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PubMed2000

A power analysis of microsatellite-based statistics for inferring past population growth.

We present results concerning the power to detect past population growth using three microsatellite-based statistics available in the current literature: (1) that based on between-locus variability, (2) that based on the shape of allele size distribution, and (3) that based on the imbalance between variance and heterozygosity at a locus. The analysis is based on the single-step stepwise mutation model. The power of the statistics is evaluated for constant, as well as variable, mutation rates across loci. The latter case is important, since it is a standard procedure to pool data collected at a number of loci, and mutation rates at microsatellite loci are known to be different. Our analysis indicates that the statistic based on the imbalance between allele size variance and heterozygosity at a locus has the highest power for detection of population growth, particularly when mutation rates vary across loci.

Evolution, Molecular↗
PubMed2004

Statistical pixelwise inference models for planar data analysis: an application to gamma-camera uniformity monitoring.

In this paper two tests based on statistical models are presented and used to assess, quantify and provide positional information of the existence of bias and/or variations between planar images acquired at different times but under similar conditions. In the first test a linear regression model is fitted to the data in a pixelwise fashion, using three mathematical operators. In the second test a comparison using z-scoring is used based on the assumption that Poisson statistics are valid. For both tests the underlying assumptions are as simple and few as possible. The results are presented as parametric maps of either the three operators or the z-score. The z-score maps can then be thresholded to show the parts of the images which demonstrate change. Three different thresholding methods (naive, adaptive and multiple) are presented: together they cover almost all the needs for separating the signal from the background in the z-score maps. Where the expected size of the signal is known or can be estimated, a spatial correction technique (referred to as the reef correction) can be applied. These tests were applied to flood images used for the quality control of gamma camera uniformity. Simulated data were used to check the validity of the methods. Real data were acquired from four different cameras from two different institutions using a variety of acquisition parameters. The regression model found the bias in all five simulated cases and it also found patterns of unstable regions in real data where visual inspection of the flood images did not show any problems. In comparison the z-map revealed the differences in the simulated images from as low as 1.8 standard deviations from the mean, corresponding to a differential uniformity of 2.2% over the central field of view. In all cases studied, the reef correction increased significantly the sensitivity of the method and in most cases the specificity as well. The two proposed tests can be used either separately or in combination and are capable of showing trends and/or the magnitude of difference between images acquired under similar conditions with high positional and statistical precision. In addition to gamma camera quality control, they could be applied to any pair (or set) of registered planar images to detect subtle changes, e.g. a set of scintigrams or conventional radiographs of a patient before, during and after treatment.

Computer Simulation↗
PubMed2006

Statistical analysis for haplotype-based matched case-control studies.

Using unphased genotype data, we studied statistical inference for association between a disease and a haplotype in matched case-control studies. Statistical inference for haplotype data is complicated due to ambiguity of genotype phases. An estimating equation-based method is developed for estimating odds ratios and testing disease-haplotype association. The method potentially can also be applied to testing haplotype-environment interaction. Simulation studies show that the proposed method has good performance. The performance of the method in the presence of departures from Hardy-Weinberg equilibrium is also studied.

Biometry↗
PubMed2007

Appropriateness of some resampling-based inference procedures for assessing performance of prognostic classifiers derived from microarray data.

The goal of many gene-expression microarray profiling clinical studies is to develop a multivariate classifier to predict patient disease outcome from a gene-expression profile measured on some biological specimen from the patient. Often some preliminary validation of the predictive power of a profile-based classifier is carried out using the same data set that was used to derive the classifier. Techniques such as cross-validation or bootstrapping can be used in this setting to assess predictive power, and if applied correctly, can result in a less biased estimate of predictive accuracy of a classifier. However, some investigators have attempted to apply standard statistical inference procedures to assess the statistical significance of associations between true and cross-validated predicted outcomes. We demonstrate in this paper that naïve application of standard statistical inference procedures to these measures of association under null situations can result in greatly inflated testing type I error rates. Under alternatives of small to moderate associations, confidence interval coverage probabilities may be too low, although for very large associations coverage probabilities approach their intended values. Our results suggest that caution should be exercised in interpreting some of the claims of exceptional prognostic classifier performance that have been reported in prominent biomedical journals in the past few years.

Clinical Trials as Topic↗
PubMed1998

Combining different line crosses for mapping quantitative trait loci using the identical by descent-based variance component method.

Mapping quantitative trait loci (QTLs) is usually conducted with a single line cross. The power of such QTL mapping depends highly on the two parental lines. If the two lines are fixed for the same allele at a putative QTL, the QTL is undetectable. On the other hand, if a QTL is segregating in the line cross and is detected, the estimated variance of the QTL cannot be extrapolated beyond the statistical inference space of the two parental lines. To reduce the likelihood of missing a QTL and to increase the statistical inference space of the estimated QTL variance, we present a consensus QTL mapping strategy. We adopt the identical by descent (IBD)-based variance component method originally applied to human linkage analysis by combining multiple line crosses as independent families. We explore the properties of consensus QTL mapping and demonstrate the method with F2, backcross (BC), and full-sib (FS) families. In addition, we examine the effects of the QTL heritability, marker informativeness, QTL position, the number of families, and family size. We show that F2 families notably outperform BC and FS families in detecting a QTL. There is a substantial reduction in the standard deviation of the estimated QTL position and the separation of the QTL and polygenic variance. Finally, we show that the power to detect a QTL is greater when using a small number of large families than a large number of small families.

Chromosome Mapping↗
PubMed1995

Inferring identify from DNA profile evidence.

The controversy over the interpretation of DNA profile evidence in forensic identification can be attributed in part to confusion over the mode(s) of statistical inference appropriate to this setting. Although there has been substantial discussion in the literature of, for example, the role of population genetics issues, few authors have made explicit the inferential framework which underpins their arguments. This lack of clarity has led both to unnecessary debates over ill-posed or inappropriate questions and to the neglect of some issues which can have important consequences. We argue that the mode of statistical inference which seems to underlie the arguments of some authors, based on a hypothesis testing framework, is not appropriate for forensic identification. We propose instead a logically coherent framework in which, for example, the roles both of the population genetics issues and of the nonscientific evidence in a case are incorporated. Our analysis highlights several widely held misconceptions in the DNA profiling debate. For example, the profile frequency is not directly relevant to forensic inference. Further, very small match probabilities may in some settings be consistent with acquittal. Although DNA evidence is typically very strong, our analysis of the coherent approach highlights situations which can arise in practice where alternative methods for assessing DNA evidence may be misleading.

Criminal Law↗
PubMed2003

Assessing treatment efficacy in noninferiority trials.

Often one of the primary objectives of an active-controlled noninferiority trial without a placebo arm is to assert that an experimental treatment would have been more effective than a putative placebo had the placebo been included in the trial. This may be an important consideration for regulatory applications. To achieve this objective, such a noninferiority analysis entails cross-trial statistical inference. Because of the uncertainty and difficulty surrounding cross-trial inference, the noninferiority analysis often aims to demonstrate that the experimental treatment preserves a specified fraction of the effect of the active control. The rationale is that by demonstrating the percent effect retention, the efficacy of the experimental treatment can be established with a great level of confidence. The confidence interval approach and synthesized test approach have been used for inferring the percent effect preservation. In this work we evaluate the type I error rates of these approaches to the cross-trial statistical inference for establishing treatment efficacy. The evaluation provides guidance as to what percentage of the control effect needs to be preserved so that through noninferiority testing of effect retention one can assert the treatment efficacy within a desired level of the error rate.

Clinical Trials as Topic↗
PubMed1993

Clinical importance, statistical significance and the assessment of economic and quality-of-life outcomes.

The assessment of economic and quality-of-life outcomes of health care interventions is moving into a new era, with such assessments increasingly being made within the context of controlled clinical trials. Traditionally the measurement of many variables in economic evaluations, particularly costs, has been deterministic. In the context of clinical trials the measurement of variables is stochastic, with the standard principles of statistical inference being applied to analyse differences between treatments in terms of effectiveness. Economists participating in clinical research are therefore being called upon to specify the sample size for the economic component of the evaluation and to undertake statistical tests for differences in cost or cost-effectiveness. This paper discusses the current methodological issues surrounding stochastic measurement in clinical trials, discusses the additional issues raised by the assessment of economic and quality-of-life outcomes and specifies the challenges facing economists if they are to answer the questions now being posed about economic analysis by statisticians and clinical researchers. It is concluded that application of the standard principles of statistical inference to economic data is not straightforward and will require value judgements to be made about statistical significance and economic importance, which may differ from those already made in purely clinical studies.

Confidence Intervals↗
PubMed1991

Statistical significance and fragility criteria for assessing a difference of two proportions.

This paper compares the traditional methods of statistical inference on the data from biomedical studies with a proposed index of fragility in the results. In general, for any given study there are 8 possible combinations of conclusions regarding statistical significance, quantitative significance and fragility. The 8 possibilities are considered in turn with respect to how studies in each group might be interpreted. Numerical examples show that not all 8 possibilities need be attainable with a given study design, and that the relative likelihood of them occurring can vary widely. It is concluded that the fragility index may be a useful adjunct to conventional statistical inference, with certain intuitive appeal, but that more empirical experience is needed with the fragility method.

Analysis of Variance↗
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↗
PubMed1999

Commentary: On the limited role of the "single-subject" design in psychology: hypothesis generating but not testing.

The "single-subject" design (which really denotes a design that employs too few subjects to allow statistical inferences concerning significance to be made) is useful only for the generation, but not for the testing or evaluation, of hypotheses concerning any psychological function. Those hypotheses that may be suggested by the "single-subject" design include ones about within-subject developmental effects (which may need to be studied over multiple sessions), as well as individual-difference-related variables. To adequately test any of those hypotheses, however, it is necessary to employ designs that vary both within- and between-subject factors, and that also examine various correlations in such a way that all effects (including correlational ones) can be evaluated by conventional modes of statistical inference.

Data Interpretation, Statistical↗
PubMed1992

An analytical method for assessing patterns of familial aggregation in case-control studies.

This paper describes an analytical method that is used to assess patterns of disease aggregation within family based on family history information collected in case-control studies. In such a study, cases and controls are thought of as probands whose relatives are identified, and relatives' phenotypes and other covariates such as age, sex, and genealogical relationship with the probands are recorded. By modeling the dependence of relatives' phenotypes on case-control status and other covariates, this method yields adjusted odds ratios that quantify familial aggregation. The estimated standard errors are obtained for statistical inference since the method acknowledges the potential correlations between relatives' phenotypes by using the estimating equations technique. In population-based case-control studies, the estimates and statistical inferences are generalizable to the general population. To illustrate this method, we analyzed a case-control study of colorectal cancer involving 5,190 relatives of 792 cases and 4,478 relatives of 680 population-based controls conducted in Hawaii. Although detailed results will be presented elsewhere, the colorectal cancer was found to aggregate within family with an odds ratio of 2.74 (95% confidence interval (CI): 1.78-4.21). Among parents, the odds ratio for familial aggregation was 2.38 (95% CI: 1.25-4.54). The corresponding value for siblings was 3.09 (95% CI: 1.87-5.11). It was also found that the odds ratio increases from about 2.00 for relatives of the probands who were 50 years or older to 7.66 and 12.84 for relatives of the probands who were between 40 and 50 years and under 40 years, respectively, suggesting that the familial aggregation of colorectal cancer decreases as probands' age increases.

Adult↗
PubMed1999

Statistical limitations in functional neuroimaging. I. Non-inferential methods and statistical models.

Functional neuroimaging (FNI) provides experimental access to the intact living brain making it possible to study higher cognitive functions in humans. In this review and in a companion paper in this issue, we discuss some common methods used to analyse FNI data. The emphasis in both papers is on assumptions and limitations of the methods reviewed. There are several methods available to analyse FNI data indicating that none is optimal for all purposes. In order to make optimal use of the methods available it is important to know the limits of applicability. For the interpretation of FNI results it is also important to take into account the assumptions, approximations and inherent limitations of the methods used. This paper gives a brief overview over some non-inferential descriptive methods and common statistical models used in FNI. Issues relating to the complex problem of model selection are discussed. In general, proper model selection is a necessary prerequisite for the validity of the subsequent statistical inference. The non-inferential section describes methods that, combined with inspection of parameter estimates and other simple measures, can aid in the process of model selection and verification of assumptions. The section on statistical models covers approaches to global normalization and some aspects of univariate, multivariate, and Bayesian models. Finally, approaches to functional connectivity and effective connectivity are discussed. In the companion paper we review issues related to signal detection and statistical inference.

Bayes Theorem↗
PubMed2001

Bootstrapping cluster analysis: assessing the reliability of conclusions from microarray experiments.

We introduce a general technique for making statistical inference from clustering tools applied to gene expression microarray data. The approach utilizes an analysis of variance model to achieve normalization and estimate differential expression of genes across multiple conditions. Statistical inference is based on the application of a randomization technique, bootstrapping. Bootstrapping has previously been used to obtain confidence intervals for estimates of differential expression for individual genes. Here we apply bootstrapping to assess the stability of results from a cluster analysis. We illustrate the technique with a publicly available data set and draw conclusions about the reliability of clustering results in light of variation in the data. The bootstrapping procedure relies on experimental replication. We discuss the implications of replication and good design in microarray experiments.

Analysis of Variance↗
PubMed2003

Analysis of higher-order neuronal interactions based on conditional inference.

Higher-order neural interactions, i.e., interactions that cannot be reduced to interactions between pairs of cells, have received increasing attention in the context of recent attempts to understand the cooperative dynamics in cortical neural networks. Typically, likelihood-ratio tests of log-linear models are being employed for statistical inference. The parameter estimation of these models for simultaneously recorded single-neuron spiking activities is a crucial ingredient of this approach. Extending a previous investigation of a two-neuron system, we present here the general formulation of an exact test suited for the detection of positive higher-order interactions between m neurons. This procedure does not require the estimation of any interaction parameters and additionally optimizes the test power of the statistical inference. We apply the approach to a three-neuron system and show how second-order and third-order interactions can be reliably distinguished. We study the performance of the method as a function of the interaction strength.

Action Potentials↗
PubMed1995

A measurement-theoretic analysis of the fuzzy logic model of perception.

The fuzzy logic model of perception (FLMP) is analyzed from a measurement-theoretic perspective. FLMP has an impressive history of fitting factorial data, suggesting that its probabilistic form is valid. The authors raise questions about the underlying processing assumptions of FLMP. Although FLMP parameters are interpreted as fuzzy logic truth values, the authors demonstrate that for several factorial designs widely used in choice experiments, most desirable fuzzy truth value properties fail to hold under permissible rescalings, suggesting that the fuzzy logic interpretation may be unwarranted. The authors show that FLMP's choice rule is equivalent to a version of G. Rasch's (1960) item response theory model, and the nature of FLMP measurement scales is transparent when stated in this form. Statistical inference theory exists for the Rasch model and its equivalent forms. In fact, FLMP can be reparameterized as a simple 2-category logit model, thereby facilitating interpretation of its measurement scales and allowing access to commercially available software for performing statistical inference.

Attention↗
PubMed2002

Teaching hypothesis tests--time for significant change?

Confusion in the teaching of statistical inference dates back to the conflict of Fisher's P-values and significance tests with the Neyman-Pearson hypothesis testing approach. To avoid the well-known pitfalls arising from over-reliance on significance tests and the division of results into 'significant' or 'not significant', many medical journals now insist that presentation of statistical analyses includes confidence intervals as well as or instead of P-values. The confusion over how to report statistical analyses which is evident in the recent medical literature is matched by divergent teaching of hypothesis tests between the 16 U.K. medical schools represented at the April 2000 Burwalls meeting. Suggested guidelines for the teaching of statistical inference to medical students are presented, and possible future developments are discussed.

Confidence Intervals↗