CWL: A conditional weighted likelihood method to account for the delayed joint toxicity–efficacy outcomes for phase I/II clinical trials

The delayed outcome issue is common in early phase dose-finding clinical trials. This problem becomes more intractable in phase I/II clinical trials because both toxicity and efficacy responses are subject to the delayed outcome issue. The existing methods applying for the phase I trials cannot be used directly for the phase I/II trial due to a lack of capability to model the joint toxicity–efficacy distribution. In this paper, we propose a conditional weighted likelihood (CWL) method to circumvent this issue. The key idea of the CWL method is to decompose the joint probability into the product of marginal and conditional probabilities and then weight each probability based on each patient’s actual follow-up time. The CWL method makes no parametric model assumption on either the dose–response curve or the toxicity–efficacy correlation and therefore can be applied to any existing phase I/II trial design. Numerical trial applications show that the proposed CWL method yields desirable operating characteristics.