.1036	0.0972	0.1988	0.1467	0.0521	0.1982	0.1583	0.0400	0.1926	0.1665	0.0261