Statistics methodology

Detailed illustrations and examples are used throughout to develop basic statistical methodology for deahng with a broad area of applications. However, in addition to this material, there are many specialized topics as well as some veiy subtle areas which have not been discussed. The references should be used for more detailed information. 

I Andricioaei, JE Straub. On Monte Carlo and molecular dynamics methods inspired by Tsallis statistics Methodology, optimization, and application to atomic clusters. J Chem Phys 107 9117-9124, 1997. 

A problem may lie in the knowledge that is required as an essential input to such approaches, being both statistical in nature and from the authors own experiences, often diificult to obtain and interpret generally. Unfortunately, experienced designers will not use statistical methodology, although statistical methods should play an important role in the design and manufacture of reliable products (Amster and... 

Other examples in the Gottheb and Kubitzki (1983) paper, following similar statistical methodology and logic, concern chemical changes in the evolution of Aniba (Lauraceae) in the Amazon, and associated river basins and relationships among genera of Papilionoideae as a function of their accumulated alkaloids. These are complex examples that would repay careful study by interested readers. 

Overall, Brown s paper is a wonderful paper, despite the fact that there are some criticisms. The fact that it directly attacks the issue of nonlinearity in NIR is one reason to be so pleased to see it, but the other main reason is that it uses well-known and well-proven statistical methodology to do so. It is delightful to see classical Statistical tools used as the primary tool for analyzing this data set. 

Two of the major points to be made throughout this chapter are (1) the use of the appropriate statistical tests, and (2) the effects of small sample sizes (as is often the case in toxicology) on our selection of statistical techniques. Frequently, simple examination of the nature and distribution of data collected from a study can also suggest patterns and results which were unanticipated and for which the use of additional or alternative statistical methodology is warranted. It was these three points which caused the author to consider a section on scattergrams and their use essential for toxicologists. 

The Log-Rank Test is a statistical methodology for comparing the distribution of time until the occurrence of the event in independent groups. In toxicology, the most common event of interest is death or occurrence of a tumor, but it could just as well be liver failure, neurotoxicity, or any other event which occurs only once in an individual. The elapsed time from initial treatment or observation until the event is the event time, often referred to as survival time , even when the event is not death . 

Ho CK (2004) Probabilistic modeling of peracutaneous absorption for risk-based exposure assessments and transdermal drug delivery. Statistical Methodology 1 47-69... 

Discussion of Statistical Methodology. Previous work using similar statistical methods to these are given by Garden,... 

The research that we conducted, the Evergreen Project, was designed to avoid these problems. It was the largest study of its kind ever undertaken. We analyzed over 60,000 pages of information from 200 firms in multiple industries. In all, ten years of data were collected. The firms that were studied varied in size, and we complemented these broad extensive analyses with focused, in-depth exploration of issues of special interest. Both researchers and practitioners were involved. Fourteen prominent academics from Dartmouth, Harvard, Wharton, and other leading business schools were involved. Twenty-one practitioners implemented the study in coordination with the academic researchers. We interviewed journalists, executives, and Wall Street analysts. We let the answers come from the data, and then tested specific hypotheses to explore promising possibilities. And finally, we invented new statistical methodology that is appropriate to this level of complexity. 

For continuous data, there are still a number of outstanding issues regarding the benchmark including (Crump 2002) (1) definition of an adverse effect (2) whether to calculate the BMD from a continuous health outcome, or first convert the continuous response to a binary (yes/no) response (3) quantitative definition of the BMD, in particular in such a manner that BMD from continuous and binary data are commensurate (4) selection of a mathematical dose-response model for calculating a BMD (5) selection of the level of risk to which the BMD corresponds and (6) selection of a statistical methodology for implementing the calculation. 

Instances have occcured where claims have been based on published papers in which the arithmetic and/or statistical methodology was incorrect. Accordingly, before statistical information is included in promotional material it must have been subjected to statistical appraisal. 

ML is the approach most commonly used to fit a distribution of a given type (Madgett 1998 Vose 2000). An advantage of ML estimation is that it is part of a broad statistical framework of likelihood-based statistical methodology, which provides statistical hypothesis tests (likelihood-ratio tests) and confidence intervals (Wald and profile likelihood intervals) as well as point estimates (Meeker and Escobar 1995). MLEs are invariant under parameter transformations (the MLE for some 1-to-l function of a parameter is obtained by applying the function to the untransformed parameter). In most situations of interest to risk assessors, MLEs are consistent and sufficient (a distribution for which sufficient statistics fewer than n do not exist, MLEs or otherwise, is the Weibull distribution, which is not an exponential family). When MLEs are biased, the bias ordinarily disappears asymptotically (as data accumulate). ML may or may not require numerical optimization skills (for optimization of the likelihood function), depending on the distributional model. 

With regard to relevant statistical methodologies, it is possible to dehne 2 situations, which can be termed a meta-analysis context and a shrinkage estimation context. Similar statistical models, in particular random-effects models, may be applicable in both situations. However, the results of such a model will be used somewhat differently. 

WHO Collaborating Centre for Drug Statistics Methodology. 2004. Guidelines for ATC Classification and DDD Assignment. Oslo Norwegian Institute. 

Since the publication of ICH E9 there has been considerable debate about the validity of dynamic allocation, even with the random element. There is a school of thought which has some sympathy within regulatory circles that supports the view that the properties of standard statistical methodologies, notably p-values and confidence intervals, are not strictly valid when such allocation schemes are used. As a result regulators are very cautious ... 

The regulatory framework is forever changing and undoubtedly our statistical methodology will itself change to meet these new requirements. A new CHMP statistics guideline is planned, for example, in relation to conditional approval while the FDA are considering more therapeutic-specific recommendations in relation to the choice of the non-inferiority margin. 

It is important to enlist the help of statistical colleagues when putting publications together, not only in terms of the actual analysis, but in terms of the interpretation and reporting in the publication itself. Further, do cast a critical eye over the statistical methodology in the papers you review in order to spot these problem areas and again request the help of your statistical colleagues. 

---