Peter Westfall | Texas Tech University (original) (raw)

Papers by Peter Westfall

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.

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.

SAS Institute eBooks, 2000

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.

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.

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

Biometrical Journal, Oct 1, 2008

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

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.

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.

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.

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.

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.

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. ...

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

Journal of Statistical Computation and Simulation, 1990

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.

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.

SAS Institute eBooks, 2000

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.

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.

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

Biometrical Journal, Oct 1, 2008

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

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.

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.

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.

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.

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.

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. ...

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

Journal of Statistical Computation and Simulation, 1990