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Results for “statistical inference”

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PubMed1992

Statistical properties of the ordinary least-squares, generalized least-squares, and minimum-evolution methods of phylogenetic inference.

Statistical properties of the ordinary least-squares (OLS), generalized least-squares (GLS), and minimum-evolution (ME) methods of phylogenetic inference were studied by considering the case of four DNA sequences. Analytical study has shown that all three methods are statistically consistent in the sense that as the number of nucleotides examined (m) increases they tend to choose the true tree as long as the evolutionary distances used are unbiased. When evolutionary distances (dij's) are large and sequences under study are not very long, however, the OLS criterion is often biased and may choose an incorrect tree more often than expected under random choice. It is also shown that the variance-covariance matrix of dij's becomes singular as dij's approach zero and thus the GLS may not be applicable when dij's are small. The ME method suffers from neither of these problems, and the ME criterion is statistically unbiased. Computer simulation has shown that the ME method is more efficient in obtaining the true tree than the OLS and GLS methods and that the OLS is more efficient than the GLS when dij's are small, but otherwise the GLS is more efficient.

Biological Evolution↗
PubMed2003

Randomized clinical trial: myths around elementary statistical principles.

In discussing design and results of randomized clinical trials, in particular with clinical oncologists, one often encounters the opinion that a phase III trial is a complicated, highly costly, and difficult task. Part of this opinion seems to originate in myths around underlying biostatistical principles such as randomization, sampling and sample size, statistical hypotheses, statistical error probabilities, and statistical power. This work clarifies basic statistical issues of randomized clinical trials and the interpretation of their results. Six issues ('myths') relevant for the design of clinical trials and the interpretation of their results are addressed. They concern choice of study design, choice of participating centers, and recruitment of patients as well as statistical questions of establishing study hypotheses and interpreting p values. These myths are shown to be caused primarily through a misunderstanding of statistical inference and statistical thinking that can be avoided when a rational understanding of statistical principles is translated into a clinical research approach. We also conclude that before clinical evidence is summarized from different studies each study should be examined thoroughly.

Bias↗
PubMed1985

[Problems of multiple tests and evaluations in drug research].

The well known inferential statistical procedures only take into account the test of a single hypothesis or the estimation of a single parameter. In practical drug research the scientist in most cases is interested in multiple tests of several hypotheses or a simultaneous estimation of several parameters. After introducing the principal problems of simultaneous statistical inference several statistical methods are discussed. These methods can be applied to a variety of problems in drug research.

Pharmacology↗
PubMed2002

Approximate Bayesian computation in population genetics.

We propose a new method for approximate Bayesian statistical inference on the basis of summary statistics. The method is suited to complex problems that arise in population genetics, extending ideas developed in this setting by earlier authors. Properties of the posterior distribution of a parameter, such as its mean or density curve, are approximated without explicit likelihood calculations. This is achieved by fitting a local-linear regression of simulated parameter values on simulated summary statistics, and then substituting the observed summary statistics into the regression equation. The method combines many of the advantages of Bayesian statistical inference with the computational efficiency of methods based on summary statistics. A key advantage of the method is that the nuisance parameters are automatically integrated out in the simulation step, so that the large numbers of nuisance parameters that arise in population genetics problems can be handled without difficulty. Simulation results indicate computational and statistical efficiency that compares favorably with those of alternative methods previously proposed in the literature. We also compare the relative efficiency of inferences obtained using methods based on summary statistics with those obtained directly from the data using MCMC.

Bayes Theorem↗
PubMed2003

Bayesian analysis of quantitative antimicrobial assays.

Quantitative antimicrobial assays are used to assess the efficacy of chemical germicides. Standard methods for statistical analysis use log reduction (LR), the difference on the log scale between average surviving microbes for control and test carriers, as an efficacy measure. These methods have several deficiencies. The LR parameter is not on the original response scale, which complicates its interpretation. The presence of two different definitions of LR makes the statistical inference even more difficult. Current statistical methods for antimicrobial assay analysis rely on asymptotic normal theory, which might not work well for small samples. In addition, they do not appropriately incorporate censored ('too numerous to be counted') observations in the analysis. To overcome those problems, a new Bayesian approach is introduced here. It has also the advantages of more flexible statistical inference, and incorporated prior information in the model.

Bacteria↗
PubMed2006

Model weights and the foundations of multimodel inference.

Statistical thinking in wildlife biology and ecology has been profoundly influenced by the introduction of AIC (Akaike's information criterion) as a tool for model selection and as a basis for model averaging. In this paper, we advocate the Bayesian paradigm as a broader framework for multimodel inference, one in which model averaging and model selection are naturally linked, and in which the performance of AIC-based tools is naturally evaluated. Prior model weights implicitly associated with the use of AIC are seen to highly favor complex models: in some cases, all but the most highly parameterized models in the model set are virtually ignored a priori. We suggest the usefulness of the weighted BIC (Bayesian information criterion) as a computationally simple alternative to AIC, based on explicit selection of prior model probabilities rather than acceptance of default priors associated with AIC. We note, however, that both procedures are only approximate to the use of exact Bayes factors. We discuss and illustrate technical difficulties associated with Bayes factors, and suggest approaches to avoiding these difficulties in the context of model selection for a logistic regression. Our example highlights the predisposition of AIC weighting to favor complex models and suggests a need for caution in using the BIC for computing approximate posterior model weights.

Animals↗
PubMed2005

Misuse of statistical tests in Archives of Clinical Neuropsychology publications.

This article reviews the (mis)use of statistical tests in neuropsychology research studies published in the Archives of Clinical Neuropsychology in the years 1990-1992 and 1996-2000, and 2001-2004, prior to, commensurate with the internet-based and paper-based release, and following the release of the American Psychological Association's Task Force on Statistical Inference. The authors focused on four statistical errors: inappropriate use of null hypothesis tests, inappropriate use of P-values, neglect of effect size, and inflation of Type I error rates. Despite the recommendations of the Task Force on Statistical Inference published in 1999, the present study recorded instances of these statistical errors both pre- and post-APA's report, with only the reporting of effect size increasing after the release of the report. Neuropsychologists involved in empirical research should be better aware of the limitations and boundaries of hypothesis testing as well as the theoretical aspects of research methodology.

Bibliometrics↗
PubMed2006

Selecting the right statistical model for analysis of insect count data by using information theoretic measures.

Researchers and regulatory agencies often make statistical inferences from insect count data using modelling approaches that assume homogeneous variance. Such models do not allow for formal appraisal of variability which in its different forms is the subject of interest in ecology. Therefore, the objectives of this paper were to (i) compare models suitable for handling variance heterogeneity and (ii) select optimal models to ensure valid statistical inferences from insect count data. The log-normal, standard Poisson, Poisson corrected for overdispersion, zero-inflated Poisson, the negative binomial distribution and zero-inflated negative binomial models were compared using six count datasets on foliage-dwelling insects and five families of soil-dwelling insects. Akaike's and Schwarz Bayesian information criteria were used for comparing the various models. Over 50% of the counts were zeros even in locally abundant species such as Ootheca bennigseni Weise, Mesoplatys ochroptera Stål and Diaecoderus spp. The Poisson model after correction for overdispersion and the standard negative binomial distribution model provided better description of the probability distribution of seven out of the 11 insects than the log-normal, standard Poisson, zero-inflated Poisson or zero-inflated negative binomial models. It is concluded that excess zeros and variance heterogeneity are common data phenomena in insect counts. If not properly modelled, these properties can invalidate the normal distribution assumptions resulting in biased estimation of ecological effects and jeopardizing the integrity of the scientific inferences. Therefore, it is recommended that statistical models appropriate for handling these data properties be selected using objective criteria to ensure efficient statistical inference.

Animals↗
PubMed2004

Modeling missingness for time-to-event data: a case study in osteoporosis.

Clinical trials of long duration are often hampered by high dropout rates, making statistical inference and interpretation of results difficult. Statistical inference should be based on models selected according to whether missingness is independent of response [missing completely at random (MCAR)], or depends on response either through observed responses only [missing at random (MAR)] or through unobserved responses [nonignorable missing (NIM)]. If the dropout rate is high and little is known about the dropout mechanism, plausible nonignorable missing scenarios should be investigated as a sensitivity tool, offering the data analyst an understanding of the robustness of conclusions. Modeling missingness is illustrated by an analysis of an interval censored time-to-event outcome from a 5-year clinical trial on fracture response in osteoporosis in which the overall dropout rate was substantial. In this article, we provide an overview of a reanalysis accounting for possible nonignorable missingness, emphasize the importance of modeling the dropout and response mechanisms jointly, and highlight critical points arising in missing data problems.

Aged↗
PubMed2005

Correlation between gene expression levels and limitations of the empirical bayes methodology for finding differentially expressed genes.

Stochastic dependence between gene expression levels in microarray data is of critical importance for the methods of statistical inference that resort to pooling test statistics across genes. The empirical Bayes methodology in the nonparametric and parametric formulations, as well as closely related methods employing a two-component mixture model, represent typical examples. It is frequently assumed that dependence between gene expressions (or associated test statistics) is sufficiently weak to justify the application of such methods for selecting differentially expressed genes. By applying resampling techniques to simulated and real biological data sets, we have studied a potential impact of the correlation between gene expression levels on the statistical inference based on the empirical Bayes methodology. We report evidence from these analyses that this impact may be quite strong, leading to a high variance of the number of differentially expressed genes. This study also pinpoints specific components of the empirical Bayes method where the reported effect manifests itself.

Journal Article↗
PubMed2005

It's time.

Statistical inference involves taking the results of models and knowledge about probability to make decisions about the relationship in question. This commentary explains the usefulness of statistical inference to the drug development process, as well as some common pitfalls. It also examines reasons why statistical inference does not seem to be fully integrated into pharmacometric modeling. An example is shown that demonstrates the inferential advantages of mechanistic models. Both statisticians and pharmacometricians ought to take note of these advantages and integrate their efforts in order to maximize the decision-making potential of clinical research.

Analysis of Variance↗
PubMed2000

Inferring the statistical interpretation of quantum mechanics from the classical limit

It is widely believed that the statistical interpretation of quantum mechanics cannot be inferred from the Schrodinger equation itself, and must be stated as an additional independent axiom. Here I propose that the situation is not so stark. For systems that have both continuous and discrete degrees of freedom (such as coordinates and spin respectively), the statistical interpretation for the discrete variables is implied by requiring that the system's gross motion can be classically described under circumstances specified by the Schrodinger equation. However, this is not a full-fledged derivation of the statistical interpretation because it does not apply to the continuous variables of classical mechanics.

Journal Article↗
PubMed1989

Methodology for measuring health-state preferences--I: Measurement strategies.

Values play a critical part in decision making at both the individual and policy levels. Numerous methodologies for determining the preferences of individuals and groups have been proposed, but agreement has not been reached regarding their scientific adequacy and feasibility. This is the first of a four-part series of papers that analyzes and critiques the state-of-the-art in measuring preferences, particularly the measurement of health-state preferences. In this first paper we discuss the selection of relevant attributes to comprise the health-state descriptions, and the relative merits of three measurement strategies: holistic, explicitly decomposed, and statistically inferred decomposed. The functional measurement approach, a statistically inferred decomposed strategy, is recommended because it simultaneously validates the process by which judges combine attributes, the scale values they assign to health states, and the interval property of the scale.

Attitude to Health↗
PubMed2001

Prediction of crude protein and amino acid passage to the duodenum of lactating cows by models compared with in vivo data.

To determine whether statistical inferences obtained from predictions by models were similar to those of measured data from individual cows, data from six research trials published between 1989 and 1997 were simulated using the 1989 National Research Council Model, the Mepron Dairy Ration Evaluator (version 1.1), The University of Pennsylvania release of the Net Carbohydrate and Protein System (version 2.12p), The Cornell Net Carbohydrate and Protein System (version 3), and the CPM Dairy (version 1.0). Both predicted and measured protein fractions were analyzed by ANOVA and compared to determine whether statistical inferences among treatments from predictions by the models were similar to those from the measured data. The interpretations and statistical inferences of measured data did not always agree with those for predicted data. All models responded to changes in diet composition and often predicted that dietary changes would result in statistically different amounts of protein and amino acids passing to the duodenum than were observed in the measured data. The direction of predicted change among treatments for passage of nitrogen fractions to the duodenum also did not agree with the measured data a large percentage of the time. Discrepancies in ANOVA and interpretations between predicted and measured data may be due to the reduction in variation associated with modeling biological systems, associative effects of feeds not accounted for by models, inadequate equations in the models, inadequate description of feeds, or experimental error in measured data. Before model simulations of duodenal flow of crude protein and amino acids can be substituted for experimental measurements, better descriptors of main dietary effects, microbial protein production, ruminal protein degradation, and interactions among dietary factors must be developed.

Amino Acids↗
PubMed2000

Estimation and detection of event-related fMRI signals with temporally correlated noise: a statistically efficient and unbiased approach.

Recent developments in analysis methods for event-related functional magnetic resonance imaging (fMRI) has enabled a wide range of novel experimental designs. As with selective averaging methods used in event-related potential (ERP) research, these methods allow for the estimation of the average time-locked response to particular event-types, even when these events occur in rapid succession and in an arbitrary sequence. Here we present a flexible framework for obtaining efficient and unbiased estimates of event-related hemodynamic responses, in the presence of realistic temporally correlated (nonwhite) noise. We further present statistical inference methods based upon the estimated responses, using restriction matrices to formulate temporal hypothesis tests about the shape of the evoked responses. The accuracy of the methods is assessed using synthetic noise, actual fMRI noise, and synthetic activation in actual noise. Actual false-positive rates were compared to nominal false-positive rates assuming white noise, as well as local and global noise estimates in the estimation procedure (assuming white noise resulted in inappropriate inference, while both global and local estimates corrected false-positive rates). Furthermore, both local and global noise estimates were found to increase the statistical power of the hypothesis tests, as measured by the receiver operating characteristics (ROC). This approach thus enables appropriate univariate statistical inference with improved statistical power, without requiring a priori assumptions about the shape or timing of the event-related hemodynamic response.

Artifacts↗
PubMed1995

Assessing probability of paternity and the product rule in DNA systems.

The genetic resolution of paternity disputes begins with an intricate detection of inherited traits and finishes with a statistical inference (the probability of paternity, W). Notwithstanding some initial fanfare, statistical inference is a necessary component of DNA-based paternity tests because band patterns may be rare but not yet unique, and even rare events in a vacuum are meaningless. The genetic match must be combined with other evidence for relevancy, thus a Bayesian approach is preferred when computing W. This paper reviews the standard model used to compute W and discusses the model's various properties and assumptions. The standard model is extended to include DNA systems in which alleles are operationally continuous due to measurement error. This extension avoids problems associated with 'matched/non-matched' binned decisions. After outlining the model assumptions for a single DNA system, particular attention is given to the product rule-the procedure of multiplying intermediate probabilities across genetic loci to form a combined W. An empirical alternative to the product rule is also assessed and correlated with standard procedures.

Alleles↗
PubMed1997

A comparison of different staging systems predictability of patient outcome. Thyroid carcinoma as an example.

BACKGROUND: There is no consensus regarding the comparison of staging classifications. Recently, numerous staging classifications for thyroid carcinoma have been described. This study was performed to evaluate the relative discriminating ability of these different staging systems. METHODS: A literature review was conducted to identify the available staging classifications used for thyroid carcinoma. To compare the various staging classifications, cause specific survival data from a retrospective review of 382 patients with papillary and follicular thyroid carcinoma treated at Princess Margaret Hospital were applied to the various staging classifications. The ability of these classifications to distinguish the stage groupings were compared in the following ways: 1) tabulating the numbers of patients within each stage group; 2) collapsing stage groupings into high and low risk groups and calculating mortality rates at 10 and 15 years; 3) summing observed deviations at 5, 10, and 15 years; and 4) calculating the proportion of variance explained (PVE) for each staging classification, using each classification separately as a prognostic factor in a Cox regression model. RESULTS: The application of the PVE model, the only method of the four that used statistical inference, showed no statistically significant superiority of any system over the TNM classification of the American Joint Committee on Cancer (AJCC) and the International Union Against Cancer (UICC) in their ability to discriminate stage groupings. CONCLUSIONS: Because the TNM classification of the AJCC and UICC is universally available and widely accepted for other disease sites, the authors recommend it for all reports of the treatment and outcome of patients with thyroid carcinoma. Individual research groups also may use an alternative, validated classification to report results, provided that the outcomes are also reported using the TNM classification to facilitate comparison between different centers.

Adenocarcinoma, Follicular↗