Pub Date : 2022-07-03DOI: 10.1080/00031305.2022.2074541
R. Christensen
Griffiths and Hill (2022) showed that when testing an hypothesis in linear models, it can sometimes be advantageous to incorporate components into the hypothesis that are true. They assume a true linear model and that a constraint R 2 β = d 2 is true. They are interested in comparing the powers of three F tests for H 0 : R 1 β = d 1 :
{"title":"Comment on “On the Power of the F-test for Hypotheses in a Linear Model” by Griffiths and Hill (2022)","authors":"R. Christensen","doi":"10.1080/00031305.2022.2074541","DOIUrl":"https://doi.org/10.1080/00031305.2022.2074541","url":null,"abstract":"Griffiths and Hill (2022) showed that when testing an hypothesis in linear models, it can sometimes be advantageous to incorporate components into the hypothesis that are true. They assume a true linear model and that a constraint R 2 β = d 2 is true. They are interested in comparing the powers of three F tests for H 0 : R 1 β = d 1 :","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129284825","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-03DOI: 10.1080/00031305.2022.2088201
Emilija Perkovic
the output. The sponsor NDA may alert to other inadvertent disclosures, such as having lunch or dinner with another DMC member while diners at nearby tables can overhear the discussion. Some publicly traded companies have a black-out period during the conduct of an interim where all employees are forbidden from trading stock and from sharing internal corporate news about DSMB activities while a DSMB review is underway or about to occur. In the United States, the Securities Exchange Commission (SEC) does investigate unusual stock trades that occur with public announcement of trial results such as a DSMB recommendation, or other sponsor announcements to investors. SEC may request information from sponsor employees about knowledge of a DSMB meeting or trial results. I encourage readers to purchase this book. During the pandemic there are other reports of DSMB activities, which often are briefly described on sponsor investor news, and subsequently in the press. There are additional and interesting examples of DSMB activities during the pandemic which the interested reader may find by perusing the sponsor investor news and by general internet searches.
{"title":"Leadership in Statistics and Data Science: Planning for Inclusive Excellence,","authors":"Emilija Perkovic","doi":"10.1080/00031305.2022.2088201","DOIUrl":"https://doi.org/10.1080/00031305.2022.2088201","url":null,"abstract":"the output. The sponsor NDA may alert to other inadvertent disclosures, such as having lunch or dinner with another DMC member while diners at nearby tables can overhear the discussion. Some publicly traded companies have a black-out period during the conduct of an interim where all employees are forbidden from trading stock and from sharing internal corporate news about DSMB activities while a DSMB review is underway or about to occur. In the United States, the Securities Exchange Commission (SEC) does investigate unusual stock trades that occur with public announcement of trial results such as a DSMB recommendation, or other sponsor announcements to investors. SEC may request information from sponsor employees about knowledge of a DSMB meeting or trial results. I encourage readers to purchase this book. During the pandemic there are other reports of DSMB activities, which often are briefly described on sponsor investor news, and subsequently in the press. There are additional and interesting examples of DSMB activities during the pandemic which the interested reader may find by perusing the sponsor investor news and by general internet searches.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"85 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116942714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-03DOI: 10.1080/00031305.2022.2088199
C. Barker
{"title":"Data Monitoring Committees in Clinical Trials: A Practical Perspective","authors":"C. Barker","doi":"10.1080/00031305.2022.2088199","DOIUrl":"https://doi.org/10.1080/00031305.2022.2088199","url":null,"abstract":"","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131607156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-03DOI: 10.1080/00031305.2022.2074542
W. Griffiths, R. Carter Hill
The authors would like to thank Professors Christensen and Harville for their comments. These two authors take differ-ent approaches to generalizing and improving the proof of the theorem in Griffiths and Hill (2022). Professor Christensen’s geometric approach, and Professor Harville’s meticulous matrix algebra approach, are suitable for graduate courses in linear models for statisticians in various fields. We believe that there is pedagogic value in discussing the tradeoff between the non-CONTACT centrality parameter and the numerator degrees of freedom in the F -test, and how this affects the power of the F -test. However, just to be clear, we are not advocating adding true hypotheses as a strategy. Professor Christensen’s first sentence may be taken by some to imply that. The main points in our article are also easily demonstrated via simulation, as shown in the supplemen-tary materials, making the ideas accessible to undergraduate students.
{"title":"Rejoinder to Harville (2022) and Christensen (2022) Comments on “On the Power of the F-test for Hypotheses in a Linear Model,” by Griffiths and Hill (2022)","authors":"W. Griffiths, R. Carter Hill","doi":"10.1080/00031305.2022.2074542","DOIUrl":"https://doi.org/10.1080/00031305.2022.2074542","url":null,"abstract":"The authors would like to thank Professors Christensen and Harville for their comments. These two authors take differ-ent approaches to generalizing and improving the proof of the theorem in Griffiths and Hill (2022). Professor Christensen’s geometric approach, and Professor Harville’s meticulous matrix algebra approach, are suitable for graduate courses in linear models for statisticians in various fields. We believe that there is pedagogic value in discussing the tradeoff between the non-CONTACT centrality parameter and the numerator degrees of freedom in the F -test, and how this affects the power of the F -test. However, just to be clear, we are not advocating adding true hypotheses as a strategy. Professor Christensen’s first sentence may be taken by some to imply that. The main points in our article are also easily demonstrated via simulation, as shown in the supplemen-tary materials, making the ideas accessible to undergraduate students.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133659560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-30DOI: 10.1080/00031305.2022.2096695
Bradley Lubich, D. Jeske, W. Yao
ABSTRACT A mixture of a distribution of responses from untreated patients and a shift of that distribution is a useful model for the responses from a group of treated patients. The mixture model accounts for the fact that not all the patients in the treated group will respond to the treatment and consequently their responses follow the same distribution as the responses from untreated patients. The treatment effect in this context consists of both the fraction of the treated patients that are responders and the magnitude of the shift in the distribution for the responders. In this article, we investigate asymptotic properties of method of moment estimators for the treatment effect based on a semi-supervised two-component mixture model. From these properties, we develop asymptotic confidence intervals and demonstrate their superior statistical inference performance compared to the computationally intensive bootstrap intervals and their Bias-Corrected versions.
{"title":"Statistical Inference for Method of Moments Estimators of a Semi-Supervised Two-Component Mixture Model","authors":"Bradley Lubich, D. Jeske, W. Yao","doi":"10.1080/00031305.2022.2096695","DOIUrl":"https://doi.org/10.1080/00031305.2022.2096695","url":null,"abstract":"ABSTRACT A mixture of a distribution of responses from untreated patients and a shift of that distribution is a useful model for the responses from a group of treated patients. The mixture model accounts for the fact that not all the patients in the treated group will respond to the treatment and consequently their responses follow the same distribution as the responses from untreated patients. The treatment effect in this context consists of both the fraction of the treated patients that are responders and the magnitude of the shift in the distribution for the responders. In this article, we investigate asymptotic properties of method of moment estimators for the treatment effect based on a semi-supervised two-component mixture model. From these properties, we develop asymptotic confidence intervals and demonstrate their superior statistical inference performance compared to the computationally intensive bootstrap intervals and their Bias-Corrected versions.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134014237","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-24DOI: 10.1080/00031305.2023.2216239
Samuel Pawel, A. Ly, E. Wagenmakers
We present a novel and easy-to-use method for calibrating error-rate based confidence intervals to evidence-based support intervals. Support intervals are obtained from inverting Bayes factors based on a parameter estimate and its standard error. A $k$ support interval can be interpreted as"the observed data are at least $k$ times more likely under the included parameter values than under a specified alternative". Support intervals depend on the specification of prior distributions for the parameter under the alternative, and we present several types that allow different forms of external knowledge to be encoded. We also show how prior specification can to some extent be avoided by considering a class of prior distributions and then computing so-called minimum support intervals which, for a given class of priors, have a one-to-one mapping with confidence intervals. We also illustrate how the sample size of a future study can be determined based on the concept of support. Finally, we show how the bound for the type I error rate of Bayes factors leads to a bound for the coverage of support intervals. An application to data from a clinical trial illustrates how support intervals can lead to inferences that are both intuitive and informative.
{"title":"Evidential Calibration of Confidence Intervals","authors":"Samuel Pawel, A. Ly, E. Wagenmakers","doi":"10.1080/00031305.2023.2216239","DOIUrl":"https://doi.org/10.1080/00031305.2023.2216239","url":null,"abstract":"We present a novel and easy-to-use method for calibrating error-rate based confidence intervals to evidence-based support intervals. Support intervals are obtained from inverting Bayes factors based on a parameter estimate and its standard error. A $k$ support interval can be interpreted as\"the observed data are at least $k$ times more likely under the included parameter values than under a specified alternative\". Support intervals depend on the specification of prior distributions for the parameter under the alternative, and we present several types that allow different forms of external knowledge to be encoded. We also show how prior specification can to some extent be avoided by considering a class of prior distributions and then computing so-called minimum support intervals which, for a given class of priors, have a one-to-one mapping with confidence intervals. We also illustrate how the sample size of a future study can be determined based on the concept of support. Finally, we show how the bound for the type I error rate of Bayes factors leads to a bound for the coverage of support intervals. An application to data from a clinical trial illustrates how support intervals can lead to inferences that are both intuitive and informative.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127449032","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-03DOI: 10.1080/00031305.2023.2200512
M. Matabuena, Paulo F'elix, Marc Ditzhaus, J. Vidal, F. Gudé
A frequent problem in statistical science is how to properly handle missing data in matched paired observations. There is a large body of literature coping with the univariate case. Yet, the ongoing technological progress in measuring biological systems raises the need for addressing more complex data, e.g., graphs, strings and probability distributions, among others. In order to fill this gap, this paper proposes new estimators of the maximum mean discrepancy (MMD) to handle complex matched pairs with missing data. These estimators can detect differences in data distributions under different missingness mechanisms. The validity of this approach is proven and further studied in an extensive simulation study, and results of statistical consistency are provided. Data from continuous glucose monitoring in a longitudinal population-based diabetes study are used to illustrate the application of this approach. By employing the new distributional representations together with cluster analysis, new clinical criteria on how glucose changes vary at the distributional level over five years can be explored.
{"title":"Hypothesis testing for matched pairs with missing data by maximum mean discrepancy: An application to continuous glucose monitoring","authors":"M. Matabuena, Paulo F'elix, Marc Ditzhaus, J. Vidal, F. Gudé","doi":"10.1080/00031305.2023.2200512","DOIUrl":"https://doi.org/10.1080/00031305.2023.2200512","url":null,"abstract":"A frequent problem in statistical science is how to properly handle missing data in matched paired observations. There is a large body of literature coping with the univariate case. Yet, the ongoing technological progress in measuring biological systems raises the need for addressing more complex data, e.g., graphs, strings and probability distributions, among others. In order to fill this gap, this paper proposes new estimators of the maximum mean discrepancy (MMD) to handle complex matched pairs with missing data. These estimators can detect differences in data distributions under different missingness mechanisms. The validity of this approach is proven and further studied in an extensive simulation study, and results of statistical consistency are provided. Data from continuous glucose monitoring in a longitudinal population-based diabetes study are used to illustrate the application of this approach. By employing the new distributional representations together with cluster analysis, new clinical criteria on how glucose changes vary at the distributional level over five years can be explored.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126181615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-03DOI: 10.1080/00031305.2022.2087734
Andee Kaplan, J. Bien
ABSTRACT Hierarchical clustering is one of the standard methods taught for identifying and exploring the underlying structures that may be present within a dataset. Students are shown examples in which the dendrogram, a visual representation of the hierarchical clustering, reveals a clear clustering structure. However, in practice, data analysts today frequently encounter datasets whose large scale undermines the usefulness of the dendrogram as a visualization tool. Densely packed branches obscure structure, and overlapping labels are impossible to read. In this article we present a new workflow for performing hierarchical clustering via the R package called protoshiny that aims to restore hierarchical clustering to its former role of being an effective and versatile visualization tool. Our proposal leverages interactivity combined with the ability to label internal nodes in a dendrogram with a representative data point (called a prototype). After presenting the workflow, we provide three case studies to demonstrate its utility.
{"title":"Interactive Exploration of Large Dendrograms with Prototypes","authors":"Andee Kaplan, J. Bien","doi":"10.1080/00031305.2022.2087734","DOIUrl":"https://doi.org/10.1080/00031305.2022.2087734","url":null,"abstract":"ABSTRACT Hierarchical clustering is one of the standard methods taught for identifying and exploring the underlying structures that may be present within a dataset. Students are shown examples in which the dendrogram, a visual representation of the hierarchical clustering, reveals a clear clustering structure. However, in practice, data analysts today frequently encounter datasets whose large scale undermines the usefulness of the dendrogram as a visualization tool. Densely packed branches obscure structure, and overlapping labels are impossible to read. In this article we present a new workflow for performing hierarchical clustering via the R package called protoshiny that aims to restore hierarchical clustering to its former role of being an effective and versatile visualization tool. Our proposal leverages interactivity combined with the ability to label internal nodes in a dendrogram with a representative data point (called a prototype). After presenting the workflow, we provide three case studies to demonstrate its utility.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"296 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134092931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-25DOI: 10.1080/00031305.2023.2173293
D. Paindaveine, P. Spindel
Initially proposed by Martin Gardner in the 1950s, the famous two-children problem is often presented as a paradox in probability theory. A relatively recent variant of this paradox states that, while in a two-children family for which at least one child is a girl, the probability that the other child is a boy is 2 / 3, this probability becomes 1 / 2 if the first name of the girl is disclosed (provided that two sisters may not be given the same first name). We revisit this variant of the problem and show that, if one adopts a natural model for the way first names are given to girls, then the probability that the other child is a boy may take any value in ]0 , 2 / 3[. By exploiting the concept of Schur-concavity, we study how this probability depends on model parameters.
{"title":"Revisiting the name variant of the two-children problem","authors":"D. Paindaveine, P. Spindel","doi":"10.1080/00031305.2023.2173293","DOIUrl":"https://doi.org/10.1080/00031305.2023.2173293","url":null,"abstract":"Initially proposed by Martin Gardner in the 1950s, the famous two-children problem is often presented as a paradox in probability theory. A relatively recent variant of this paradox states that, while in a two-children family for which at least one child is a girl, the probability that the other child is a boy is 2 / 3, this probability becomes 1 / 2 if the first name of the girl is disclosed (provided that two sisters may not be given the same first name). We revisit this variant of the problem and show that, if one adopts a natural model for the way first names are given to girls, then the probability that the other child is a boy may take any value in ]0 , 2 / 3[. By exploiting the concept of Schur-concavity, we study how this probability depends on model parameters.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131249882","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-11DOI: 10.1080/00031305.2022.2076743
S. Portnoy
ABSTRACT Best linear unbiased estimators (BLUE’s) are known to be optimal in many respects under normal assumptions. Since variance minimization doesn’t depend on normality and unbiasedness is often considered reasonable, many statisticians have felt that BLUE’s ought to preform relatively well in some generality. The result here considers the general linear model and shows that any measurable estimator that is unbiased over a moderately large family of distributions must be linear. Thus, imposing unbiasedness cannot offer any improvement over imposing linearity. The problem was suggested by Hansen, who showed that any estimator unbiased for nearly all error distributions (with finite covariance) must have a variance no smaller than that of the best linear estimator in some parametric subfamily. Specifically, the hypothesis of linearity can be dropped from the classical Gauss–Markov Theorem. This might suggest that the best unbiased estimator should provide superior performance, but the result here shows that the best unbiased regression estimator can be no better than the best linear estimator.
{"title":"Linearity of Unbiased Linear Model Estimators","authors":"S. Portnoy","doi":"10.1080/00031305.2022.2076743","DOIUrl":"https://doi.org/10.1080/00031305.2022.2076743","url":null,"abstract":"ABSTRACT Best linear unbiased estimators (BLUE’s) are known to be optimal in many respects under normal assumptions. Since variance minimization doesn’t depend on normality and unbiasedness is often considered reasonable, many statisticians have felt that BLUE’s ought to preform relatively well in some generality. The result here considers the general linear model and shows that any measurable estimator that is unbiased over a moderately large family of distributions must be linear. Thus, imposing unbiasedness cannot offer any improvement over imposing linearity. The problem was suggested by Hansen, who showed that any estimator unbiased for nearly all error distributions (with finite covariance) must have a variance no smaller than that of the best linear estimator in some parametric subfamily. Specifically, the hypothesis of linearity can be dropped from the classical Gauss–Markov Theorem. This might suggest that the best unbiased estimator should provide superior performance, but the result here shows that the best unbiased regression estimator can be no better than the best linear estimator.","PeriodicalId":342642,"journal":{"name":"The American Statistician","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124752743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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