Generating random correlation matrices with fixed values: An application to the evaluation of multivariate surrogate endpoints

Abstract

When assessing surrogate endpoints in clinical studies under a causal-inference framework, a simulation-based sensitivity analysis is required, so as to sample the unidentifiable parameters across plausible values. To be precise, correlation matrices need to be sampled with only some of their entries identified from the data, known as the matrix completion problem. The positive-definiteness constraints are cumbersome functions involving all matrix entries, making this a challenging task. Some existing algorithms rely on sampling and then rejecting invalid solutions. A very efficient algorithm is built on previous work to generate large correlation matrices with some a prior fixed elements. The proposed methodology is applied to tackle a difficult problem in the surrogate marker field, namely, the evaluation of multivariate, potentially high-dimensional, surrogate endpoints. Whereas existing methods are limited to very low-dimensional surrogates, the new proposal is stable, fast, shows good properties, and is implemented in a user-friendly and freely available R package. (C) 2019 Elsevier B.V. All rights reserved.