The New England Journal of Statistics in Data Science

In oncology therapy development, Simon’s two-stage design is commonly employed in early-phase clinical trials to assess the preliminary efficacy of a single dose, typically the maximum tolerable dose (MTD) or the maximum assessed dose (MAD). In this design, a dose may be terminated at the first stage if the anti-tumor activity is insufficient or it may proceed to the second stage for further evaluation with more subjects. To enhance the design for better benefit-risk profile dose selection and to meet the increasing needs for study designs that explore dose-response relationships, we extend Simon’s two-stage design to evaluate two doses and to include early termination for success in addition to futility. The proposed method derives decision rules and sample sizes for optimal study designs that minimize the expected or overall sample sizes while controlling type I error and meeting desired power.

Subdata selection from big data is an active area of research that facilitates inferences based on big data with limited computational expense. For linear regression models, the optimal design-inspired Information-Based Optimal Subdata Selection (IBOSS) method is a computationally efficient method for selecting subdata that has excellent statistical properties. But the method can only be used if the subdata size, k, is at last twice the number of regression variables, p. In addition, even when $k\ge 2p$, under the assumption of effect sparsity, one can expect to obtain subdata with better statistical properties by trying to focus on active variables. Inspired by recent efforts to extend the IBOSS method to situations with a large number of variables p, we introduce a method called Combining Lasso And Subdata Selection (CLASS) that, as shown, improves on other proposed methods in terms of variable selection and building a predictive model based on subdata when the full data size n is very large and the number of variables p is large. In terms of computational expense, CLASS is more expensive than recent competitors for moderately large values of n, but the roles reverse under effect sparsity for extremely large values of n.