Optimal design and the model validity range

Optimal dose-finding designs with correlated continuous and discrete responses

In dose-finding clinical studies, it is common that multiple endpoints are of interest. For instance, in phase I/II studies, efficacy and toxicity are often the primary endpoints, which are observed simultaneously and which need to be evaluated together. Motivated by this, we confine ourselves to bivariate responses and focus on the most analytically difficult case: a mixture of continuous and categorical responses. We adopt the bivariate probit dose-response model and quantify our goal by a utility function. We study locally optimal designs, two-stage optimal designs, and fully adaptive designs under different ethical and cost constraints in the experiments. We assess the performance of two-stage designs and fully adaptive designs via simulations. Our simulations suggest that the two-stage designs are as efficient as and may be more efficient than the fully adaptive designs if there is a moderate sample size in the initial stage. In addition, two-stage designs are easier to construct and implement and thus can be a useful approach in practice.

Estimation of the Treatment Difference in Multicenter Trials

The three fixed effects estimators of a treatment,difference are compared under conditions of random enrollment in a multicenter clinical trial. These comparisons are performed by assuming five different enrollment schemes. The estimators are compared via simulation using their expected mean squared errors. Unlike previous discussions of these three estimators, we take explicit account of the effect of centers that fail to enroll patients to one or both treatment arms. Within each center, we assume enrollment follows a Poisson process and consider the two situations in which the mean rate of this process is the same in every center and in which the mean rates are sampled from a gamma distribution. The effect of patient dropout is studied as well as the effect of increasing the number of centers. Simulations show that for many sound scenarios, the simpler estimator corresponding to the simplest model works better, even for the cases when data are generated by more complex models.

The design of multicentre trials

The analysis of data collected in multicentre trials offers challenges because the data from the individual centres must be combined in some way to give an overall evaluation of the differences between the treatments in the trial. We propose that the combined response to treatment (CRT) be used as this overall measure. The definition and estimation of the CRT can be derived from either a fixed-effects or a random-effects model. For the latter we introduce the ECRT--the expected combined response to treatment. We describe and compare both types of model and express our preference for the random-effects model. We stress that the number of patients enrolled at a centre is a random variable and show that this source of randomness inflates the variance of the estimated ECRT. Variability in enrolment rates over the centres further inflates this variance. A simple conclusion from our results is that if variability in the treatment and centre effects, in the enrolment time, in the number of patients enrolled at a centre and in the enrolment rates is not properly accounted for, then an underpowered trial may result. Using properties of estimators generated by the random-effects model we propose methods for determining the optimal number of centres and total number of patients to enrol in a trial to minimize a loss function that accounts for centre and patient costs and loss of revenue. We discuss variants of the loss function and corresponding optimization problems for different types of enrolment. We end the paper with brief generalizations of the developed techniques to the case where the response is binary.