Between- and within-patient n-level response surface pathway design in dose-finding studies

Figures & data

Table 1 Pattern of changes in cumulative dose in the between-patient three-level response surface pathway design

Dose at design level 1	Adverse events obtained at design level 1	Dose at design level 2	Adverse events obtained at design level 2	Dose at design level 3
m (0.64 mg/kg BW)	None to mild (1)	m+m/k (0.96 mg/kg BW)	None to mild	m+m/k+m/k^2 (1.12 mg/kg BW)
			Moderate	m+m/k+m/k^3 (1.04 mg/kg BW)
			Severe	m+m/k-m/k^3 (0.88 mg/kg BW)
			Life-threatening	m+m/k-m/k^2 (0.80 mg/kg BW)
	Moderate (2)	m+m/k^2 (0.80 mg/kg BW)	None to mild	m+m/k^2+m/k^3 (0.88 mg/kg BW)
			Moderate	m+m/k^2+m/k^4 (0.84 mg/kg BW)
			Severe	m+m/k^2-m/k^4 (0.76 mg/kg BW)
			Life-threatening	m+m/k^2-m/k^3 (0.72 mg/kg BW)
	Severe (3)	m-m/k^2 (0.48 mg/kg BW)	None to mild	m-m/k^2+m/k^3 (0.56 mg/kg BW)
			Moderate	m-m/k^2+m/k^4 (0.52 mg/kg BW)
			Severe	m-m/k^2-m/k^4 (0.44 mg/kg BW)
			Life-threatening	m-m/k^2-m/k^3 (0.40 mg/kg BW)
	Life threatening (4)	m-m/k (0.32 mg/kg BW)	None to mild	m-m/k+m/k^2 (0.48 mg/kg BW)
			Moderate	m-m/k+m/k^3 (0.40 mg/kg BW)
			Severe	m-m/k-m/k^3 (0.24 mg/kg BW)
			Life-threatening	m-m/k-m/k^2 (0.16 mg/kg BW)

Note: The chosen cumulative starting dose is indicated by m=0.64 mg/kg BW and the k-adjustment factor is calculated at k=2.

Abbreviation: BW, body weight.

Figure 1 Dose escalation and de-escalation procedures in a between-patient and a within-patient response surface pathway design.

Notes: m represents the starting dose with numbers 1–4 indicating toxic severity. The functions in volve m and the k-adjustment factor to calculate the doses to be used at the design levels.

Figure 2 The pathway when estimating the maximum tolerated dose of BP-C1 in women with stage IV breast cancer using a between-patient response surface pathway design.

Notes: The number of patients included at each design level is provided within the hexagon boxes and the numbers within each circle represent the treatment results at the different design levels. None/mild, moderate, severe, and life-threatening represent grades of adverse events, based on the National Cancer Institute Common Toxicity Criteria.²⁵
Abbreviation: BW, body weight.

Figure 3 The pathway when estimating the maximum tolerated dose of BP-C1 in dogs with metastatic mammary cancer using a within-patient response surface pathway design.

Notes: The number of canine patients included at each design level is provided within the hexagon boxes and the numbers within each circle represent the treatment results at the different design levels. None/mild, moderate, severe, and life-threatening represent grades of adverse events, based on the Veterinary Co-operative Oncology Group – Common Terminology Criteria for Adverse Events.²⁷
Abbreviation: BW, body weight.

Table 2 Performance of the traditional 3+3 design and response surface pathway design in three scenarios

	Scenario 1		Scenario 2		Scenario 3
	3+3 design	RSP design	3+3 design	RSP design	3+3 design	RSP design
Target MTD	250	250	400	400	550	550
Median estimated MTD	100	295	250	422	400	549
Twenty-five percent quantile MTD	0	250	100	341.5	250	489.5
Seventy-five percent quantile MTD	250	350	250	477	400	600
Median percent difference between estimated MTD and target MTD	−60	18	−37.5	5.50	−27.3	−0.18
Percent of trials with estimated MTD within 20 percent of target MTD	18	25	15	55	12	81
Median number of samples	12	15	12	15	18	15
Median percent of patients with a DLT (grade 3 or 4)	25	46.7	23.2	33.3	16.7	26.7
Median percent of patients treated above estimated MTD	50	92.8	50	53	33.3	23.3
Percent of trials with estimated MTD at DLT rate >40%	19	55	8	16	2	4

Abbreviations: DLT, dose-limiting toxicity; MTD, maximum tolerated dose; RSP, response surface pathway.

Common Toxicity Criteria (CTC) version 2.0 [webpage on the Internet]. Bethesda: National Cancer Institute; 1999. Available from: http://ctep.cancer.gov/protocolDevelopment/electronic_applications/ctc.htm. Accessed August 17, 2007.

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