Applications of statistical analysis in diagnostic histopathology and cytopathology

Corresponding to the rapid increase in the amount of data available for use in clinical diagnoses, there is an increased need for procedures that can provide the diagnostician with meaningful statistical summaries of data and with statements concerning the statistical significance associated with a diagnostic evaluation. It has been demonstrated that multivariate statistical assessment of clinical material can provide consistent, reliable and highly sensitive diagnostic clues, even in instances in which trained personnel are unable to see any change. Several examples of applications of statistical analyses in diagnostic cytology and histopathology are given in this paper. The examples were chosen to be illustrative of the different types of problems for which statistical analyses have been found useful. These problems differ with respect to the extent of the statistical methods thus far developed and the difficulty involved in developing further analyses. For many problems, appropriate statistical analyses are readily available; other problems require definition of custom-made test statistics and, in some cases, also definition of new statistical distributions. The problems discussed here are only a small sample of the existing problems, but they provide at least an indication of the scope of the role that statistics plays in cytopathologic and histopathologic diagnosis.     

A statistical mechanical theory of unfolding of globular proteins induced by preferential binding of solvent components in water-organic solvent systems

A statistical mechanical model was developed for use in connection with the problem of preferential binding of solvent components to proteins and of conformational transition in water-organic solvent systems. The model is a statistical one for the conformational transition of globular proteins induced by the adsorption of solutes in the solution, considered as a nearest-neighbor problem in statistical mechanics. Although a few illustrative examples are given, the actual interpretations of the experimental data using this theory are reserved for a later paper.     

powerlaw: A Python Package for Analysis of Heavy-Tailed Distributions

Power laws are theoretically interesting probability distributions that are also frequently used to describe empirical data. In recent years, effective statistical methods for fitting power laws have been developed, but appropriate use of these techniques requires significant programming and statistical insight. In order to greatly decrease the barriers to using good statistical methods for fitting power law distributions, we developed the powerlaw Python package. This software package provides easy commands for basic fitting and statistical analysis of distributions. Notably, it also seeks to support a variety of user needs by being exhaustive in the options available to the user. The source code is publicly available and easily extensible.     

An application of statistical models in mental health research

Two statistical models are presented to describe the admission-discharge process of a psychiatric unit. Both models have the form of Markov processes. Common statistical terms such as length of stay in hospital, time off books, patients on books, and number of admissions are related to characteristics of the models. The models permit an assessment of the effect of studying statistical data based on cohorts of individuals rather than individuals considered separately. In addition, with refinement, it is expected that these models will permit the use of more sophisticated statistical methods in psychiatric research problems. The authors wish to acknowledge the continuing support of the Psychiatric Services Branch, Saskatchewan Department of Health and National Health Grant 607-7-129.     

Statistics of disulfide bond formation in proteins

A new set of statistical expressions describing the reformation of disulfide bonds from SH groups is proposed. The results of the statistical calculations of disulfide bond reformation are discussed in terms of protein folding.     

Pairwise statistical significance of local sequence alignment using sequence-specific and position-specific substitution matrices

Pairwise sequence alignment is a central problem in bioinformatics, which forms the basis of various other applications. Two related sequences are expected to have a high alignment score, but relatedness is usually judged by statistical significance rather than by alignment score. Recently, it was shown that pairwise statistical significance gives promising results as an alternative to database statistical significance for getting individual significance estimates of pairwise alignment scores. The improvement was mainly attributed to making the statistical significance estimation process more sequence-specific and database-independent. In this paper, we use sequence-specific and position-specific substitution matrices to derive the estimates of pairwise statistical significance, which is expected to use more sequence-specific information in estimating pairwise statistical significance. Experiments on a benchmark database with sequence-specific substitution matrices at different levels of sequence-specific contribution were conducted, and results confirm that using sequence-specific substitution matrices for estimating pairwise statistical significance is significantly better than using a standard matrix like BLOSUM62, and than database statistical significance estimates reported by popular database search programs like BLAST, PSI-BLAST (without pretrained PSSMs), and SSEARCH on a benchmark database, but with pretrained PSSMs, PSI-BLAST results are significantly better. Further, using position-specific substitution matrices for estimating pairwise statistical significance gives significantly better results even than PSI-BLAST using pretrained PSSMs.     

The statistical implications of autocorrelation for detection in environmental health assessment

Many environmental health and risk assessment techniques and models aim at estimating the fluctuations of selected biological endpoints through the time domain as a means of assessing changes in the environment or the probability of a particular measurement level occurring. In either case, estimates of the sample variance and mean of the sample variance are crucial to making appropriate statistical inferences. The commonly employed statistical techniques for estimating both measures presume the data were generated by a covariance stationary process. In such cases, the observations are treated as independently and identically distributed and classical statistical testing methods are applied. However, if the assumption of covariance stationarity is violated, the resulting sample variance and variance of the sample mean estimates are biased. The bias compromises statistical testing procedures by increasing the probability of detecting significance in tests of mean and variance differences. This can lead to inappropriate decisions being made about the severity of environmental damage. Accordingly, it is argued that data sets be examined for correlation in the time domain and appropriate adjustments be made to the required estimators before they are used in statistical hypothesis testing. Only then can credible and scientifically defensible decisions be made by environmental decision makers and regulators.     

Informational parameters of nucleic acid and molecular evolution

From the point of view of information theory, a statistical analysis of 2000 nucleic acid sequences (732 coding regions and 1177 non-coding regions) is given. The sequences are grouped into 20 categories. The probability-order-difference (POD) matrix is defined which is used to analyse the evolutionary distance of any two categories of sequences. The informational parameters D1, D2 and X = (1 + D1/D2)-1 and F are calculated for each sequence and averaged in each category. The statistical dependence of these parameters on molecular evolution is discussed. It is found that [X] is a good statistical quantity which describes the vocabulary compositions as well as the grammatical constructions of the genetic language. From the statistical analysis it is shown that [X] may play an important role in investigating the evolutionary level of nucleic acid molecules.     

Wise use of statistical tools in ecological field studies

The currently dominating hypothetico-deductive research paradigm for ecology has statistical hypothesis testing as a basic element. Classic statistical hypothesis testing does, however, present the ecologist with two fundamental dilemmas when field data are to be analyzed: (1) that the statistically motivated demand for a random and representative sample and the ecologically motivated demand for representation of variation in the study area cannot be fully met at the same time; and (2) that the statistically motivated demand for independence of errors calls for sampling distances that exceed the scales of relevant pattern-generating processes, so that samples with statistically desirable properties will be ecologically irrelevant. Reasons for these dilemmas are explained by consideration of the classic statistical Neyman-Pearson test procedure, properties of ecological variables, properties of sampling designs, interactions between properties of the ecological variables and properties of sampling designs, and specific assumptions of the statistical methods. Analytic solutions to problems underlying the dilemmas are briefly reviewed. I conclude that several important research objectives cannot be approached without subjective elements in sampling designs. I argue that a research strategy entirely based on rigorous statistical testing of hypotheses is insufficient for field ecological data and that inductive and deductive approaches are complementary in the process of building ecological knowledge. I recommend that great care is taken when statistical tests are applied to ecological field data. Use of less formal modelling approaches is recommended for cases when formal testing is not strictly needed. Sets of recommendations, “Guidelines for wise use of statistical tools”, are proposed both for testing and for modelling. Important elements of wise-use guidelines are parallel use of methods that preferably belong to different methodologies, selection of methods with few and less rigorous assumptions, conservative interpretation of results, and abandonment of definitive decisions based a predefined significance level.     

SpA: web-accessible spectratype analysis: data management, statistical analysis and visualization

SUMMARY: SpA is a web-accessible system for the management, visualization and statistical analysis of T-cell receptor spectratype data. Users upload data from their spectratype analyzers to SpA, which saves the raw data and user-defined supplementary covariates to a secure database. The statistical engine performs several data analyses and statistical summaries. The visualization engine displays spectratype histograms in a Java applet and in an image file suitable for download. All of these results are also saved to the database and remain accessible to the user. Additional statistical tools specific to the analysis of multiple spectratypes are also available through the SpA interface. AVAILABILITY: The service is freely accessible via the web at http://www.duke.edu/~kepler/spa.html. Additional technical support and specialized statistical analysis and consultation are available by arrangement with the authors and, depending on the service requested, may be subject to fee.     

Problems with the statistical testing of panbiogeographic hypotheses

Abstract

Croizat regarded generalised tracks as having a statistical basis, their degree of justification being directly related to the number of individual tracks consistent with them. In order to be logically valid, however, such an approach needs to have an explicit statistical basis. Page (1987) attempts to provide this, proposing the following protocol. Tracks are treated as geographic minimum-spanning trees which in turn are represented numerically as binary connectivity matrices. The statistical significance of similarities between two connectivity matrices is assessed using a permutation-test of association, a test that was developed for comparing distancematrices. The null hypothesis for this test is defined by the set of alternative connectivity matrices corresponding to all possible permutations of the track-vertices. There are however, a number of problems with this statistical test when applied to connectivity matrices derived from panbiogeographic tracks, and these render invalid the procedure advocated by Page.     

The Concept of Additivity of Drug Combinations in the Case of Quantal Response

The concept of additivity of drug combinations is widely accepted in pharmacology and toxicology. Up to now, no general statistical methods to test that property are available. The present paper gives a mathematical formulation of additivity, a method to fit dose response surfaces under additivity assumption and a statistical test.     

The use of statistical tools in field testing of putative effects of genetically modified plants on nontarget organisms

To fulfill existing guidelines, applicants that aim to place their genetically modified (GM) insect‐resistant crop plants on the market are required to provide data from field experiments that address the potential impacts of the GM plants on nontarget organisms (NTO's). Such data may be based on varied experimental designs. The recent EFSA guidance document for environmental risk assessment (2010) does not provide clear and structured suggestions that address the statistics of field trials on effects on NTO's. This review examines existing practices in GM plant field testing such as the way of randomization, replication, and pseudoreplication. Emphasis is placed on the importance of design features used for the field trials in which effects on NTO's are assessed. The importance of statistical power and the positive and negative aspects of various statistical models are discussed. Equivalence and difference testing are compared, and the importance of checking the distribution of experimental data is stressed to decide on the selection of the proper statistical model. While for continuous data (e.g., pH and temperature) classical statistical approaches – for example, analysis of variance (ANOVA) – are appropriate, for discontinuous data (counts) only generalized linear models (GLM) are shown to be efficient. There is no golden rule as to which statistical test is the most appropriate for any experimental situation. In particular, in experiments in which block designs are used and covariates play a role GLMs should be used. Generic advice is offered that will help in both the setting up of field testing and the interpretation and data analysis of the data obtained in this testing. The combination of decision trees and a checklist for field trials, which are provided, will help in the interpretation of the statistical analyses of field trials and to assess whether such analyses were correctly applied.     

Making sense of score statistics for sequence alignments

The search for similarity between two biological sequences lies at the core of many applications in bioinformatics. This paper aims to highlight a few of the principles that should be kept in mind when evaluating the statistical significance of alignments between sequences. The extreme value distribution is first introduced, which in most cases describes the distribution of alignment scores between a query and a database. The effects of the similarity matrix and gap penalty values on the score distribution are then examined, and it is shown that the alignment statistics can undergo an abrupt phase transition. A few types of random sequence databases used in the estimation of statistical significance are presented, and the statistics employed by the BLAST, FASTA and PRSS programs are compared. Finally the different strategies used to assess the statistical significance of the matches produced by profiles and hidden Markov models are presented.     

Statistical predictions for the dynamics of a low-speed system: newtonian versus special-relativistic mechanics

The newtonian and special-relativistic statistical predictions for the mean, standard deviation and probability density function of the position and momentum are compared for the periodically-delta-kicked particle at low speed. Contrary to expectation, we find that the statistical predictions, which are calculated from the same parameters and initial gaussian ensemble of trajectories, do not always agree if the initial ensemble is sufficiently well-localized in phase space. Moreover, the breakdown of agreement is very fast if the trajectories in the ensemble are chaotic, but very slow if the trajectories in the ensemble are non-chaotic. The breakdown of agreement implies that special-relativistic mechanics must be used, instead of the standard practice of using newtonian mechanics, to correctly calculate the statistical predictions for the dynamics of a low-speed system.     

CTX-BLAST: context sensitive version of protein BLAST

We present a software tool CTX-BLAST that incorporates contextual alignment model into the popular protein BLAST program. Our alignment tool allows us to investigate the effect of context-dependency in the protein alignment much more efficient than using previous dynamic algorithms. The software makes use of non-symmetric contextual substitution tables and calculates the statistical significance of a given alignment according to the contextual statistical model. AVAILABILITY: CTX-BLAST is an open source software freely available from www.sourceforge.net/projects/CTX-BLAST. A program for statistical estimation of E-value parameters and the contextual substitution table CTX-BLOSUM62 are also provided. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Natural and orthogonal interaction framework for modeling gene-environment interactions with application to lung cancer

Objectives: We aimed at extending the Natural and Orthogonal Interaction (NOIA) framework, developed for modeling gene-gene interactions in the analysis of quantitative traits, to allow for reduced genetic models, dichotomous traits, and gene-environment interactions. We evaluate the performance of the NOIA statistical models using simulated data and lung cancer data. Methods: The NOIA statistical models are developed for additive, dominant, and recessive genetic models as well as for a binary environmental exposure. Using the Kronecker product rule, a NOIA statistical model is built to model gene-environment interactions. By treating the genotypic values as the logarithm of odds, the NOIA statistical models are extended to the analysis of case-control data. Results: Our simulations showed that power for testing associations while allowing for interaction using the NOIA statistical model is much higher than using functional models for most of the scenarios we simulated. When applied to lung cancer data, much smaller p values were obtained using the NOIA statistical model for either the main effects or the SNP-smoking interactions for some of the SNPs tested. Conclusion: The NOIA statistical models are usually more powerful than the functional models in detecting main effects and interaction effects for both quantitative traits and binary traits.