Importance sampling to evaluate bivariate probabilities with an application to sequential Phase II trials

Abstract

In this paper we propose an importance sampling method for evaluating probabilities associated with the margins of a 2 × 2 table in a fixed or multistage design. These probabilities arise in the work of Conaway and Petroni (1994) on sequential phase I1 trials with bivariate endpoints. The importance sampling method proposed in this paper provides an efficient method, relative to exact enumeration and Monte Carlo techniques with no variance reduction, of estimating these probabilities. The method can also be adapted to estimate probabilities for the designs of Jennison and Turnbull (1993).