Joint modelling of a binary and a continuous outcome measured at two cycles to determine the optimal dose

The optimal dose of targeted treatment in oncology may not be the maximal tolerated dose. Evaluating jointly toxicity and efficacy data is then desirable. We propose an adaptive dose finding approach to identify a dose based on repeated binary toxicity and continuous efficacy outcomes from the first two cycles. Probit and linear Gaussian models are used for the toxicity and efficacy at each cycle respectively. The correlation between toxicity and efficacy outcome is modelled via a latent Gaussian variable. Maximum likelihood estimators are used. Two steps in this design are defined: dose escalation with decision rules based only on toxicity observed at the first cycle; the expansion cohort with decision rules based on both repeated toxicity and efficacy outcomes by using the joint model. We perform simulation studies to assess the operating characteristics of our design. The design has good performance for different scenarios. The percentage of correct selection dose varies from 54% to 84%. There is no effect on the estimation parameters with missing data of toxicity or efficacy at cycle 2. The design then has similar performance. Using repeated toxicity and efficacy data in dose finding trials provides more reliable information to estimate the optimal dose for further trials.