Peter Westfall - Profile on Academia.edu (original) (raw)
Papers by Peter Westfall
How Well Do Multiple Testing Methods Scale Up when Both n and k Increase?
Journal of Biopharmaceutical Statistics, Apr 22, 2011
With increasingly massive data sets in biopharmaceutical research, particularly in genomic and re... more With increasingly massive data sets in biopharmaceutical research, particularly in genomic and related applications, there is concern about how well multiple comparisons methods "scale up" with increasing number of tests (k). Familywise error rate-controlling methods do not scale up well, and false discovery rate-controlling methods do scale up well with increasing k. But neither method scales up well with increasing sample size (n) when testing point nulls. We develop a loss function approach to investigate scale-up properties of various methods; we find that while Efron's recent proposal scales up best when both sample size n and number of tests k increase, but its performance otherwise can be erratic.
Directional Error Rates of Closed Testing Procedures
Statistics in Biopharmaceutical Research, Nov 1, 2013
ABSTRACT Closed multiple testing procedures are common in biopharmaceutical protocols. Whether th... more ABSTRACT Closed multiple testing procedures are common in biopharmaceutical protocols. Whether their directional error rates are controlled is largely an open problem. In this article, directional error rates are investigated using analytical, numerical, and Monte Carlo methods. This article presents a Monte Carlo variance-reduction method amenable to this purpose. A factorial design is used to identify possible problem areas, and directional error rates are simulated. No cases of excess directional error are found for typical applications involving noncentral multivariate T distributions. However, directional error rates in excess of the nominal are found when using regression function tests with nearly collinear linear combinations, both for one-sided and two-sided tests.
Using the SAS system : workbook
SAS Institute eBooks, 2000
Bayesian hypothesis testing for selected regression coefficients
Communications in Statistics, Jan 29, 2016
ABSTRACT We develop new Bayesian regression tests for prespecified regression coefficients. Simpl... more ABSTRACT We develop new Bayesian regression tests for prespecified regression coefficients. Simple, closed forms of the Bayes factors are derived that depend only on the regression t-statistic and F-statistic and the usual associated t and F distributions. The priors that allow those forms are simple and also meaningful, requiring minimal but practically important subjective inputs.
Is Bonferroni Admissible for Largem?
American Journal of Mathematical and Management Sciences, 2009
ABSTRACT Modern methods of multiple comparisons, particularly those based on controlling the fals... more ABSTRACT Modern methods of multiple comparisons, particularly those based on controlling the false discovery rate, are lax relative to the Bonferroni method in their assignment of significances; they are relatively more lax as m, the number of tests, increases. We point out that this laxness is based on an assumption concerning the size of the loss due to Type I errors relative to the loss due to Type II errors, and challenge the generality of this assumption, providing an alternative loss function for which the Bonferroni method is asymptotically (as m→∞) optimal.
Evaluation of the ability of power to predict low frequency lifting capacity
Ergonomics, Aug 1, 1998
An experiment was conducted to examine the role that maximal lifting power has in predicting maxi... more An experiment was conducted to examine the role that maximal lifting power has in predicting maximum acceptable weight of lift (MAWL) for a frequency of one lift per 8 h. The secondary aim of the study was to compare the ability of power to predict MAWL to previously used measures of capacity including two measures of isometric strength, five measures of isokinetic strength, and isoinertial capacity on an incremental lifting test. Twenty-five male subjects volunteered to participate in the experiment. The isometric tests involved maximum voluntary contractions for composite lifting strength at vertical heights of 15 and 75 cm. Peak isokinetic strength was measured at velocities of 0.1, 0.2, 0.4, 0.6 and 0.8 m s-1 using a modified CYBEX II isokinetic dynamometer. Isoinertial lifting capacity was measured on the X-factor incremental lifting machine and peak power was measured on the incremental lifting machine by having subjects lift a 25 kg load as quickly as possible. The results indicate that peak isoinertial power is significantly correlated with MAWL, and this correlation was higher than any of the correlations between the other predictor variables and MAWL. The relationships between the isokinetic strength measures and MAWL were stronger than the relationships between the isometric measures and MAWL. Overall, the results suggest that tests used to predict MAWL should be dynamic rather than static.
International Journal of Industrial Ergonomics, Jun 1, 1997
Despite extensive research efforts, disability due to work-related low-back disorders continues t... more Despite extensive research efforts, disability due to work-related low-back disorders continues to pose a significant economic burden to industry, and significant pain and economic loss to workers. Numerous epidemiological studies have been conducted, but many of these studies have resulted in qualitative guidelines rather than explicit quantitative guidelines. Furthermore, there is considerable disagreement and controversy concerning the validity of manual materials handling criteria based on biomechanical, physiological, and psychophysical theory and research. There is a pressing need for epidemiological field evaluation of such criteria, as well as epidemiologically-based models that provide estimates of low-back disability risk given a set of task, workplace and worker characteristics. A critical tool in such investigations is the statistical method chosen to model risk. The statistical appropriateness of previously used methods are reviewed and critiqued. A fairly comprehensive discussion of the statistical models available for modeling disability risk is then presented, with a focus on models that provide explicit estimates of risk. Recent advances in computer speed have significantly advanced the power and flexibility of statistical modeling techniques. These techniques have the potential to provide considerable insight into the etiology of low-back disability and to provide explicit quantitative design criteria for the ergonomics practitioner. Relevance to industry Statistical methods available for modeling the risk of low-back disability are discussed and previous methodologies used are critiqued. The methods discussed will aid researchers conducting epidemiological studies of low-back disorders in industry, and the discussion of these methods will aid practitioners faced with interpreting results of previous studies.
Biometrical Journal, Oct 1, 2008
Resampling-based multiple testing methods that control the Familywise Error Rate in the strong se... more Resampling-based multiple testing methods that control the Familywise Error Rate in the strong sense are presented. It is shown that no assumptions whatsoever on the data-generating process are required to obtain a reasonably powerful and flexible class of multiple testing procedures. Improvements are obtained with mild assumptions. The methods are applicable to gene expression data in particular, but more generally to any multivariate, multiple group data that may be character or numeric. The role of the disputed "subset pivotality" condition is clarified.
Multiple Comparisons and Multiple Tests Using SAS, Second Edition
Page 1. SAS® Press Multiple Comparisons and Multiple Tests Using SAS® Second Edition Peter H. Wes... more Page 1. SAS® Press Multiple Comparisons and Multiple Tests Using SAS® Second Edition Peter H. Westfall Randall D. Tobias Russell D. Wolfinger ... The correct bibliographic citation for this manual is as follows: Westfall, Peter H., Randall D. Tobias, and Russell D. Wolfinger. ...
Journal of Statistical Planning and Inference, Jun 1, 2011
We consider the multiple comparison problem where multiple outcomes are each compared among sever... more We consider the multiple comparison problem where multiple outcomes are each compared among several different collections of groups in a multiple group setting. In this case there are several different types of hypotheses, with each specifying equality of the distributions of a single outcome over a different collection of groups. Each type of hypothesis requires a different permutational approach. We show that under a certain multivariate condition it is possible to use closure over all hypotheses, although intersection hypotheses are tested using Boole's inequality in conjunction with permutation distributions in some cases. Shortcut tests are then found so that the resulting testing procedure is easily performed. The error rate and power of the new method is compared to existing competitors through simulation of correlated data. An example is analyzed, consisting of multiple adverse events in a clinical trial.
Robustness and Power of Tests for a Null Variance Ratio
Biometrika, Jun 1, 1988
SUMMARY A locally optimal test for a null variance ratio is considered in the context of the one-... more SUMMARY A locally optimal test for a null variance ratio is considered in the context of the one-way random effects model, when normality is assumed. Using an asymptotic design sequence with an increasing number of groups with bounded but unequal sizes, this test has the correct asymptotic level of significance for nonnormal data, a property which is not shared by the competing Wald test. Asymptotic power calculations demonstrate that the locally optimal test may be more powerful than the Wald test even in situations where the actual significance level of the Wald test overstates the nominal level.
The effect of error correlation on interfactor correlation in psychometric measurement
This article shows how interfactor correlation is affected by error correlations. Theoretical and... more This article shows how interfactor correlation is affected by error correlations. Theoretical and practical justifications for error correlations are given, and a new equivalence class of models is presented to explain the relationship between interfactor correlation and error correlations. The class allows simple, parsimonious modeling of error correlations via prespecifying reliabilities. Within the class, the correlation between latent factors can be as high as 1.0, and as low as the correlation between certain component scores. The models are indistinguishable in terms of parameter parsimony, identifiability, and fit statistics, implying that interfactor correlation is not identifiable within the class. The existence of the class is problematic for psychometric measurement, because estimates of interfactor correlation form the foundation of much of the literature.
Asymptotic Efficiencies of MINQUE and ANOVA Variance Component Estimates in the Nonnormal Random Model
The following question is addressed: For which quadratic unbiased estimates of variance component... more The following question is addressed: For which quadratic unbiased estimates of variance components, and under what asymptotic assumptions, are the estimates as efficient as estimates based on the random effects themselves, with or without the normality assumption? Westfall and Bremer (1993) have identified sufficient asymptotic conditions under which such an efficiency property holds for the ‘cell means estimates’ in the general k-way classification model. In this paper, the asymptotic behavior of MINQUE, ANOVA, and cell means estimates is considered in the one-way random model.
Simple and flexible Bayesian inferences for standardized regression coefficients
Journal of Applied Statistics, Feb 27, 2019
ABSTRACT In statistical practice, inferences on standardized regression coefficients are often re... more ABSTRACT In statistical practice, inferences on standardized regression coefficients are often required, but complicated by the fact that they are nonlinear functions of the parameters, and thus standard textbook results are simply wrong. Within the frequentist domain, asymptotic delta methods can be used to construct confidence intervals of the standardized coefficients with proper coverage probabilities. Alternatively, Bayesian methods solve similar and other inferential problems by simulating data from the posterior distribution of the coefficients. In this paper, we present Bayesian procedures that provide comprehensive solutions for inferences on the standardized coefficients. Simple computing algorithms are developed to generate posterior samples with no autocorrelation and based on both noninformative improper and informative proper prior distributions. Simulation studies show that Bayesian credible intervals constructed by our approaches have comparable and even better statistical properties than their frequentist counterparts, particularly in the presence of collinearity. In addition, our approaches solve some meaningful inferential problems that are difficult if not impossible from the frequentist standpoint, including identifying joint rankings of multiple standardized coefficients and making optimal decisions concerning their sizes and comparisons. We illustrate applications of our approaches through examples and make sample R functions available for implementing our proposed methods.
Field Evaluation of the Revised Niosh Lifting Equation
Proceedings of the Human Factors and Ergonomics Society ... Annual Meeting, Jul 1, 2000
The preliminary results of a prospective epidemiological study of the revised NIOSH lifting equat... more The preliminary results of a prospective epidemiological study of the revised NIOSH lifting equation are presented. The baseline evaluations included assessment of lifting and lowering tasks with the revised NIOSH equation, as well as a questionnaire regarding personal variables. Subject follow-up was primarily accomplished through postal questionnaires, telephone interviews, and surveillance for workers' compensation claims for low-back disorders. The preliminary results reported are based on approximately 375 person-years of exposure; however, the follow-up period is still in progress. Important findings related to the usability of the revised NIOSH equation across several types of common exposures are also discussed.
Evaluation of a weighted multiple comparison procedure
Pharmaceutical Statistics, 2005
... Received \60\re /teci *Correspondence to: Matthew Somerville, Statistics and Programming, Gla... more ... Received \60\re /teci *Correspondence to: Matthew Somerville, Statistics and Programming, GlaxoSmithKline, PO Box 13398, Research Triangle Park, NC 27709, USA. yE-mail:matt.c.somerville@gsk.com Page 2. ... Statistics in Medicine 1988; 7:877–888. 2. Moye LA. ...
The Power Function of Conditional Log-Linear Model Tests
Journal of the American Statistical Association, Mar 1, 1988
Abstract In fitting a log-linear model to data, it is common to examine the P values associated w... more Abstract In fitting a log-linear model to data, it is common to examine the P values associated with the conditional likelihood-ratio tests corresponding to a nested sequence of candidate log-linear models. For an appropriate Pitman sequence of models these test statistics are asymptotically independent and chi-squared in distribution. This article is an analytic study of the noncentrality parameters of these limiting distributions, pointing out factors that determine the powers of these tests. The conditional likelihood-ratio tests corresponding to a given nested sequence of log-linear models depend only on the models, but not on their parameterizations. The noncentrality parameters of their limiting chi-squared distributions depend on the pair of models compared, the true model, and the limiting model, but not on their parameterizations. Often a nested sequence of log-linear models is specified by a particular parameterization with adjacent models in the sequence differing only in the presence or absenc...
The American Statistician, 2018
Many Bayes factors have been proposed for comparing population means in two-sample (independent s... more Many Bayes factors have been proposed for comparing population means in two-sample (independent samples) studies. Recently, Wang and Liu (2015) presented an "objective" Bayes factor (BF) as an alternative to a "subjective" one presented by Gönen et al. (2005). Their report was evidently intended to show the superiority of their BF based on "undesirable behavior" of the latter. A wonderful aspect of Bayesian models is that they provide an opportunity to "lay all cards on the table." What distinguishes the various BFs in the two-sample problem is the choice of priors (cards) for the model parameters. This article discusses desiderata of BFs that have been proposed, and proposes a new criterion to compare BFs, no matter whether subjectively or objectively determined: A BF may be preferred if it correctly classifies the data as coming from the correct model most often. The criterion is based on a famous result in classification theory to minimize the total probability of misclassification. This criterion is objective, easily verified by simulation, shows clearly the effects (positive or negative) of assuming particular priors, provides new insights into the appropriateness of BFs in general, and provides a new answer to the question, "Which BF is best?"
Monte Carlo estimation of significance levels for carcinogenicity tests using univariate and multivariate models
Journal of Statistical Computation and Simulation, 1990
Special section: Teaching Bayes to nonstatistics graduate students
The American Statistician
How Well Do Multiple Testing Methods Scale Up when Both n and k Increase?
Journal of Biopharmaceutical Statistics, Apr 22, 2011
With increasingly massive data sets in biopharmaceutical research, particularly in genomic and re... more With increasingly massive data sets in biopharmaceutical research, particularly in genomic and related applications, there is concern about how well multiple comparisons methods "scale up" with increasing number of tests (k). Familywise error rate-controlling methods do not scale up well, and false discovery rate-controlling methods do scale up well with increasing k. But neither method scales up well with increasing sample size (n) when testing point nulls. We develop a loss function approach to investigate scale-up properties of various methods; we find that while Efron's recent proposal scales up best when both sample size n and number of tests k increase, but its performance otherwise can be erratic.
Directional Error Rates of Closed Testing Procedures
Statistics in Biopharmaceutical Research, Nov 1, 2013
ABSTRACT Closed multiple testing procedures are common in biopharmaceutical protocols. Whether th... more ABSTRACT Closed multiple testing procedures are common in biopharmaceutical protocols. Whether their directional error rates are controlled is largely an open problem. In this article, directional error rates are investigated using analytical, numerical, and Monte Carlo methods. This article presents a Monte Carlo variance-reduction method amenable to this purpose. A factorial design is used to identify possible problem areas, and directional error rates are simulated. No cases of excess directional error are found for typical applications involving noncentral multivariate T distributions. However, directional error rates in excess of the nominal are found when using regression function tests with nearly collinear linear combinations, both for one-sided and two-sided tests.
Using the SAS system : workbook
SAS Institute eBooks, 2000
Bayesian hypothesis testing for selected regression coefficients
Communications in Statistics, Jan 29, 2016
ABSTRACT We develop new Bayesian regression tests for prespecified regression coefficients. Simpl... more ABSTRACT We develop new Bayesian regression tests for prespecified regression coefficients. Simple, closed forms of the Bayes factors are derived that depend only on the regression t-statistic and F-statistic and the usual associated t and F distributions. The priors that allow those forms are simple and also meaningful, requiring minimal but practically important subjective inputs.
Is Bonferroni Admissible for Largem?
American Journal of Mathematical and Management Sciences, 2009
ABSTRACT Modern methods of multiple comparisons, particularly those based on controlling the fals... more ABSTRACT Modern methods of multiple comparisons, particularly those based on controlling the false discovery rate, are lax relative to the Bonferroni method in their assignment of significances; they are relatively more lax as m, the number of tests, increases. We point out that this laxness is based on an assumption concerning the size of the loss due to Type I errors relative to the loss due to Type II errors, and challenge the generality of this assumption, providing an alternative loss function for which the Bonferroni method is asymptotically (as m→∞) optimal.
Evaluation of the ability of power to predict low frequency lifting capacity
Ergonomics, Aug 1, 1998
An experiment was conducted to examine the role that maximal lifting power has in predicting maxi... more An experiment was conducted to examine the role that maximal lifting power has in predicting maximum acceptable weight of lift (MAWL) for a frequency of one lift per 8 h. The secondary aim of the study was to compare the ability of power to predict MAWL to previously used measures of capacity including two measures of isometric strength, five measures of isokinetic strength, and isoinertial capacity on an incremental lifting test. Twenty-five male subjects volunteered to participate in the experiment. The isometric tests involved maximum voluntary contractions for composite lifting strength at vertical heights of 15 and 75 cm. Peak isokinetic strength was measured at velocities of 0.1, 0.2, 0.4, 0.6 and 0.8 m s-1 using a modified CYBEX II isokinetic dynamometer. Isoinertial lifting capacity was measured on the X-factor incremental lifting machine and peak power was measured on the incremental lifting machine by having subjects lift a 25 kg load as quickly as possible. The results indicate that peak isoinertial power is significantly correlated with MAWL, and this correlation was higher than any of the correlations between the other predictor variables and MAWL. The relationships between the isokinetic strength measures and MAWL were stronger than the relationships between the isometric measures and MAWL. Overall, the results suggest that tests used to predict MAWL should be dynamic rather than static.
International Journal of Industrial Ergonomics, Jun 1, 1997
Despite extensive research efforts, disability due to work-related low-back disorders continues t... more Despite extensive research efforts, disability due to work-related low-back disorders continues to pose a significant economic burden to industry, and significant pain and economic loss to workers. Numerous epidemiological studies have been conducted, but many of these studies have resulted in qualitative guidelines rather than explicit quantitative guidelines. Furthermore, there is considerable disagreement and controversy concerning the validity of manual materials handling criteria based on biomechanical, physiological, and psychophysical theory and research. There is a pressing need for epidemiological field evaluation of such criteria, as well as epidemiologically-based models that provide estimates of low-back disability risk given a set of task, workplace and worker characteristics. A critical tool in such investigations is the statistical method chosen to model risk. The statistical appropriateness of previously used methods are reviewed and critiqued. A fairly comprehensive discussion of the statistical models available for modeling disability risk is then presented, with a focus on models that provide explicit estimates of risk. Recent advances in computer speed have significantly advanced the power and flexibility of statistical modeling techniques. These techniques have the potential to provide considerable insight into the etiology of low-back disability and to provide explicit quantitative design criteria for the ergonomics practitioner. Relevance to industry Statistical methods available for modeling the risk of low-back disability are discussed and previous methodologies used are critiqued. The methods discussed will aid researchers conducting epidemiological studies of low-back disorders in industry, and the discussion of these methods will aid practitioners faced with interpreting results of previous studies.
Biometrical Journal, Oct 1, 2008
Resampling-based multiple testing methods that control the Familywise Error Rate in the strong se... more Resampling-based multiple testing methods that control the Familywise Error Rate in the strong sense are presented. It is shown that no assumptions whatsoever on the data-generating process are required to obtain a reasonably powerful and flexible class of multiple testing procedures. Improvements are obtained with mild assumptions. The methods are applicable to gene expression data in particular, but more generally to any multivariate, multiple group data that may be character or numeric. The role of the disputed "subset pivotality" condition is clarified.
Multiple Comparisons and Multiple Tests Using SAS, Second Edition
Page 1. SAS® Press Multiple Comparisons and Multiple Tests Using SAS® Second Edition Peter H. Wes... more Page 1. SAS® Press Multiple Comparisons and Multiple Tests Using SAS® Second Edition Peter H. Westfall Randall D. Tobias Russell D. Wolfinger ... The correct bibliographic citation for this manual is as follows: Westfall, Peter H., Randall D. Tobias, and Russell D. Wolfinger. ...
Journal of Statistical Planning and Inference, Jun 1, 2011
We consider the multiple comparison problem where multiple outcomes are each compared among sever... more We consider the multiple comparison problem where multiple outcomes are each compared among several different collections of groups in a multiple group setting. In this case there are several different types of hypotheses, with each specifying equality of the distributions of a single outcome over a different collection of groups. Each type of hypothesis requires a different permutational approach. We show that under a certain multivariate condition it is possible to use closure over all hypotheses, although intersection hypotheses are tested using Boole's inequality in conjunction with permutation distributions in some cases. Shortcut tests are then found so that the resulting testing procedure is easily performed. The error rate and power of the new method is compared to existing competitors through simulation of correlated data. An example is analyzed, consisting of multiple adverse events in a clinical trial.
Robustness and Power of Tests for a Null Variance Ratio
Biometrika, Jun 1, 1988
SUMMARY A locally optimal test for a null variance ratio is considered in the context of the one-... more SUMMARY A locally optimal test for a null variance ratio is considered in the context of the one-way random effects model, when normality is assumed. Using an asymptotic design sequence with an increasing number of groups with bounded but unequal sizes, this test has the correct asymptotic level of significance for nonnormal data, a property which is not shared by the competing Wald test. Asymptotic power calculations demonstrate that the locally optimal test may be more powerful than the Wald test even in situations where the actual significance level of the Wald test overstates the nominal level.
The effect of error correlation on interfactor correlation in psychometric measurement
This article shows how interfactor correlation is affected by error correlations. Theoretical and... more This article shows how interfactor correlation is affected by error correlations. Theoretical and practical justifications for error correlations are given, and a new equivalence class of models is presented to explain the relationship between interfactor correlation and error correlations. The class allows simple, parsimonious modeling of error correlations via prespecifying reliabilities. Within the class, the correlation between latent factors can be as high as 1.0, and as low as the correlation between certain component scores. The models are indistinguishable in terms of parameter parsimony, identifiability, and fit statistics, implying that interfactor correlation is not identifiable within the class. The existence of the class is problematic for psychometric measurement, because estimates of interfactor correlation form the foundation of much of the literature.
Asymptotic Efficiencies of MINQUE and ANOVA Variance Component Estimates in the Nonnormal Random Model
The following question is addressed: For which quadratic unbiased estimates of variance component... more The following question is addressed: For which quadratic unbiased estimates of variance components, and under what asymptotic assumptions, are the estimates as efficient as estimates based on the random effects themselves, with or without the normality assumption? Westfall and Bremer (1993) have identified sufficient asymptotic conditions under which such an efficiency property holds for the ‘cell means estimates’ in the general k-way classification model. In this paper, the asymptotic behavior of MINQUE, ANOVA, and cell means estimates is considered in the one-way random model.
Simple and flexible Bayesian inferences for standardized regression coefficients
Journal of Applied Statistics, Feb 27, 2019
ABSTRACT In statistical practice, inferences on standardized regression coefficients are often re... more ABSTRACT In statistical practice, inferences on standardized regression coefficients are often required, but complicated by the fact that they are nonlinear functions of the parameters, and thus standard textbook results are simply wrong. Within the frequentist domain, asymptotic delta methods can be used to construct confidence intervals of the standardized coefficients with proper coverage probabilities. Alternatively, Bayesian methods solve similar and other inferential problems by simulating data from the posterior distribution of the coefficients. In this paper, we present Bayesian procedures that provide comprehensive solutions for inferences on the standardized coefficients. Simple computing algorithms are developed to generate posterior samples with no autocorrelation and based on both noninformative improper and informative proper prior distributions. Simulation studies show that Bayesian credible intervals constructed by our approaches have comparable and even better statistical properties than their frequentist counterparts, particularly in the presence of collinearity. In addition, our approaches solve some meaningful inferential problems that are difficult if not impossible from the frequentist standpoint, including identifying joint rankings of multiple standardized coefficients and making optimal decisions concerning their sizes and comparisons. We illustrate applications of our approaches through examples and make sample R functions available for implementing our proposed methods.
Field Evaluation of the Revised Niosh Lifting Equation
Proceedings of the Human Factors and Ergonomics Society ... Annual Meeting, Jul 1, 2000
The preliminary results of a prospective epidemiological study of the revised NIOSH lifting equat... more The preliminary results of a prospective epidemiological study of the revised NIOSH lifting equation are presented. The baseline evaluations included assessment of lifting and lowering tasks with the revised NIOSH equation, as well as a questionnaire regarding personal variables. Subject follow-up was primarily accomplished through postal questionnaires, telephone interviews, and surveillance for workers' compensation claims for low-back disorders. The preliminary results reported are based on approximately 375 person-years of exposure; however, the follow-up period is still in progress. Important findings related to the usability of the revised NIOSH equation across several types of common exposures are also discussed.
Evaluation of a weighted multiple comparison procedure
Pharmaceutical Statistics, 2005
... Received \60\re /teci *Correspondence to: Matthew Somerville, Statistics and Programming, Gla... more ... Received \60\re /teci *Correspondence to: Matthew Somerville, Statistics and Programming, GlaxoSmithKline, PO Box 13398, Research Triangle Park, NC 27709, USA. yE-mail:matt.c.somerville@gsk.com Page 2. ... Statistics in Medicine 1988; 7:877–888. 2. Moye LA. ...
The Power Function of Conditional Log-Linear Model Tests
Journal of the American Statistical Association, Mar 1, 1988
Abstract In fitting a log-linear model to data, it is common to examine the P values associated w... more Abstract In fitting a log-linear model to data, it is common to examine the P values associated with the conditional likelihood-ratio tests corresponding to a nested sequence of candidate log-linear models. For an appropriate Pitman sequence of models these test statistics are asymptotically independent and chi-squared in distribution. This article is an analytic study of the noncentrality parameters of these limiting distributions, pointing out factors that determine the powers of these tests. The conditional likelihood-ratio tests corresponding to a given nested sequence of log-linear models depend only on the models, but not on their parameterizations. The noncentrality parameters of their limiting chi-squared distributions depend on the pair of models compared, the true model, and the limiting model, but not on their parameterizations. Often a nested sequence of log-linear models is specified by a particular parameterization with adjacent models in the sequence differing only in the presence or absenc...
The American Statistician, 2018
Many Bayes factors have been proposed for comparing population means in two-sample (independent s... more Many Bayes factors have been proposed for comparing population means in two-sample (independent samples) studies. Recently, Wang and Liu (2015) presented an "objective" Bayes factor (BF) as an alternative to a "subjective" one presented by Gönen et al. (2005). Their report was evidently intended to show the superiority of their BF based on "undesirable behavior" of the latter. A wonderful aspect of Bayesian models is that they provide an opportunity to "lay all cards on the table." What distinguishes the various BFs in the two-sample problem is the choice of priors (cards) for the model parameters. This article discusses desiderata of BFs that have been proposed, and proposes a new criterion to compare BFs, no matter whether subjectively or objectively determined: A BF may be preferred if it correctly classifies the data as coming from the correct model most often. The criterion is based on a famous result in classification theory to minimize the total probability of misclassification. This criterion is objective, easily verified by simulation, shows clearly the effects (positive or negative) of assuming particular priors, provides new insights into the appropriateness of BFs in general, and provides a new answer to the question, "Which BF is best?"
Monte Carlo estimation of significance levels for carcinogenicity tests using univariate and multivariate models
Journal of Statistical Computation and Simulation, 1990
Special section: Teaching Bayes to nonstatistics graduate students
The American Statistician