Power and Sample Size Investigation for Correlated Binary Data

• Activity Number: 522
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Biopharmaceutical Section
• Author(s): Dar Shong Hwang and James Lee*+ and Chyi-Hung Hsu
• Companies: BRSI and Daiichi Sankyo Pharma Development and Janssen Pharmaceuticals, Inc.
• Keywords: Multinomial to binomial transform ; repeated measurements ; correlated binary data ; power and sample size ; exact McNemar's test ; modified Cochran's Q test

Abstract

In repeated measurements or RBD with correlated binary response data, power and sample size determination is of great practical interest. The main stumbling block to the solution: the test distribution involves hard to interpret multinomial parameters, not the desired marginal binomial parameters P1, P2, ., Pk. Lennox and Sherman (2009) document the four decade-long endeavours to the solution of the simplest case- the matched pairs design or repeated measures with k=2 time points. Hwang and Lee(2009) reported that the 2-dimentional multinomial parameters Pij involved in the Exact McNemar test may be expressed as a function of the 1-dimentional or binomial parameters P1, P2 (hence odds ratio) and correlation. This multinomial to Binomial transformation enables researchers to specify P1 and P2 of interest and compute the power and sample size for each specified value of correlation. When correlation is 0, the sample size obtained is reduced to that of Fisher's exact test. Section I presents the power and sample size tables based on this transformation. Section II extends the methodology to the k=3 treatments or time points case which is analyzed by Modified Cochran's Q test (Hwang, Lee and Hsu (2004)). Here the 3 dimensional multinomial parameters Pijk of the test distribution are transformed first to 2-dim multinomial parameters and correlations, and then to 1-dim Binomial parameters P1, P2, P3 and correlations.