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 types of trials, the same boundaries and the same simple formula for computing conditional power. Although Brownian motion may sound complicated, the authors make the approach easy by starting with a simple example and building on it, one piece at a time, ultimately showing that Brownian motion works for many different types of clinical trials.

The book will be very valuable to statisticians involved in clinical trials. The main body of the chapters is accessible to anyone with knowledge of a standard mathematical statistics text. More mathematically advanced readers will find rigorous developments in appendices at the end of chapters. Reading the book will develop insight into not only monitoring, but power, survival analysis, safety, and other statistical issues germane to clinical trials.

Michael Proschan, Gordon Lan, and Janet Wittes are elected Fellows of the American Statistical Association. All have spent formative years in the Biostatistics Research Branch of the National Heart, Lung, and Blood Institute (NHLBI/NIH). While there, they were intimately involved in the design and statistical monitoring of large-scale randomized clinical trials, developing methodology to aid in their monitoring. For example, Lan developed, with DeMets, the now widely-used spending function approach to group sequential designs, whose properties were further investigated byProschan. The B-value approach used in the book was introduced in a very influential paper by Lan and Wittes. The statistical theory behind conditional power was developed by Lan, along with Simon and Halperin, and was the cornerstone for the conditional error approach to adaptive clinical trials introduced by Proschan and Hunsberger. All three authors have expertise in adaptive methodology for clinical trials.

Michael Proschan is a Mathematical Statistician at the National Institutes of Health; Gordon Lan is Senior Director of Biometrics at Johnson & Johnson Pharmaceutical Research and Development, L.L.C.; Janet Wittes is President of Statistics Collaborative, a statistical consulting company she founded in 1990.

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 foundation in probability, the text intersperses examples that make seemingly esoteric mathematical constructs more intuitive. These examples elucidate essential elements in definitions and conditions in theorems. In addition, counterexamples further clarify nuances in meaning and expose common fallacies in logic.

This text encourages students in statistics and biostatistics to think carefully about probability. It gives them the rigorous foundation necessary to provide valid proofs and avoid paradoxes and nonsensical conclusions.

Statistical Thinking in Clinical Trials combines a relatively small number of key statistical principles and several instructive clinical trials to gently guide the reader through the statistical thinking needed in clinical trials. Randomization is the cornerstone of clinical trials and randomization-based inference is the cornerstone of this book. Read this book to learn the elegance and simplicity of re-randomization tests as the basis for statistical inference (the analyze as you randomize principle) and see how re-randomization tests can save a trial that required an unplanned, mid-course design change.

Other principles enable the reader to quickly and confidently check calculations without relying on computer programs. The `EZ’ principle says that a single sample size formula can be applied to a multitude of statistical tests. The `O minus E except after V’ principle provides a simple estimator of the log odds ratio that is ideally suited for stratified analysis with a binary outcome. The same principle can be used to estimate the log hazard ratio and facilitate stratified analysis in a survival setting. Learn these and other simple techniques that will make you an invaluable clinical trial statistician.

Statistical Thinking in Clinical Trials combines a relatively small number of key statistical principles and several instructive clinical trials to gently guide the reader through the statistical thinking needed in clinical trials. Randomization is the cornerstone of clinical trials and randomization-based inference is the cornerstone of this book. Read this book to learn the elegance and simplicity of re-randomization tests as the basis for statistical inference (the analyze as you randomize principle) and see how re-randomization tests can save a trial that required an unplanned, mid-course design change.

Other principles enable the reader to quickly and confidently check calculations without relying on computer programs. The `EZ’ principle says that a single sample size formula can be applied to a multitude of statistical tests. The `O minus E except after V’ principle provides a simple estimator of the log odds ratio that is ideally suited for stratified analysis with a binary outcome. The same principle can be used to estimate the log hazard ratio and facilitate stratified analysis in a survival setting. Learn these and other simple techniques that will make you an invaluable clinical trial statistician.

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 types of trials, the same boundaries and the same simple formula for computing conditional power. Although Brownian motion may sound complicated, the authors make the approach easy by starting with a simple example and building on it, one piece at a time, ultimately showing that Brownian motion works for many different types of clinical trials.

The book will be very valuable to statisticians involved in clinical trials. The main body of the chapters is accessible to anyone with knowledge of a standard mathematical statistics text. More mathematically advanced readers will find rigorous developments in appendices at the end of chapters. Reading the book will develop insight into not only monitoring, but power, survival analysis, safety, and other statistical issues germane to clinical trials.

Michael Proschan, Gordon Lan, and Janet Wittes are elected Fellows of the American Statistical Association. All have spent formative years in the Biostatistics Research Branch of the National Heart, Lung, and Blood Institute (NHLBI/NIH). While there, they were intimately involved in the design and statistical monitoring of large-scale randomized clinical trials, developing methodology to aid in their monitoring. For example, Lan developed, with DeMets, the now widely-used spending function approach to group sequential designs, whose properties were further investigated byProschan. The B-value approach used in the book was introduced in a very influential paper by Lan and Wittes. The statistical theory behind conditional power was developed by Lan, along with Simon and Halperin, and was the cornerstone for the conditional error approach to adaptive clinical trials introduced by Proschan and Hunsberger. All three authors have expertise in adaptive methodology for clinical trials.

Michael Proschan is a Mathematical Statistician at the National Institutes of Health; Gordon Lan is Senior Director of Biometrics at Johnson & Johnson Pharmaceutical Research and Development, L.L.C.; Janet Wittes is President of Statistics Collaborative, a statistical consulting company she founded in 1990.

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 foundation in probability, the text intersperses examples that make seemingly esoteric mathematical constructs more intuitive. These examples elucidate essential elements in definitions and conditions in theorems. In addition, counterexamples further clarify nuances in meaning and expose common fallacies in logic.

This text encourages students in statistics and biostatistics to think carefully about probability. It gives them the rigorous foundation necessary to provide valid proofs and avoid paradoxes and nonsensical conclusions.

Statistical Thinking in Clinical Trials combines a relatively small number of key statistical principles and several instructive clinical trials to gently guide the reader through the statistical thinking needed in clinical trials. Randomization is the cornerstone of clinical trials and randomization-based inference is the cornerstone of this book. Read this book to learn the elegance and simplicity of re-randomization tests as the basis for statistical inference (the analyze as you randomize principle) and see how re-randomization tests can save a trial that required an unplanned, mid-course design change.

Other principles enable the reader to quickly and confidently check calculations without relying on computer programs. The `EZ’ principle says that a single sample size formula can be applied to a multitude of statistical tests. The `O minus E except after V’ principle provides a simple estimator of the log odds ratio that is ideally suited for stratified analysis with a binary outcome. The same principle can be used to estimate the log hazard ratio and facilitate stratified analysis in a survival setting. Learn these and other simple techniques that will make you an invaluable clinical trial statistician.

Statistical Thinking in Clinical Trials combines a relatively small number of key statistical principles and several instructive clinical trials to gently guide the reader through the statistical thinking needed in clinical trials. Randomization is the cornerstone of clinical trials and randomization-based inference is the cornerstone of this book. Read this book to learn the elegance and simplicity of re-randomization tests as the basis for statistical inference (the analyze as you randomize principle) and see how re-randomization tests can save a trial that required an unplanned, mid-course design change.

Other principles enable the reader to quickly and confidently check calculations without relying on computer programs. The `EZ’ principle says that a single sample size formula can be applied to a multitude of statistical tests. The `O minus E except after V’ principle provides a simple estimator of the log odds ratio that is ideally suited for stratified analysis with a binary outcome. The same principle can be used to estimate the log hazard ratio and facilitate stratified analysis in a survival setting. Learn these and other simple techniques that will make you an invaluable clinical trial statistician.