Early termination of a two-stage study to develop and validate a panel of biomarkers

Two-stage designs to develop and validate a panel of biomarkers present a natural setting for the inclusion of stopping rules for futility in the event of poor preliminary estimates of performance. We consider the design of a two-stage study to develop and validate a panel of biomarkers where a predictive model is developed using a subset of the samples in stage 1 and the model is validated using the remainder of the samples in stage 2. First, we illustrate how we can implement a stopping rule for futility in a standard, two-stage study for developing and validating a predictive model where samples are separated into a training sample and a validation sample. Simulation results indicate that our design has type I error rate and power similar to the fixed-sample design but with a substantially reduced sample size under the null hypothesis. We then illustrate how we can include additional interim analyses in stage 2 by applying existing group sequential methodology, which results in even greater savings in the number of samples required under both the null and the alternative hypotheses. Our simulation results also illustrate that the operating characteristics of our design are robust to changes in the underlying marker distribution.