Range and trend of expected toxicity level (ETL) in standard AÂ +Â B designs: A report from the children's oncology group

The traditional algorithm-based 3 + 3 designs are most widely used for their practical simplicity in phase I clinical trials. At early stage, a common belief was that the expected toxicity level (ETL) at the maximum tolerated dose (MTD) should be 33% [Storer, B. Design and analysis of phase I clinical trials. Biometrics 1989;45;925-937, Gorden, N., Willson, J. Using toxicity grades in the design and analysis of cancer phase I clinical trials. Statistics in Medicine 1992; 11: 2063-2075, Mick, R. Phase I Clinical Trial Design. In Schilsky, R., Milano, G., Ratain, M., eds. Principles of Antineoplastic Drug Development and Pharmacology New York, NY: Marcel Dekker, 1996; 29-36]. Recently, Kang and Ahn [Kang, S., Ahn, C. The expected toxicity rate at the maximum tolerated dose in the standard phase I cancer clinical trial design. Drug Information Journal 2001; 35:1189-1199, Kang, S., Ahn, C. An investigation of the traditional algorithm-based designs for phase I cancer clinical trials. Drug Information Journal 2002; 36:865-873] found that the ETL is between 17% and 21% and He et al [He, W., Liu, J., Binkowitz, B., Quan, H. A model-based approach in the estimation of the maximum tolerated dose in phase I cancer clinical trials. Statistics in Medicine 2006; 25(12):2027-42] further reported that the ETL ranges from 19% to 24%. However they only investigated designs where the number of dose levels was at most 20. It has practical significance in designing and conducting phase I clinical trial to definitely assess the full range and trend of ETL by all possible number of tested dose levels in traditional algorithm-based A + B designs, especially 3 + 3 designs. In this simulation study, we originally find that the ETL decreases monotonically from about 30% to 0% as the number of dose levels increase from 3 to infinity, which will correct the inaccuracy in the common belief among phase I trial investigators. To help better design and conduct phase I trials, we create a table as a reference for the association between ETL and number of dose levels considered in a design when the exact shape of the dose-toxicity relationship is not well understood. We conclude that the number of specified dose levels is an important factor affecting substantially the ETL at MTD and recommend that fewer than 20 dose levels be designated.