Table 3.

Bias(×10) and variance(×10²) of the least squares recursion and the logit-MLE with m = 3, n = 15, and the fully sequentially logit-MLE(f), i.e., m = 1, n = 45, with starting dose X₁ = 0.25. The mean squared error ratio (rmse) is calculated relative to the method assuming known σ.

p	θ	Method	Logistic, b = β†			t6, b = β†			Logistic, b = 0.5β‡			t6, b = 0.5β‡
			bias	var	rmse	bias	var	rmse	bias	var	rmse	bias	var	rmse
0.1	0.25	Known σ	−0.50	1.00	—	−0.74	0.90	—	−0.56	1.43	—	−0.81	1.29	—
		Unspecified σ	−0.30	2.11	0.57	−0.40	2.02	0.67	−0.40	2.87	0.58	−0.50	2.78	0.64
		Constant σ	−0.40	2.10	0.55	−0.54	2.02	0.62	−0.53	2.79	0.57	−0.68	2.70	0.62
		logit-MLE	−0.04	2.74	0.46	−0.08	2.57	0.56	−0.49	3.16	0.51	−0.52	3.12	0.58
		logit-MLE(f)	−0.06	2.64	0.47	−0.11	2.56	0.56	−0.43	3.11	0.53	−0.46	3.04	0.60
	0.50	Known σ	−0.45	1.01	—	−0.69	0.93	—	−0.46	1.45	—	−0.70	1.40	—
		Unspecified σ	−0.25	2.40	0.49	−0.36	2.36	0.57	−0.26	3.51	0.46	−0.38	3.53	0.51
		Constant σ	−0.37	2.49	0.46	−0.55	2.58	0.49	−0.43	3.63	0.44	−0.62	3.75	0.46
		logit-MLE	−0.18	3.71	0.32	−0.19	3.68	0.38	−0.31	5.06	0.32	−0.36	4.91	0.38
		logit-MLE(f)	−0.18	3.62	0.33	−0.16	3.47	0.40	−0.37	4.76	0.34	−0.35	4.61	0.40
	0.75	Known σ	−0.36	1.03	—	−0.60	0.95	—	−0.37	1.50	—	−0.63	1.43	—
		Unspecified σ	−0.09	2.30	0.50	−0.20	2.31	0.56	−0.02	3.29	0.50	−0.15	3.36	0.54
		Constant σ	−0.21	2.40	0.47	−0.39	2.57	0.48	−0.18	3.42	0.47	−0.39	3.71	0.47
		logit-MLE	−1.19	4.89	0.18	−1.22	4.89	0.21	−0.27	4.92	0.33	−0.35	4.90	0.36
		logit-MLE(f)	−0.90	4.38	0.22	−0.95	4.36	0.25	−0.12	4.50	0.36	−0.15	4.46	0.41
0.2	0.25	Known σ	−0.47	0.78	—	−0.62	0.72	—	−0.52	1.12	—	−0.68	1.05	—
		Unspecified σ	−0.35	1.23	0.74	−0.43	1.17	0.82	−0.43	1.73	0.72	−0.51	1.66	0.78
		Constant σ	−0.42	1.24	0.71	−0.53	1.20	0.75	−0.52	1.72	0.70	−0.64	1.67	0.72
		logit-MLE	−0.08	1.47	0.68	−0.11	1.35	0.82	−0.30	1.98	0.67	−0.32	1.92	0.74
		logit-MLE(f)	−0.09	1.46	0.68	−0.11	1.34	0.82	−0.28	1.94	0.69	−0.28	1.90	0.76
	0.50	Known σ	−0.44	0.78	—	−0.58	0.72	—	−0.44	1.11	—	−0.60	1.07	—
		Unspecified σ	−0.31	1.27	0.71	−0.39	1.22	0.77	−0.32	1.83	0.68	−0.40	1.81	0.72
		Constant σ	−0.38	1.30	0.67	−0.50	1.33	0.67	−0.42	1.87	0.64	−0.56	1.95	0.63
		logit-MLE	−0.05	1.72	0.56	−0.05	1.58	0.67	−0.23	2.26	0.56	−0.25	2.18	0.64
		logit-MLE(f)	−0.08	1.67	0.58	−0.10	1.52	0.69	−0.23	2.15	0.59	−0.25	2.04	0.68
	0.75	Known σ	−0.36	0.79	—	−0.51	0.74	—	−0.38	1.14	—	−0.54	1.10	—
		Unspecified σ	−0.22	1.28	0.69	−0.29	1.23	0.76	−0.20	1.85	0.68	−0.30	1.84	0.72
		Constant σ	−0.28	1.31	0.66	−0.40	1.33	0.67	−0.30	1.89	0.65	−0.45	1.96	0.64
		logit-MLE	0.04	2.06	0.45	0.04	1.98	0.50	0.10	2.47	0.52	0.07	2.39	0.58
		logit-MLE(f)	0.05	1.85	0.50	0.04	1.76	0.57	−0.04	2.29	0.56	−0.06	2.20	0.63

^†b~ = β~ for logit-MLE;

^‡b~ = 0.5β~.