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.     

Estimation and control of multiple testing error rates for microarray studies

The analysis of microarray data often involves performing a large number of statistical tests, usually at least one test per queried gene. Each test has a certain probability of reaching an incorrect inference; therefore, it is crucial to estimate or control error rates that measure the occurrence of erroneous conclusions in reporting and interpreting the results of a microarray study. In recent years, many innovative statistical methods have been developed to estimate or control various error rates for microarray studies. Researchers need guidance choosing the appropriate statistical methods for analysing these types of data sets. This review describes a family of methods that use a set of P-values to estimate or control the false discovery rate and similar error rates. Finally, these methods are classified in a manner that suggests the appropriate method for specific applications and diagnostic procedures that can identify problems in the analysis are described.     

Least squares regression methods for clustered ROC data with discrete covariates

The receiver operating characteristic (ROC) curve is a popular tool to evaluate and compare the accuracy of diagnostic tests to distinguish the diseased group from the nondiseased group when test results from tests are continuous or ordinal. A complicated data setting occurs when multiple tests are measured on abnormal and normal locations from the same subject and the measurements are clustered within the subject. Although least squares regression methods can be used for the estimation of ROC curve from correlated data, how to develop the least squares methods to estimate the ROC curve from the clustered data has not been studied. Also, the statistical properties of the least squares methods under the clustering setting are unknown. In this article, we develop the least squares ROC methods to allow the baseline and link functions to differ, and more importantly, to accommodate clustered data with discrete covariates. The methods can generate smooth ROC curves that satisfy the inherent continuous property of the true underlying curve. The least squares methods are shown to be more efficient than the existing nonparametric ROC methods under appropriate model assumptions in simulation studies. We apply the methods to a real example in the detection of glaucomatous deterioration. We also derive the asymptotic properties of the proposed methods.     

Statistical methods for model comparison in parameter estimation problems for distributed systems

In this note we outline some recent results on the development of a statistical testing methodology for inverse problems involving partial differential equation models. Applications to several problems from biology are presented. The statistical tests, which are in the spirit of analysis of variance (ANOVA), are based on asymptotic distributional results for estimators and residuals in a least squares approach.Research supported in part under grants NSF MCS 8504316, NASA NAG-1-517, and AFOSRF-49620-86-C-0111. Part of this research was carried out while the first author was a visiting scientist at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA, which is operated under NASA contracts NASI-18107 and NASI-18605     

Simple dynamic model of the human blood pressure regulatory system as based on the orthostatic load sequence]

The two statistical parameter estimation methods, the recursive least squares and the recursive generalized least squares, are dealt with briefly. An additional noncorrelated disturbance is necessary for unbiased parameter estimation in the closed-loop system. The disturbance is realized by an orthostatic load sequence shaped according to the experimental programme. Men and women were subjected to head-up tilt between 10 degrees and 55 degrees. The disturbance, mean blood pressure and heart rate were measured. These discrete data were used for parameter estimation of transfer functions.     

Comment on analyzing flow cytometric data for comparison of mean values of the coefficient of variation of the G1 peak.

BACKGROUND: The coefficient of variation (CV) is often used to characterize and summarize the flow cytometry analysis of nuclear DNA of the Go/G1 peak in a cell population within an individual organism. CV values are frequently used in subsequent statistical analysis to compare experimental groups of individuals. METHODS: We explain why the conventional analysis of variance, linear comparisons and regressions that employ the F and t-tests are not appropriate for analyzing CV data sets. The weighted least squares procedure which utilizes the chi-square test is presented as an adequate method. We further explain why this type of data needs to be analyzed by this procedure. RESULTS: To illustrate the application of the weighted least squares procedure, we analyzed a real data set that had been previously analyzed by conventional methods. We found that a non-significant result (p = 1) using the latter was significant when re-analyzed with the weighted least squares procedure (p = 0.032). CONCLUSIONS: Significant differences between treatments established by the weighted least squares often go unidentified by the conventional analysis. Use of the weighted least squares procedure is recommended for analyzing CV data sets.     

A note on using permutation-based false discovery rate estimates to compare different analysis methods for microarray data

MOTIVATION: False discovery rate (FDR) is defined as the expected percentage of false positives among all the claimed positives. In practice, with the true FDR unknown, an estimated FDR can serve as a criterion to evaluate the performance of various statistical methods under the condition that the estimated FDR approximates the true FDR well, or at least, it does not improperly favor or disfavor any particular method. Permutation methods have become popular to estimate FDR in genomic studies. The purpose of this paper is 2-fold. First, we investigate theoretically and empirically whether the standard permutation-based FDR estimator is biased, and if so, whether the bias inappropriately favors or disfavors any method. Second, we propose a simple modification of the standard permutation to yield a better FDR estimator, which can in turn serve as a more fair criterion to evaluate various statistical methods. RESULTS: Both simulated and real data examples are used for illustration and comparison. Three commonly used test statistics, the sample mean, SAM statistic and Student's t-statistic, are considered. The results show that the standard permutation method overestimates FDR. The overestimation is the most severe for the sample mean statistic while the least for the t-statistic with the SAM-statistic lying between the two extremes, suggesting that one has to be cautious when using the standard permutation-based FDR estimates to evaluate various statistical methods. In addition, our proposed FDR estimation method is simple and outperforms the standard method.     

Fragment-based local statistical potentials derived by combining an alphabet of protein local structures with secondary structures and solvent accessibilities

General and transferable statistical potentials to quantify the compatibility between local structures and local sequences of peptide fragments in proteins were derived. In the derivation, structure clusters of fragments are obtained by clustering five-residue fragments in native proteins based on their conformations represented by a local structure alphabet (de Brevern et al., Proteins 2000;41:271-287), secondary structure states, and solvent accessibilities. On the basis of the native sequences of the structurally clustered fragments, the probabilities of different amino acid sequences were estimated for each structure cluster. From the sequence probabilities, statistical energies as a function of sequence for a given structure were directly derived. The same sequence probabilities were employed in a database-matching approach to derive statistical energies as a function of local structure for a given sequence. Compared with prior models of local statistical potentials, we provided an integrated approach in which local conformations and local environments are treated jointly, structures are treated in units of fragments instead of individual residues so that coupling between the conformations of adjacent residues is included, and strong interdependences between the conformations of overlapping or neighboring fragment units are also considered. In tests including fragment threading, pseudosequence design, and local structure predictions, the potentials performed at least comparably and, in most cases, better than a number of existing models applicable to the same contexts indicating the advantages of such an integrated approach for deriving local potentials and suggesting applicability of the statistical potentials derived here in sequence designs and structure predictions.     

Resolution of fluorescence correlation measurements

The resolution limit of fluorescence correlation spectroscopy for two-component solutions is investigated theoretically and experimentally. The autocorrelation function for two different particles in solution were computed, statistical noise was added, and the resulting curve was fitted with a least squares fit. These simulations show that the ability to distinguish between two different molecular species in solution depends strongly on the number of photons detected from each particle, their difference in size, and the concentration of each component in solution. To distinguish two components, their diffusion times must differ by at least a factor of 1.6 for comparable quantum yields and a high fluorescence signal. Experiments were conducted with Rhodamine 6G and Rhodamine-labeled bovine serum albumin. The experimental results support the simulations. In addition, they show that even with a high fluorescence signal but significantly different quantum yields, the diffusion times must differ by a factor much bigger than 1.6 to distinguish the two components. Depending on the quantum yields and the difference in size, there exists a concentration threshold for the less abundant component below which it is not possible to determine with statistical means alone that two particles are in solution.     

A case study of the interpretation of linkage data using DNA fingerprinting probes

The statistical power of the technique of DNA fingerprinting relies greatly on the ability of the investigator to make an assumption that the presence or absence of different fingerprint bands are independent. Such linkage equilibrium is unlikely if bands are tightly linked to each other. Thus, when a new organism is to be investigated it is helpful to examine the segregation of parental bands into the offspring to confirm that the bands are not linked. By considering families of the tilapia Oreochrotnis niloticus , we produce statistical tests for linkage that can be applied to DNA fingerprint information. The use of these tests is more difficult and complicated if one parent is missing, but some progress can be made. We recommend that at least ten offspring are examined for segregation in families, since smaller numbers of offspring result in coincidental perfect agreements in band distributions in the absence of any linkage.     

An intervened Poisson distribution and its medical application

Among probability distributions that are used to describe a chance mechanism whose observational apparatus becomes active only when at least one event occurs is the zero-truncated Poisson distribution (ZTPD). A modified version of the ZTPD, which we call an intervened Poisson distribution (IPD), is discussed in this paper. We give a genesis of IPD and obtain its statistical properties. A numerical example is included to illustrate the results.     

A Comparison of Aggregate P-Value Methods and Multivariate Statistics for Self-Contained Tests of Metabolic Pathway Analysis

For pathway analysis of genomic data, the most common methods involve combining p-values from individual statistical tests. However, there are several multivariate statistical methods that can be used to test whether a pathway has changed. Because of the large number of variables and pathway sizes in genomics data, some of these statistics cannot be computed. However, in metabolomics data, the number of variables and pathway sizes are typically much smaller, making such computations feasible. Of particular interest is being able to detect changes in pathways that may not be detected for the individual variables. We compare the performance of both the p-value methods and multivariate statistics for self-contained tests with an extensive simulation study and a human metabolomics study. Permutation tests, rather than asymptotic results are used to assess the statistical significance of the pathways. Furthermore, both one and two-sided alternatives hypotheses are examined. From the human metabolomic study, many pathways were statistically significant, although the majority of the individual variables in the pathway were not. Overall, the p-value methods perform at least as well as the multivariate statistics for these scenarios.     

Testing the association of phenotypes with polyploidy: An example using herbaceous and woody eudicots

Although numerous studies have surveyed the frequency with which different plant characters are associated with polyploidy, few statistical tools are available to identify the factors that potentially facilitate polyploidy. We describe a new probabilistic model, BiChroM, designed to associate the frequency of polyploidy and chromosomal change with a binary phenotypic character in a phylogeny. BiChroM provides a robust statistical framework for testing differences in rates of polyploidy associated with phenotypic characters along a phylogeny while simultaneously allowing for evolutionary transitions between character states. We used BiChroM to test whether polyploidy is more frequent in woody or herbaceous plants, based on tree with 4711 eudicot species. Although polyploidy occurs in woody species, rates of chromosome doubling were over six times higher in herbaceous species. Rates of single chromosome increases or decreases were also far higher in herbaceous than woody species. Simulation experiments indicate that BiChroM performs well with little to no bias and relatively little variance at a wide range of tree depths when trees have at least 500 taxa. Thus, BiChroM provides a first step toward a rigorous statistical framework for assessing the traits that facilitate polyploidy.     

Reflections on univariate and multivariate analysis of metabolomics data

Metabolomics experiments usually result in a large quantity of data. Univariate and multivariate analysis techniques are routinely used to extract relevant information from the data with the aim of providing biological knowledge on the problem studied. Despite the fact that statistical tools like the t test, analysis of variance, principal component analysis, and partial least squares discriminant analysis constitute the backbone of the statistical part of the vast majority of metabolomics papers, it seems that many basic but rather fundamental questions are still often asked, like: Why do the results of univariate and multivariate analyses differ? Why apply univariate methods if you have already applied a multivariate method? Why if I do not see something univariately I see something multivariately? In the present paper we address some aspects of univariate and multivariate analysis, with the scope of clarifying in simple terms the main differences between the two approaches. Applications of the t test, analysis of variance, principal component analysis and partial least squares discriminant analysis will be shown on both real and simulated metabolomics data examples to provide an overview on fundamental aspects of univariate and multivariate methods.     

The Total Least Squares Method in Individual Bioequivalence Evaluation

We propose a simple method for comparison of series of matched observations. While in all our examples we address “individual bioequivalence” (IBE), which is the subject of much discussion in pharmaceutical statistics, the methodology can be applied to a wide class of cross‐over experiments, including cross‐over imaging. From the statistical point of view the considered models belong to the class of the “error‐in‐variables” models. In computational statistics the corresponding optimization method is referred to as the “least squares distance” and the “total least squares” method. The derived confidence regions for both intercept and slope provide the basis for formulation of the IBE criteria and methods for its assessing. Simple simulations show that the proposed approach is very intuitive and transparent, and, at the same time, has a solid statistical and computational background.     

COMPARATIVE METHODS FOR THE ANALYSIS OF CONTINUOUS VARIABLES: GEOMETRIC INTERPRETATIONS

Abstract This study is concerned with statistical methods used for the analysis of comparative data (in which observations are not expected to be independent because they are sampled across phylogenetically related species). The phylogenetically independent contrasts (PIC), phylogenetic generalized least‐squares (PGLS), and phylogenetic autocorrelation (PA) methods are compared. Although the independent contrasts are not orthogonal, they are independent if the data conform to the Brownian motion model of evolution on which they are based. It is shown that uncentered correlations and regressions through the origin using the PIC method are identical to those obtained using PGLS with an intercept included in the model. The PIC method is a special case of PGLS. Corrected standard errors are given for estimates of the ancestral states based on the PGLS approach. The treatment of trees with hard polytomies is discussed and is shown to be an algorithmic rather than a statistical problem. Some of the relationships among the methods are shown graphically using the multivariate space in which variables are represented as vectors with respect to OTUs used as coordinate axes. The maximum‐likelihood estimate of the autoregressive parameter, ρ, has not been computed correctly in previous studies (an appendix with MATLAB code provides a corrected algorithm). The importance of the eigenvalues and eigenvectors of the connection matrix, W, for the distribution of ρ is discussed. The PA method is shown to have several problems that limit its usefulness in comparative studies. Although the PA method is a generalized least‐squares procedure, it cannot be made equivalent to the PGLS method using a phylogenetic model.     

Practolol in Treatment of Angina Pectoris. A Double-blind Trial

Twenty-four patients with angina pectoris entered a double-blind trial of the cardioselective beta-adrenergic blocking agent practolol. Seventeen experienced less angina and consumed fewer glyceryl trinitrate tablets when on the active preparation. There was also a decrease in the mean number of attacks suffered by patients while on practolol and a reduction in the number of glyceryl trinitrate tablets taken. These results are of statistical significance at, at least, the 5% level.     

The “χ” of the Matter: Testing the Relationship between Paleoenvironments and Three Theropod Clades

The view of spinosaurs as dinosaurs of semi-aquatic habits and strongly associated with marginal and coastal habitats are deeply rooted in both scientific and popular knowledge, but it was never statistically tested. Inspired by a previous analysis of other dinosaur clades and major paleoenvironmental categories, here we present our own statistical evaluation of the association between coastal and terrestrial paleoenvironments and spinosaurids, along with other two theropod taxa: abelisaurids and carcharodontosaurids. We also included a taphonomic perspective and classified the occurrences in categories related to potential biases in order to better address our interpretations. Our main results can be summarized as follows: 1) the taxon with the largest amount of statistical evidence showing it positively associated to coastal paleoenvironments is Spinosauridae; 2) abelisaurids and carcharodontosaurids had more statistical evidence showing them positively associated with terrestrial paleoenvironments; 3) it is likely that spinosaurids also occupied spatially inland areas in a way somehow comparable at least to carcharodontosaurids; 4) abelisaurids may have been more common than the other two taxa in inland habitats.