A discrete markov chain representation of The sequential probability ratio test

Properties of the Sequential Probability Ratio Test (SPRT) are approximated by tests which can be represented exactly by discrete Markov chains with absorbing barriers. The approximating test S(d) is constructed by rounding the values of the cumulative sum test statistic of the SPRT to the nearest unit of size d > 0. Exact expressions are given for the properties of S(d) and approximations are obtained using the Perron Frobenius Theorem. The approach can be applied to both truncated and untruncated SPRT's based on either discrete or continuous test statistics. Examples are given for the sequential two sample grouped rank test of Wilcoxon, Rhodes, and Bradley (1963).