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The approach taken in this book is to studies monitored over time, what the Central Limit Theorem is to studies with only one analysis. Just as the Central Limit Theorem shows that test statistics involving very different types of clinical trial outcomes are asymptotically normal, this book shows that the joint distribution of the test statistics at different analysis times is asymptotically multivariate normal with the correlation structure of Brownian motion ("the B-value") irrespective of the test statistic. The so-called B-value approach to monitoring allows us to use, for different...

The approach taken in this book is to studies monitored over time, what the Central Limit Theorem is to studies with only one analysis. Just as the Central Limit Theorem shows that test statistics involving very different types of clinical trial outcomes are asymptotically normal, this book shows that the joint distribution of the test statistics at different analysis times is asymptotically multivariate normal with the correlation structure of Brownian motion ("the B-value") irrespective of the test statistic. The so-called B-value approach to monitoring allows us to use, for different...

Essentials of Probability Theory for Statisticians provides graduate students with a rigorous treatment of probability theory, with an emphasis on results central to theoretical statistics. It presents classical probability theory motivated with illustrative examples in biostatistics, such as outlier tests, monitoring clinical trials, and using adaptive methods to make design changes based on accumulating data. The authors explain different methods of proofs and show how they are useful for establishing classic probability results.

After building a...