After an overview of the Food and Drugs Administration's 2012 draft guidance on enrichment strategies for clinical trials to support drug/biologic approval, we describe subsequent advances in adaptive enrichment designs in this direction. We also provide a concrete application in the enrichment design of the Diffusion and Perfusion Imaging Evaluation for Understanding Stroke Evolution 3 trial comparing a new endovascular treatment with standard of care for ischemic stroke patients.

The past decade witnessed major developments in innovative designs of confirmatory clinical trials, and adaptive designs represent the most active area of these developments. We give an overview of the developments and associated statistical methods in several classes of adaptive designs of confirmatory trials. We also discuss their statistical difficulties and implementation challenges, and show how these problems are connected to other branches of mainstream Statistics, which we then apply to resolve the difficulties and bypass the bottlenecks in the development of adaptive designs for the next decade.

This paper begins with a brief review of multivariate time series analysis, covering canonical correlation analysis and scalar components of vector ARMA models, pioneered by Tiao and his collaborators, and vector ARMAX models in linear systems theory. It then presents a fast stepwise regression procedure that includes parsimonious variable selection followed by rank selection in stochastic regression models. The procedure overcomes a long-standing difficulty with parameter estimation in these models, the dauntingly large number of parameters in the matrix of regression coefficients relative to the sample size n. Recent attempts to address this difficulty have used group lasso and hard thresholding of small singular values to take advantage of coefficient and rank sparsity. However, the underlying theory is based on non-random or independent regressors, whereas the procedure and its underlying theory developed herein are applicable to stochastic regressors in multivariate time series models.

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