The authors present a highly theoretical book designed for a graduate course in biostatistics. The idea is not new. In 1971 Efron wrote a very popular article on a method of using a biased coin to force balance in a sequential experiment. That was one of the early ideas of this type and with the new popularity of adaptive designs in clinical trials the research in this area has advanced greatly. Although Efron's approach was practical and possible to impliment it was not used very often. My sense is that the new developments in this topic will lead to more use, justs as group sequential methods have allowed the mathematics of sequential analysis to more readily be used in applications.
The most common and most frequently taught approach to statistical inference is the frequentist approach. In the frequentist approach the observed sample is viewed as though it were independently drawn from a population with a specific but unknown probability distribution associated with it. In most courses this construct for the data is taken for granted, However it does have practical limitations. A rare attribute of this book is that it points out the practical limitations and sometimes artificial nature of the frequentist approach. These authors take a completely different approach to statistical inference which may be called the randomization approach. This approach may fall under the category of Fisherian inference that was the method of inference developed by R. A. Fisher at the same time as Neyman and Pearson were developing hypothesis testing and confidence intervals based on a frequentist approach.
The advantage of the authors' approach is that they do not need the concepts of sample space and repeated sampling to construct an probabilistic model for inference. Instead their model is based on the data being a reference set that is compared to other outcomes that could have arisen had the observations been permuted to mix up the allocation of the observed values among the treatment groups. So the inference is based on a permutation distribution that is valid under the null hypothesis that there is no difference between the observations in the two groups. If there were a difference the observed statistic would fall in one of the extreme tails of the permutation distribution.
In practice what is necessary to make this work is to have a well-defined randomization procedure for the allocation of the subjects to the treatment groups. This is typically done in phase III pharmaceutical trials where the FDA usually requires a randomized controlled clinical trial to establish the safety and efficacy of a new treatment.
Although this approach seems less restrictive then the frequentist approach and can also be used in observational studies where the frquentist approach breaks down, it requires the reader to know or learn a new statistical paradigm which technically draws a different kind of conclusion than the standard frequentist approach has to hypothesis testing and interval estimation of parameters.
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