## A Class of Sequential Procedures for Medical Trials |

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### Contents

The Optimal Stopping Problem | 5 |

The Case 9 9n | 11 |

General Properties of the Stopping Sets | 18 |

4 other sections not shown

### Common terms and phrases

A+BT Approximate Power approximate upper bound arbitrary ASN Values ASN(p asymptotic risk asymptotic theory Bayesian binomial distribution Brownian motion process concave concave functions convex hull corresponding cost per observation defined denote Doctor of Philosophy E2YN error term Exact and Approximate expected loss expected sampling cost finite fixed sample func GSPRT half plane bounded Hence inf{n inner boundary Kiefer and Weiss Lemma 3-l line with slope lower boundary line LQ(n,sn LR statistics LR's martingale maximum sample min(e min(L minimize 2.6 n-s s n-s n,sn n>sn normal distribution null hypothesis optimal stopping rule optimal test parameter posterior probabilities Power and ASN power function problem Proof random variables random walk recursively rejection region resp rules which take sample size test Section SPRT STANFORD UNIVERSITY stopping and continuation Stopping Regions stopping sets test based treatment is inferior Various Sequential Tests Weiss 12 yields