### Inference and ethics in clinical trials for comparing two treatments in the presence of covariates

Giovagnoli , A *(Bologna)*

Thursday 14 August 2008, 14:30-15:00

Seminar Room 1, Newton Institute

#### Abstract

In the medical profession physicians are expected to act in the best interests of each patient under their care, and this attitude is also reflected in special ethical considerations surrounding clinical trials. When the trial is adaptive, possible choices are either to try to do what appears to be best at each step for that particular patient, or else to aim at an overall benefit for the entire sample of patients involved in the trial. When the scope of the trial is comparing the probabilities of success of two treatments, a typical example of the former approach is the Play-the-Winner rule, while examples of the latter are trying to minimize the total number of patients assigned to the inferior treatment, or to maximize the number of expected "successes". Clearly the need for ethics and the need for experimental evidence are often conflicting demands, so a compromise is called for. But what weight should be assigned to ethics and what to the inferential criterion? In general, it is reasonable to suppose that the more significantly different the two success probabilities are, the more important an ethical allocation will be. In this presentation we propose a compromise criterion such that the weight of ethics is an increasing function of the absolute difference between the success probabilities. We suggest an adaptive allocation method based on sequential estimation of the unknown target by maximum likelihood, and show that this particular Sequential Maximum Likelihood Design converges to a treatment allocation that optimizes the compromise criterion. The approach is extended to account for the presence of random normal covariates, allowing for treatment-covariate interactions, which makes the need for an ethical allocation even more stringent. A proof of the convergence will be given for this case too. Our design is compared to some existing ones in the literature.

#### Presentation

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