Dr Fisher's casebook

It is an urban myth that the question most commonly asked of a medical statistician is "How large should my sample be?". In fact this is only the case when the statistician has a limited clientèle who have been well educated in statistics and know to come before conducting a study. Otherwise, the commonest questions are "Are these results significant?" and "What test should I apply?".     

Optimal Sequential Design in a Controlled Non-parametric Regression

Abstract. In a non‐parametric regression, the heteroscedasticity (dependence of the variance of the regression error on the predictor) can be a serious complication in estimation or visualization of an underlying regression function. If a controlled sampling is permitted, then the statistician can choose the design of predictors which attenuates the effect of heteroscedasticity. It is proposed to use a design which minimizes the mean integrated squared error of the regression function estimation. Then the corresponding optimal design density is proportional to the standard deviation of the regression error (the so‐called scale function). Because in general the statistician does not know an underlying scale function, the natural question is as follows: is it possible to suggest a sequential design which performs as well as an oracle that knows the underlying scale function? The answer is ‘yes’, and a corresponding sequential procedure is developed. It is proved, for the first time in the literature, that a data‐driven sequential design, together with an adaptive regression estimator, can mimic the oracle and be sharp minimax. Further, it is shown that the suggested method is feasible for small samples.     

Career story: Consultant Forensic Statistician

Ian Evett works for the Forensic Science Service as a consultant statistician. He tells Helen Joyce about the contribution a statistician can make to analysing handwriting, glass, DNA and other forensic materials, as well as to understanding the fundamentals of evidence interpretation.     

A century of t-tests

One hundred years ago, an author under the pseudonym of "Student" published a paper which was to become famous. It was entitled "The probable error of a mean". But what we now know as Student's t -test attracted little attention. It took another statistician of genius, R. A. Fisher, to amend, publicise and make it ubiquitous. But both Student's and Fisher's published versions were based upon faulty data. Stephen Senn reminds us of the third dedicated researcher and the quarter of a century delay before the story behind Student's t -test emerged.     

Career story: Pharmaceutical Statistician

Nobody could accuse the Royal Statistical Society's President Andy Grieve of looking for a quiet life. As well as being a consultant statistician for pharmaceuticals company Pfizer, he has for many years been heavily involved with the Society and Statisticians in the Pharmaceutical Industry. However, he claims to Helen Joyce that his early career was shaped by a fondness for "taking the easy option".     

The Scottish spoiled ballot: where was statistics?

In May 2007, Scotland went to the polls to elect both local constituency and regional members to the Scottish Parliament. Astonishingly, 100000 votes were rejected as "spoiled". Voters had misunderstood the new form of ballot paper—3% had marked a single cross despite having two votes. Parties contesting the election described it as "a debacle", "a shambles", "totally unsatisfactory". One American called it more flawed than Florida's notorious "hanging chad" ballot that gave the 2000 Presidential election to George Bush. What went wrong? Sheila Bird looks into the Scottish ballot paper.     

The Teacher's Corner: A Visual Derivation of Some Elementary Discrete Distributions

As a member of a clinical investigative team developing a protocol for a clinical trial, the statistician has broad responsibilities for ensuring the scientific integrity of the product. To prepare for this role, the statistician must study and learn in detail the clinical subject matter and must be prepared, if necessary, to teach the statistical principles of clinical trials to collaborators. This article discusses various issues that arise in the design of a clinical trial and how the statistician can participate in their resolution.     

Systematic handling of missing data in complex study designs – experiences from the Health 2000 and 2011 Surveys

We present a systematic approach to the practical and comprehensive handling of missing data motivated by our experiences of analyzing longitudinal survey data. We consider the Health 2000 and 2011 Surveys (BRIF8901) where increased non-response and non-participation from 2000 to 2011 was a major issue. The model assumptions involved in the complex sampling design, repeated measurements design, non-participation mechanisms and associations are presented graphically using methodology previously defined as a causal model with design, i.e. a functional causal model extended with the study design. This tool forces the statistician to make the study design and the missing-data mechanism explicit. Using the systematic approach, the sampling probabilities and the participation probabilities can be considered separately. This is beneficial when the performance of missing-data methods are to be compared. Using data from Health 2000 and 2011 Surveys and from national registries, it was found that multiple imputation removed almost all differences between full sample and estimated prevalences. The inverse probability weighting removed more than half and the doubly robust method 60% of the differences. These findings are encouraging since decreasing participation rates are a major problem in population surveys worldwide.     

Tweedie's Formula and Selection Bias

We suppose that the statistician observes some large number of estimates z(i), each with its own unobserved expectation parameter μ(i). The largest few of the z(i)'s are likely to substantially overestimate their corresponding μ(i)'s, this being an example of selection bias, or regression to the mean. Tweedie's formula, first reported by Robbins in 1956, offers a simple empirical Bayes approach for correcting selection bias. This paper investigates its merits and limitations. In addition to the methodology, Tweedie's formula raises more general questions concerning empirical Bayes theory, discussed here as "relevance" and "empirical Bayes information." There is a close connection between applications of the formula and James-Stein estimation.     

Statistical review by research ethics committees

This paper discusses some of the issues surrounding statistical review by research ethics committees (RECs). A survey of local RECs in 1997 revealed that only 27/184 (15%) included a statistician member at that time, although 70/175 (40%) recognized the need for such. The role of the statistician member is considered and the paper includes a summary of a meeting of the Royal Statistical Society to discuss statistical issues that frequently arise in the review of REC applications. A list of minimum qualifications which RECs should expect from anyone claiming to be a statistician would be useful, together with a list of statisticians who are well qualified and willing to serve on RECs, and a list of training courses for REC members covering the appropriate statistical issues.     

Issues with using baseline in last observation carried forward analysis

The topic of this paper was prompted by a study for which one of us was the statistician. It was submitted to Annals of Internal Medicine. The paper had positive reviewer comment; however, the statistical reviewer stated that for the analysis to be acceptable for publication, the missing data had to be accounted for in the analysis through the use of baseline in a last observation carried forward imputation. We discuss the issues associated with this form of imputation and recommend that it should not be undertaken as a primary analysis.     

Cousins: Charles Darwin, Sir Francis Galton and the birth of eugenics

Sir Francis Galton, scientist, African Explorer and statistician, was a key figure in statistical history. He was the man who devised the statistical concepts of regression and correlation. He was also Charles Darwin's cousin. And, inspired by his reading of Darwin, he was the founder of eugenics: the "science" of improving the human race through selective breeding. Nicholas Gillham tells of a darker side to statistics and heredity.     

THE CONTRIBUTION OF W. H. ARCHER TO VITAL STATISTICS IN THE COLONY OF VICTORIA

William Henry Archer, as Assistant Registrar General, was responsible for implementing the 1854 Registration Act in the colony of Victoria, and thereby helped establish the framework for official statistics in Australia. Eminently suitable for this role, having served his apprenticeship as an actuary and statistician in London prior to emigration in 1852, his career paralleled that of Dr. William Farr, the famous vital statistician. The greatest contribution Archer made to statistics in Australia was to put the lessons learnt by the statisticians of early Victorian England to advantage and place government statistical practices on a sound footing. Archer had a special interest in infant and childhood mortality, then accounting for one-half of all deaths in the new colony, and showed that a major factor was the extent of dysentery and diarrhoea during the warmer part of the year. Despite the high prevalence, Archer calculated the incidence of infant mortality to be less than in Europe at the time. Had he established links with the medical profession or with persons in the Social sciences who could have appreciated the valuable information being collected in the new government records, as in England where the sanitary reformers made great use of data collected by Farr for their own ends, Archer could have had a far greater impact on the intellectual and medical life of Victoria. Instead he was deflected into an administrative career which ended prematurely for political and religious reasons.     

The megalithic story of Professor Alexander Thom

Fifty years ago Alexander Thom, engineer, master surveyor and statistician, published a famous paper in a Royal Statistical Society journal and started a controversy. Our ancient ancestors, he said, had used a standard and astonishingly accurate measurement, the megalithic yard, to construct Stonehenge and hundreds of other megalithic monuments, all across northern Europe, and to align them as lunar observatories. Edmund Sixsmith rakes the ashes of Thom's intriguing claims.     

Back to basics: explaining sample size in outcome trials,are statisticians doing a thorough job?

Time to event outcome trials in clinical research are typically large, expensive and high‐profile affairs. Such trials are commonplace in oncology and cardiovascular therapeutic areas but are also seen in other areas such as respiratory in indications like chronic obstructive pulmonary disease. Their progress is closely monitored and results are often eagerly awaited. Once available, the top line result is often big news, at least within the therapeutic area in which it was conducted, and the data are subsequently fully scrutinized in a series of high‐profile publications. In such circumstances, the statistician has a vital role to play in the design, conduct, analysis and reporting of the trial. In particular, in drug development it is incumbent on the statistician to ensure at the outset that the sizing of the trial is fully appreciated by their medical, and other non‐statistical, drug development team colleagues and that the risk of delivering a statistically significant but clinically unpersuasive result is minimized. The statistician also has a key role in advising the team when, early in the life of an outcomes trial, a lower than anticipated event rate appears to be emerging. This paper highlights some of the important features relating to outcome trial sample sizing and makes a number of simple recommendations aimed at ensuring a better, common understanding of the interplay between sample size and power and the final result required to provide a statistically positive and clinically persuasive outcome. Copyright © 2009 John Wiley & Sons, Ltd.     

Life and death decisions

It has recently been suggested 1 that many clinical trials should have a data monitoring and ethics committee, and that on this committee should be a statistician. Such committees are attached to individual trials and are distinct from local ethics committees, which are not required to have a statistician and are not concerned solely with trials. Given the plethora of trials, there will be increasing demand for statisticians to sit on these committees. Although it is both an honour and a privilege, Mike Campbell warns that membership should not be undertaken lightly.     

Statistical games against a prophet-proof of a minimax conjecture

“Prophet theory” quantifies the price a statistician has to pay for his lack of information in stochastic sequences. In a recent paper, Schmitz (1991) gave a game-theoretical interpretation of this situation and he formulated in particular a minimax conjecture for the difference case. In this note we prove that conjecture and, moreover, present minimax ran domized stopping times (minimax procedures for the statistician).     

Opinion Poll Statistician

Bess Kemp works as a statistician for National Opinion Polls, the people who survey us to find out what we buy, what we watch, what we think. She tells all.     

Career story: Inside National Statistics

Karen Dunnell has worked as a government statistician for most of her career, and when Len Cook resigned as National Statistician earlier this year she was appointed to take over from him. She tells Helen Joyce about her career and the challenges that lie ahead.     

论《统计法》罚款对象的设定与完善——对第二十七条罚则的思索

《中华人民共和国统计法》(以下简称《统计法》)自1996年修正以来,至今已近十年,为统计事业的发展提供了坚实的法律保证。这十年中,统计的对象和所面临的社会经济环境变化很大,进一步完善统计法律法规,使之与时俱进,顺应社会经济的发展与进步,更好满足统计实践的需要,对《统计法》进行局部修订补充是必要的和必然的。结合多年来的基层统计执法感受,现行《统计法》对法律责任条款的部分规定尚有欠缺,尤其是《统计法》第二十七条有关罚款对象的设定亟待完善,疑需商榷改进。《统计法》第二十七条是法律责任的核心条款,也是基层统计执法查处违法…