Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models
TL;DR: In this paper, the maximum penalized likelihood estimates of binomial generalized linear models are derived for a broad class of logistic regression models, including probit and log-log models.
Abstract: Penalization of the likelihood by Jeffreys’ invariant prior, or a positive power thereof, is shown to produce finite-valued maximum penalized likelihood estimates in a broad class of binomial generalized linear models. The class of models includes logistic regression, where the Jeffreys-prior penalty is known additionally to reduce the asymptotic bias of the maximum likelihood estimator, and models with other commonly used link functions, such as probit and log-log. Shrinkage towards equiprobability across observations, relative to the maximum likelihood estimator, is established theoretically and studied through illustrative examples. Some implications of finiteness and shrinkage for inference are discussed, particularly when inference is based on Wald-type procedures. A widely applicable procedure is developed for computation of maximum penalized likelihood estimates, by using repeated maximum likelihood fits with iteratively adjusted binomial responses and totals. These theoretical results and methods underpin the increasingly widespread use of reduced-bias and similarly penalized binomial regression models in many applied fields.
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TL;DR: The MSK-MET cohort as discussed by the authors , a pan-cancer cohort of over 25,000 patients with metastatic diseases, was used to identify associations between genomic alterations and patterns of metastatic dissemination.
116 citations
TL;DR: The MSK-MET dataset as discussed by the authors is an integrated pan-cancer cohort of tumor genomic and clinical outcome data from more than 25,000 patients to identify associations between tumor genomic alterations and patterns of metastatic dissemination across 50 tumor types.
Abstract: Progression to metastatic disease remains the main cause of cancer death. Yet, the underlying genomic mechanisms driving metastasis remain largely unknown. Here, we present MSK-MET, an integrated pan-cancer cohort of tumor genomic and clinical outcome data from more than 25,000 patients. We analyzed this dataset to identify associations between tumor genomic alterations and patterns of metastatic dissemination across 50 tumor types. We found that chromosomal instability is strongly correlated with metastatic burden in some tumor types, including prostate adenocarcinoma, lung adenocarcinoma and HR-positive breast ductal carcinoma, but not in others, such as colorectal adenocarcinoma, pancreatic adenocarcinoma and high-grade serous ovarian cancer. We also identified specific somatic alterations associated with increased metastatic burden and specific routes of metastatic spread. Our data offer a unique resource for the investigation of the biological basis for metastatic spread and highlight the crucial role of chromosomal instability in cancer progression.
108 citations
TL;DR: SCT was associated with preexisting kidney comorbidities, increased CO VID-19 mortality, and kidney morbidity, and among the 4 clinical outcomes of COVID-19, SCT wasassociated with an increased COVID -19 mortality in individuals of African ancestry.
Abstract: Importance
Sickle cell trait (SCT), defined as the presence of 1 hemoglobin beta sickle allele (rs334-T) and 1 normal beta allele, is prevalent in millions of people in the US, particularly in individuals of African and Hispanic ancestry. However, the association of SCT with COVID-19 is unclear.
Objective
To assess the association of SCT with the prepandemic health conditions in participants of the Million Veteran Program (MVP) and to assess the severity and sequelae of COVID-19.
Design, Setting, and Participants
COVID-19 clinical data include 2729 persons with SCT, of whom 353 had COVID-19, and 129 848 SCT-negative individuals, of whom 13 488 had COVID-19. Associations between SCT and COVID-19 outcomes were examined using firth regression. Analyses were performed by ancestry and adjusted for sex, age, age squared, and ancestral principal components to account for population stratification. Data for the study were collected between March 2020 and February 2021.
Exposures
The hemoglobin beta S (HbS) allele (rs334-T).
Main Outcomes and Measures
This study evaluated 4 COVID-19 outcomes derived from the World Health Organization severity scale and phenotypes derived from International Classification of Diseases codes in the electronic health records.
Results
Of the 132 577 MVP participants with COVID-19 data, mean (SD) age at the index date was 64.8 (13.1) years. Sickle cell trait was present in 7.8% of individuals of African ancestry and associated with a history of chronic kidney disease, diabetic kidney disease, hypertensive kidney disease, pulmonary embolism, and cerebrovascular disease. Among the 4 clinical outcomes of COVID-19, SCT was associated with an increased COVID-19 mortality in individuals of African ancestry (n = 3749; odds ratio, 1.77; 95% CI, 1.13 to 2.77; P = .01). In the 60 days following COVID-19, SCT was associated with an increased incidence of acute kidney failure. A counterfactual mediation framework estimated that on average, 20.7% (95% CI, -3.8% to 56.0%) of the total effect of SCT on COVID-19 fatalities was due to acute kidney failure.
Conclusions and Relevance
In this genetic association study, SCT was associated with preexisting kidney comorbidities, increased COVID-19 mortality, and kidney morbidity.
14 citations
TL;DR: Noninvasive MR lymphangiography identifies distinct signal patterns indicating SAT edema and lymphatic load in participants with lipedema.
Abstract: Lipedema exhibits excessive lower‐extremity subcutaneous adipose tissue (SAT) deposition, which is frequently misidentified as obesity until lymphedema presents. MR lymphangiography may have relevance to distinguish lipedema from obesity or lymphedema.
8 citations
TL;DR: In this article , the authors investigated whether temperature-related cognitive impairments could be a driver of bee declines by exploring the effect of short-term increases in ambient temperature on learning and memory.
Abstract: Global warming has been identified as a key driver of bee declines around the world. While it is clear that elevated temperatures during the spring and summer months—the principal activity period of many bee species—is a factor in this decline, exactly how temperature affects bee survival is unknown. In vertebrates, there is clear evidence that elevated ambient temperatures impair cognition but whether and how heat affects the cognitive abilities of invertebrates remains unclear. Cognitive skills in bees are essential for their survival as, to supply the hive with nutrition, workers must be able to learn and remember the location of the most rewarding floral resources. Here, we investigate whether temperature‐related cognitive impairments could be a driver of bee declines by exploring the effect of short‐term increases in ambient temperature on learning and memory. We found that, in comparison to bees that were tested at 25°C (a temperature that they would typically experience in summer), bees that were exposed to 32°C (a temperature that they will becoming increasingly exposed to during heatwave events) were significantly worse at forming an association between a coloured light and a sucrose reward and that their capacity to remember this association after just 1 h was abolished. This study provides novel experimental evidence that even just a few hours of exposure to heatwave‐like temperatures can severely impair the cognitive performance of insects. Such temperature‐induced cognitive deficits could play an important role in explaining recent and future bee population declines.
5 citations
References
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Journal Article•
TL;DR: Copyright (©) 1999–2012 R Foundation for Statistical Computing; permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and permission notice are preserved on all copies.
Abstract: Copyright (©) 1999–2012 R Foundation for Statistical Computing. Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies. Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. Permission is granted to copy and distribute translations of this manual into another language, under the above conditions for modified versions, except that this permission notice may be stated in a translation approved by the R Core Team.
272,030 citations
"Jeffreys-prior penalty, finiteness ..." refers background in this paper
..., R., Heinze, G., Nold, M., Lusa, L. & Geroldinger, A. (2017). Firth’s logistic regression with rare events: accurate eect estimates and predictions? Statistics in Medicine 36, 2302{2317. R Core Team (2020). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. Sartori, N. (2003). Modied prole likelihoods in models with stratum nuisance param...
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Book•
01 Jan 1989
TL;DR: Hosmer and Lemeshow as discussed by the authors provide an accessible introduction to the logistic regression model while incorporating advances of the last decade, including a variety of software packages for the analysis of data sets.
Abstract: From the reviews of the First Edition. "An interesting, useful, and well-written book on logistic regression models... Hosmer and Lemeshow have used very little mathematics, have presented difficult concepts heuristically and through illustrative examples, and have included references."- Choice "Well written, clearly organized, and comprehensive... the authors carefully walk the reader through the estimation of interpretation of coefficients from a wide variety of logistic regression models . . . their careful explication of the quantitative re-expression of coefficients from these various models is excellent." - Contemporary Sociology "An extremely well-written book that will certainly prove an invaluable acquisition to the practicing statistician who finds other literature on analysis of discrete data hard to follow or heavily theoretical."-The Statistician In this revised and updated edition of their popular book, David Hosmer and Stanley Lemeshow continue to provide an amazingly accessible introduction to the logistic regression model while incorporating advances of the last decade, including a variety of software packages for the analysis of data sets. Hosmer and Lemeshow extend the discussion from biostatistics and epidemiology to cutting-edge applications in data mining and machine learning, guiding readers step-by-step through the use of modeling techniques for dichotomous data in diverse fields. Ample new topics and expanded discussions of existing material are accompanied by a wealth of real-world examples-with extensive data sets available over the Internet.
35,847 citations
TL;DR: In this paper, the first-order term is removed from the asymptotic bias of maximum likelihood estimates by a suitable modification of the score function, and the effect is to penalize the likelihood by the Jeffreys invariant prior.
Abstract: SUMMARY It is shown how, in regular parametric problems, the first-order term is removed from the asymptotic bias of maximum likelihood estimates by a suitable modification of the score function. In exponential families with canonical parameterization the effect is to penalize the likelihood by the Jeffreys invariant prior. In binomial logistic models, Poisson log linear models and certain other generalized linear models, the Jeffreys prior penalty function can be imposed in standard regression software using a scheme of iterative adjustments to the data.
3,362 citations
"Jeffreys-prior penalty, finiteness ..." refers background or methods in this paper
...For non-logistic links, such estimators no longer coincide with the bias-reduced estimator of Firth (1993)....
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...These new theoretical results justify and motivate the use of the RB estimator in even more complex applied settings than the one covered by the framework of Firth (1993) — settings where more involved adjustments such as modified profile likelihoods are the norm for recovering inferential accuracy (see, for example Sartori, 2003)....
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...At the time of writing, Google Scholar records approximately 2700 citations of Firth (1993), more than half of which are from 2015 or later....
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...…results justify and motivate use of the reduced-bias estimator in even more complex applied settings than the one covered by the framework of Firth (1993); in such settings, more involved methods such as modified profile likelihoods (see, for example Sartori, 2003) and approximate…...
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...The apparent finiteness and shrinkage properties of the RB estimator of Firth (1993), coupled with the fact that the estimator has the same asymptotic distribution that the ML estimator has in general, are key reasons for the increasingly widespread and diverse use of Jeffreys-penalized logistic regression in applied work....
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Book•
01 Apr 1988
TL;DR: In this article, the authors discuss the properties of Vectors and Matrices, the Vec-Operator, the Moore-Penrose Inverse Miscellaneous Matrix Results, and the Linear Regression Model.
Abstract: Preface MATRICES: Basic Properties of Vectors and Matrices Kronecker Products, the Vec-Operator and the Moore- Penrose Inverse Miscellaneous Matrix Results DIFFERENTIALS: THE THEORY: Mathematical Preliminaries Differentials and Differentiability The Second Differential Static Optimization DIFFERENTIALS: THE PRACTICE: Some Important Differentials First- Order Differentials and Jacobian Matrices Second-Order Differentials and Hessian Matrices INEQUALITIES: Inequalities THE LINEAR MODEL: Statistical Preliminaries The Linear Regression Model Further Topics in the Linear Model APPLICATIONS TO MAXIMUM LIKELIHOOD ESTIMATION: Maximum Likelihood Estimation Simultaneous Equations Topics in Psychometrics Subject Index Bibliography.
2,868 citations
12 Nov 2013
TL;DR: Categorical data analysis, Categorical Data Analysis (CDA) as discussed by the authors, کتابخانه الکرونیک و دیجیتال - آذرسا
Abstract: Categorical data analysis , Categorical data analysis , کتابخانه الکترونیک و دیجیتال - آذرسا
2,147 citations