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PubMed2003

Adjusting for population heterogeneity: a framework for characterizing statistical information and developing efficient test statistics.

The focus of this work is the TDT-type and family-based test statistics used for adjusting for potential confounding due to population heterogeneity or misspecified allele frequencies. A variety of heuristics have been used to motivate and derive these statistics, and the statistics have been developed for a variety of analytic goals. There appears to be no general theoretical framework, however, that may be used to evaluate competing approaches. Furthermore, there is no framework to guide the development of efficient TDT-type and family-based methods for analytic goals for which methods have not yet been proposed. The purpose of this paper is to present a theoretical framework that serves both to identify the information which is available to methods that are immune to confounding due to population heterogeneity or misspecified allele frequencies, and to inform the construction of efficient unbiased tests in novel settings. The development relies on the existence of a characterization of the null hypothesis in terms of a completely specified conditional distribution of transmitted genotypes. An important observation is that, with such a characterization, when the conditioning event is unobserved or incomplete, there is statistical information that cannot be exploited by any exact conditional test. The main technical result of this work is an approach to computing test statistics for local alternatives that exploit all of the available statistical information.

Data Interpretation, Statistical↗
PubMed2003

Further statistics in dentistry. Part 9: Bayesian statistics.

Statistics can be defined as the methods used to assimilate data, so that guidance can be given, and conclusions drawn, in situations which involve uncertainty. In particular, statistical inference is concerned with drawing conclusions about particular aspects of a population when that population cannot be studied in full. Uncertainty arises here because the totality of the information is not available. Instead, to make inferences about the population, it is necessary to rely on a sample of data which is selected from the population; this sample data may be augmented, in certain circumstances, by auxiliary information which is obtained independently of the sample data. Clearly, uncertainty lies at the heart of statistics and statistical inference. This uncertainty is measured by a probability which therefore forms the crux of statistics and must be properly understood in order to interpret a statistical analysis.

Algorithms↗
PubMed2003

Tutorials in clinical research: part VII. Understanding comparative statistics (contrast)--part A: general concepts of statistical significance.

OBJECTIVES/HYPOTHESIS: The present tutorial is the seventh in a series of Tutorials in Clinical Research. The specific purpose of the tutorial (Part A) and its sequel (Part B) is to introduce and explain three commonly used statistical tools for assessing contrast in the comparison between two groups. STUDY DESIGN: Tutorial. METHODS: The authors met weekly for 10 months discussing clinical research studies and the applied statistics. The difficulty was not in the material but in the effort to make the report easy to read and as short as possible. RESULTS: The tutorial is organized into two parts. Part A, which is the present report, focuses on the fundamental concepts of the null hypothesis and comparative statistical significance. The sequel, Part B, discusses the application of three common statistical indexes of contrast, the chi2, Mann-Whitney U, and Student t tests. CONCLUSIONS: Assessing the validity of medical studies requires a working knowledge of research design and statistics; obtaining this knowledge need not be beyond the ability of the busy surgeon. The authors have tried to construct an accurate, easy-to-read, easy-to-apply, basic introduction to comparing two groups. The long-term goal of the present tutorial and others in the series is to facilitate basic understanding of clinical research, thereby stimulating reading of some of the numerous well-written research design and statistical texts. This knowledge may then be applied to the continuing educational review of the literature and the systematic prospective analysis of individual practices.

Bias↗
PubMed1998

Statistical methods in epidemiology: I. Statistical errors in hypothesis testing.

PURPOSE: Although scientific journal editors are making use of statisticians in the review process, the quality of statistical reporting in many journals remains poor. In many cases the problem for the scientist would appear to be a lack of understanding of basic statistics. The focus of the scientist is on showing 'p < 0.05', when what is actually required is a statement about effect size and interval estimation. The aim of this paper is to show the inadequacy of reporting of results using p-values alone. This paper is the first in a series detailing common statistical methods, with a view to aiding potential authors in their statistical presentation of data. METHOD: A review of the basic hypothesis test, using examples from the author's own teaching experiences. RESULTS: Type I and type II errors are defined; the problem of multiple comparisons is highlighted; interval estimation is introduced. CONCLUSIONS: The case for considering the p-value as an error probability is made which suggests ways of improving statistical presentation and thus expediting the statistical review process.

Confidence Intervals↗
PubMed2001

Improved statistical inference from DNA microarray data using analysis of variance and a Bayesian statistical framework. Analysis of global gene expression in Escherichia coli K12.

We describe statistical methods based on the t test that can be conveniently used on high density array data to test for statistically significant differences between treatments. These t tests employ either the observed variance among replicates within treatments or a Bayesian estimate of the variance among replicates within treatments based on a prior estimate obtained from a local estimate of the standard deviation. The Bayesian prior allows statistical inference to be made from microarray data even when experiments are only replicated at nominal levels. We apply these new statistical tests to a data set that examined differential gene expression patterns in IHF(+) and IHF(-) Escherichia coli cells (Arfin, S. M., Long, A. D., Ito, E. T., Tolleri, L., Riehle, M. M., Paegle, E. S., and Hatfield, G. W. (2000) J. Biol. Chem. 275, 29672-29684). These analyses identify a more biologically reasonable set of candidate genes than those identified using statistical tests not incorporating a Bayesian prior. We also show that statistical tests based on analysis of variance and a Bayesian prior identify genes that are up- or down-regulated following an experimental manipulation more reliably than approaches based only on a t test or fold change. All the described tests are implemented in a simple-to-use web interface called Cyber-T that is located on the University of California at Irvine genomics web site.

Bayes Theorem↗
PubMed1998

Can census offices publish statistics for more than one small area geography? An analysis of the differencing problem in statistical disclosure.

"The paper describes a problem faced by National Statistical Offices when publishing the results of decennial censuses for small geographical areas. If they publish statistical tables for two or more sets of areas, users can compare the tables and produce new statistics for the areas formed by differencing, which may have populations below confidentiality thresholds. To investigate the problem, the authors construct a software system and carry out a series of experiments using a large synthetic population base for Yorkshire and Humberside [in England]. The results indicate that publishing statistics for zones close in size to the primary areas is not safe unless the zones have been carefully designed. However, publishing statistics for sufficiently large areas such as 5km grid squares or postal sectors alongside enumeration districts is safe."

Censuses↗
PubMed1989

Statistical significance versus clinical relevance. Part I. The essential role of the power of a statistical test.

When comparing two treatment groups, hypothesis testing is widely used. However, clinical trialists should be more interested in statistical methods which elicit the magnitude of the differences between treatment groups, rather than a simple indication of whether or not the differences are statistically significant. Statistical significance does not necessarily imply clinical relevance. If the true difference between two treatment groups is so small that it is clinically irrelevant, a sample size can be found for which this difference is statistically significant. On the other hand, if the difference between treatment groups is statistically non-significant, it may still be clinically important. The limitations of conventional hypothesis testing of equal true means as such are highlighted. The need to control the power of the test--which takes into account the difference in treatment means which is considered important (clinically relevant) by the researcher--is discussed.

Clinical Trials as Topic↗
PubMed2001

Statistical learning in a serial reaction time task: access to separable statistical cues by individual learners.

The ability of adult learners to exploit the joint and conditional probabilities in a serial reaction time task containing both deterministic and probabilistic information was investigated. Learners used the statistical information embedded in a continuous input stream to improve their performance for certain transitions by simultaneously exploiting differences in the predictability of 2 or more underlying statistics. Analysis of individual learners revealed that although most acquired the underlying statistical structure veridically, others used an alternate strategy that was partially predictive of the sequences. The findings show that learners possess a robust learning device well suited to exploiting the relative predictability of more than I source of statistical information at the same time. This work expands on previous studies of statistical learning, as well as studies of artificial grammar learning and implicit sequence learning.

Adult↗
PubMed2000

An examination of graduate students' statistical judgments: statistical and fuzzy set approaches.

The present study examined how statistical significance levels are treated and interpreted by graduate students who use hypothesis-testing in their scientific investigation. To test underlying psychological aspects of hypothesis-testing, the idea of fuzzy set theory was employed to identify the uncertain points in judgments. 34 graduate students in a psychology department made judgments about hypothetical statistical decisions. The results indicated that (1) the majority of these students treated significance levels on a continuum and rated them according to the magnitude of statistical significance; (2) the subjects shifted their decisions based on the types of hypothetical scenarios but not by the sample sizes; instead, they interpreted a smaller sample size as being less reliable. (3) The subjects frequently chose formally used statistical terms, e.g., Significant and Not Significant, more than graduated verbal expressions, e.g., Marginally Significant and Borderline Significant; and (4) the Fuzziness (degree of confidence in decision-making) was dependent on individuals and existed more in the critical points of transition where judgments are most difficult. The Fuzziness Index illustrated the subtle shifts of human decision-making patterns in statistical judgments. Underlying decision uncertainties and difficulties can be illustrated by functions generated from fuzzy set theory, which may more closely resemble human psychological mechanism. This integrative study of fuzzy set theory and behavioral measurements appears to provide a technique that is more natural for examining and understanding imprecise boundaries of human decisions.

Adult↗
PubMed2004

Improved statistical test for nonstationarity using recurrence time statistics.

We have recently introduced a measure for nonstationarity using a recurrence time statistic to assess stationarity. In this paper we propose an extension of this method based on a detailed study of the statistics for the case of stationary systems. We derive a simple scheme that allows us to estimate the effective number of degrees of freedom relevant for this statistic. This substantially improves the statistical significance of the method and can be used to improve the significance of various other nonlinear statistics.

Journal Article↗
PubMed1989

Analysis of surveillance data: a rationale for statistical tests with comments on confidence intervals and statistical models.

In the examination of differences between subgroups in surveillance data, whether through simple counting or through sophisticated statistical modelling, the comparison is not between simple random samples from two or more populations. The rationale for statistical tests rests on an appeal to a model of random permutation of demographic and disease factors for the observed population during the surveillance period. The testing evaluates chance as a possible explanation for the observed results. In the analysis of internal structure in a surveillance data set, statistical tests produce a conceptually simple result that lends itself to concise presentation and flexible interpretation. Tests limit emphasis on probabilistic manipulation and on parameter estimates. They cannot stand alone, and thus encourage descriptive presentation of observations. In contrast, statistical models and confidence intervals emphasize parameters rather than distributions and compete with the data for limited space.

Data Interpretation, Statistical↗
PubMed1998

Recommendations for statistical designs of in vivo mutagenicity tests with regard to subsequent statistical analysis.

A workshop was held on September 13 and 14, 1993, at the GSF, Neuherberg, Germany, to start a discussion of experimental design and statistical analysis issues for three in vivo mutagenicity test systems, the micronucleus test in mouse bone marrow/peripheral blood, the chromosomal aberration tests in mouse bone marrow/differentiating spermatogonia, and the mouse dominant lethal test. The discussion has now come to conclusions which we would like to make generally known. Rather than dwell upon specific statistical tests which could be used for data analysis, serious consideration was given to test design. However, the test design, its power of detecting a given increase of adverse effects and the test statistics are interrelated. Detailed analyses of historical negative control data led to important recommendations for each test system. Concerning the statistical sensitivity parameters, a type I error of 0.05 (one tailed), a type II error of 0.20 and a dose related increase of twice the background (negative control) frequencies were generally adopted. It was recommended that sufficient observations (cells, implants) be planned for each analysis unit (animal) so that at least one adverse outcome (micronucleus, aberrant cell, dead implant) would likely be observed. The treated animal was the smallest unit of analysis allowed. On the basis of these general consideration the sample size was determined for each of the three assays. A minimum of 2000 immature erythrocytes/animal should be scored for micronuclei from each of at least 4 animals in each comparison group in the micronucleus assays. A minimum of 200 cells should be scored for chromosomal aberrations from each of at least 5 animals in each comparison group in the aberration assays. In the dominant lethal test, a minimum of 400 implants (40-50 pregnant females) are required per dose group for each mating period. The analysis unit for the dominant lethal test would be the treated male unless the background frequency of dead implants (DI) is so low that multiple males would need to be integrated to meet the minimum observation of one adverse outcome (DI) per analysis unit. A three-step strategy of data analysis was proposed for the cytogenetic assays. Use of negative historical controls was allowed in certain circumstances for interpretation of results from micronucleus tests and chromosomal aberration tests.

Animals↗
PubMedDate not supplied

Looking for statistical stability: a new method of evaluating reliability of statistical tests.

A new method of looking for statistical reliability, stability calculation, is described and is applied to statistical tests. Alike the power of statistical tests, stability calculation enables us to assess reliability of the latter. It belongs to the category of subsampling techniques that require using subsamples taken from the original sample. It provides descriptive and non-inferential results indicating the stability percentage: the percentage of sample elements to be removed, in order to change results obtained with the original sample. The higher is the stability percentage the more reliable is the statistical test. Stability percentage and power are correlated. Stability calculation provides informations about the elements in the sample, the most powerful points.

Computer Simulation↗
PubMed1998

Statistical quality control methods in infection control and hospital epidemiology, Part II: Chart use, statistical properties, and research issues.

This is the second in a two-part series discussing and illustrating the application of statistical process control (SPC) in hospital epidemiology. The basic philosophical and theoretical foundations of statistical quality control and their relation to epidemiology are emphasized in order to expand the mutual understanding and cross-fertilization between these two disciplines. Part I provided an overview of the philosophy and general approach of SPC, illustrated common types of control charts, and provided references for further information or statistical formulae. Part II now discusses alternate possible SPC approaches, statistical properties of control charts, chart-design issues and optimal control limit widths, some common misunderstandings, and more advanced issues. The focus of both articles is mostly nonmathematical, emphasizing important concepts and practical examples rather than academic theory and exhaustive calculations.

Data Display↗
PubMed2003

Methodological and statistical techniques: what do residents really need to know about statistics?

The purpose of this study was to catalog the statistical methods used in six journals two each from the fields of Family Practice, Emergency Medicine, and Obstetrics and Gynecology. We reviewed the quantitative articles from January 1998 through December 2000 from the Journal of Family Practice, the Journal of Family Medicine, the Annals of Emergency Medicine, the Journal of Academic Emergency Medicine. Articles from January 2000 through December 2000 of Obstetrics and Gynecology and the American Journal of Obstetrics and Gynecology were also included. Case reports and editorials were not included in this analysis. There were a total of 1828 articles reviewed (666 from Emergency Medicine articles, 380 from Family Practice, and 782 from Obstetrics and Gynecology). The distribution of study types (cross-sectional or survey, retrospective, or prospective) did not differ between the selected journals within Emergency Medicine, Family Practice, or Obstetrics and Gynecology. Pearson's chi-square/Fisher's Exact test was the statistic of choice overall (47.5%) followed by Student's t-test (33.1%). Analysis-of-variance was used in 23.3% of the studies, nonparametric methods (8.1%), linear regression (17.6%), and odds ratios/logistic regression (17.4%). Other statistical procedures were used less than 10% of the time. These results show that a physician who comfortably comprehends the appropriate use of descriptive statistics Student's t-test, Pearson's chi-square/Fisher's Exact test will be able to read and interpret at least 70% of the published medical literature. Educational efforts should focus on appropriate study design and analysis.

Clinical Competence↗