Exact Sequential and Multistage Inference with Binary Response

• Activity Number: 351
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Health Policy Statistics Section
• Author(s): Iliana Ignatova*+ and Don Edwards and Roland C. Deutsch
• Companies: Cal Poly and University of South Carolina and The University of North Carolina at Greensboro
• Keywords: binary data ; Pascal's triangle ; SPRT ; sequential sampling

Abstract

We consider closed sequential or multistage sampling, with or without replacement, from a lot of N items, where each item can be identified as defective (in error, tainted, etc.) or not. The goal is inference on the proportion p of defectives in the lot. Until just a few years ago, inference on p was typically done approximately, even with a fixed sample size. In this paper we show that conservative inference on p using general elimination boundaries is completely tractable numerically and not at all inconvenient using modern statistical software. Functions for this purpose written in R are showcased. Results are applicable under either Frequentist or Bayesian approaches. Examples are provided for (1) sharpening Wald's (1947) SPRT for use in closed industrial acceptance sampling, and (2) two-stage sampling for auditing Medicare providers suspected of billing abuse.