Statisticians early

Up to this point we have used the symbol x with a subscript to indicate a factor (e.g., Xi, Xj, X3). In the early days of experimental design, however, a capital letter was usually used to represent a factor [see, for example, Davies (1956)]. Thus, what we would now call factor x, the early workers might have called factor A. What we would now call factor X2, statisticians might have called factor B. The notation x would represent factor C. An x x. interaction would be called an AB interaction. And so on. 

The likely effectiveness of the product, derived from the preclinical and early clinical work, will determine study design, complexity and size. It is a mistake to try to answer too many questions in a single study, despite the apparent commercial attractiveness of such a strategy. A study overburdened by many secondary objectives is more likely to fail when the design is implemented in many centres worldwide. What seems a good idea in head office can often be hard to implement in the clinic. Statistical advice is vital, and statisticians offer excellent opinions about the utility of complex study designs. 

Nevertheless, this approach is very popular in many exploratory situations and has the additional advantage that the data are easy to analyse. It is important to recognise, however, that experimental design has a long history, and a major influence on the minds of early experimentalists and statisticians has always been ease of calculation. Sometimes extra experiments are performed simply to produce a design that could be readily analysed using pencil and paper. It cannot be over-stressed that inverse matrices were very difficult to calculate manually, but modem computers now remove this difficulty. 

Richard Korherr was the leading statistician of the Third Reich. In early 1943, on Himmler s instructions, he drew up a report on the trends which European Jewish population statistics had exhibited since the NS had come to power. Himmler wanted to submit this report to Hitler. After several discussions and some correspondence with Himmler, Korherr revised and shortened his first report.82 These two reports as well as the correspondence that goes with them are counted among the allegedly central pieces of evidence proving the Holocaust, on whose basis G. Wellers, for example, believes he can set the number of victims of the Holocaust at approximately 2 million by late March 1943 alone.83... 

At rather infrequent intervals, statistical issues in the pharmaceutical industry have been debated by the Royal Statistical Society. Three read papers contain much of relevance to the work of the pharmaceutical statistician. Even though the first (Lewis, 1983), appeared nearly twenty-five years ago (at the time of writing), it is interesting to note that a number of the issues are still live. The second paper (Racine et al., 1986) is an early exposition of the use of Bayesian methods within the pharmaceutical industry, which, despite the fact that it pre-dates the Markov chain Monte-Carlo revolution introduced by Gelfand and Smith (1990) is still ahead of current practice in many respects. The third (Senn, 2000a) was written by me and, as might be expected, touches on a number of issues covered in this book. 

This Is an issue where consensus now seems to have been achieved. An ingenious theorem due to Fieller (Fieller, 1940, 1944) enables one to calculate a confidence interval for the ratio of two means. The approach does not require transformation of the original data. (Edgar C. Fieller, 1907—1960, is an early example of a statistician employed in the pharmaceutical industry. He worked for the Boots company in the late 1930s and 1940s.) For many years this was a common approach to making inferences about the ratio of the two mean AUCs in the standard bioequivalence experiment (Locke, 1984). 

Research conducted in the early 1960s tested the notion that people behave as intuitive statisticians who gather evidence and apply it in accordance with the Bayesian model of inference (Peterson and Beach 1967). Several studies evaluated how good people are at estimating statistical parameters, such as means, variances, and proportions. Other studies have compared human inferences obtained from probabilistic evidence to the prescriptions of Bayes rule. 

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