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Open accessJournal ArticleDOI: 10.1093/BIOMET/ASAA052

Jeffreys-prior penalty, finiteness and shrinkage in binomial-response generalized linear models

02 Mar 2021-Biometrika (Oxford University Press (OUP))-Vol. 108, Iss: 1, pp 71-82
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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Topics: Jeffreys prior (59%), Binomial regression (59%), Generalized linear model (56%) ... show more
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17 results found


Journal ArticleDOI: 10.1093/BIOMET/ASAA100
Tao Yang1, Ying Huang1, Youyi Fong1Institutions (1)
15 Nov 2021-Biometrika
Abstract: We consider the use of threshold-based regression models for evaluating immune response biomarkers as principal surrogate markers of a vaccine's protective effect. Threshold-based regression models, which allow the relationship between a clinical outcome and a covariate to change dramatically across a threshold value in the covariate, have been studied by various authors under fully observed data. Limited research, however, has examined these models in the presence of missing covariates, such as the counterfactual potential immune responses of a participant in the placebo arm of a standard vaccine trial had s/he been assigned to the vaccine arm instead. Based on a hinge model for a threshold effect of the principal surrogate on vaccine efficacy, we develop a regression methodology that consists of two components: (1) The estimated likelihood method is employed to handle missing potential outcomes, and (2) a penalty is imposed on the estimated likelihood to ensure satisfactory finite sample performance. We develop a method that allows joint estimation of all model parameters as well as a two-step method that separates the estimation of the threshold parameter from the rest of the parameters. Stable iterative algorithms are developed to implement the two methods and the asymptotic properties of the proposed estimators are established. In simulation studies, the proposed estimators are shown to have satisfactory finite sample performance. The proposed methods are applied to analyze a real dataset collected from dengue vaccine efficacy trials to predict how vaccine efficacy varies with an individual's potential immune response if receiving vaccine.

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Topics: Inference (54%)

1 Citations


Open accessPosted ContentDOI: 10.1101/2021.02.12.430958
Sarah Catherine Paul1, Mueller C1Institutions (1)
13 Feb 2021-bioRxiv
Abstract: Studies on intraspecific contest behaviour predominantly focus on contests between individuals of the same sex, however contest behaviour is also expected to occur between individuals of the opposite sex including possible mates. Here we investigate potential trade-offs between mating and fighting behaviour in the turnip sawfly (Athalia rosae). Adults of this species collect chemical defence compounds (clerodanoids) directly from plants but also indirectly by nibbling on conspecifics that have already obtained clerodanoids themselves, a highly aggressive behavioural interaction. An A. rosae individual without clerodanoids may therefore be the potential mate or attacker of an individual of the opposite sex that has gained clerodanoids. We paired males and females with or without clerodanoid access and manipulated body mass differences between the sexes via the early life starvation of females. We show that asymmetrical clerodanoid acquisition between male-female pairs causes an increase in agonistic nibbling behaviour, irrespective of sex. Moreover, fighting over clerodanoids disrupted mating behaviour, and the frequency of aggressive nibbling behaviour in these pairs was determined by the comparative body mass of the attacking individual. Our study highlights the vital importance of investigating agonistic intersex interactions not only over mating but also over resources.

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Topics: Agonistic behaviour (61%), Mating (56%)

1 Citations


Open accessPosted ContentDOI: 10.1101/2021.09.28.21263911
Anurag Verma1, Anurag Verma2, Jessica Minnier3, Jennifer E. Huffman4  +58 moreInstitutions (22)
29 Sep 2021-medRxiv
Abstract: Rationale A common MUC5B gene polymorphism, rs35705950-T, is associated with idiopathic pulmonary fibrosis, but its role in the SARS-CoV-2 infection and disease severity is unclear. Objectives To assess whether rs35705950-T confers differential risk for clinical outcomes associated with COVID-19 infection among participants in the Million Veteran Program (MVP) and COVID-19 Host Genetics Initiative (HGI). Methods MVP participants were examined for an association between the incidence or severity of COVID-19 and the presence of a MUC5B rs35705950-T allele. Comorbidities and clinical events were extracted from the electronic health records (EHR). The analysis was performed within each ancestry group in the MVP, adjusting for sex, age, age2, and first twenty principal components followed by a trans-ethnic meta-analysis. We then pursued replication and performed a meta-analysis with the trans-ethnic summary statistics from the HGI. A phenome-wide association study (PheWAS) of the rs35705950-T was conducted to explore associated pathophysiologic conditions. Measurements and Main Results A COVID-19 severity scale was modified from the World Health Organization criteria, and phenotypes derived from the International Classification of Disease-9/10 were extracted from EHR. Presence of rs35705950-T was associated with fewer hospitalizations (Ncases=25353, Ncontrols=631,024; OR=0.86 [0.80-0.93], p=7.4 × 10−5) in trans-ethnic meta-analysis within MVP and joint meta-analyses with the HGI (N=1641311; OR=0.89 [0.85-0.93], p =1.9 × 10−6). Moreover, individuals of European Ancestry with at least one copy of rs35705950-T had fewer post-COVID-19 pneumonia events (OR=0.85 [0.76-0.96], p =0.008). PheWAS exclusively revealed pulmonary involvement. Conclusions The MUC5B variant rs35705950-T is protective in COVID-19 infection.

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1 Citations


Open accessPosted ContentDOI: 10.1101/2021.06.28.450217
30 Jun 2021-bioRxiv
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.

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Topics: Adenocarcinoma (58%), Metastasis (56%), Cancer (55%) ... show more

Open accessJournal ArticleDOI: 10.1007/S00268-021-06368-X
Andrea Kopp Lugli1, Walter R. Marti, Lilian Salm, Edin Mujagic1  +8 moreInstitutions (1)
Abstract: Patients with diabetes mellitus type 2 (DM2) inhere impaired peripheral insulin action leading to higher perioperative morbidity and mortality rates, with hospital-acquired infections being one important complication. This post hoc, observational study aimed to analyze the impact of surgical and metabolic stress as defined by the surrogate marker hemoglobin A1c (HbA1c), in relation to self-reported DM2, on perioperative infection rates in a subcohort of the Surgical Site Infection (SSI) Trial population. All patients of the SSI study were screened for HbA1c levels measured perioperatively for elective or emergency surgery and classified according to the American Diabetes Association HbA1c cutoff values. SSI and nosocomial infections, self-reported state of DM2 and type of surgery (minor, major) were assessed. HbA1c levels were measured in 139 of 5175 patients (2.7%) of the complete SSI study group. Seventy patients (50.4%) self-reported DM2, while 69 (49.6%) self-reported to be non-diabetic. HbA1c levels indicating pre-diabetes were found in 48 patients (34.5%) and diabetic state in 64 patients (46%). Forty-five patients of the group self-reporting no diabetes (65.2%) were previously unaware of their metabolic derangement (35 pre-diabetic and 10 diabetic). Eighteen infections were detected. Most infections (17 of 18 events) were found in patients with HbA1c levels indicating pre-/diabetic state. The odds for an infection was 3.9-fold (95% CI 1.4 to 11.3) higher for patients undergoing major compared to minor interventions. The highest percentage of infections (38.5%) was found in the group of patients with an undiagnosed pre-/diabetic state undergoing major surgery. These results encourage investment in further studies evaluating a more generous and specific use of HbA1c screening in patients without self-reported diabetes undergoing major surgery. Trial registration Clinicaltrials.gov identifier: NCT 01790529

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Topics: Perioperative (57%), Diabetes mellitus (52%), Abdominal surgery (51%) ... show more

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27 results found


Open accessJournal Article
01 Jan 2014-MSOR connections
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.

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Topics: R Programming Language (78%)

229,202 Citations


Open accessBook
01 Jan 1989-
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.

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35,821 Citations


Journal ArticleDOI: 10.1093/BIOMET/80.1.27
01 Mar 1993-Biometrika
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.

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Topics: Jeffreys prior (66%), Restricted maximum likelihood (64%), Prior probability (60%) ... show more

2,936 Citations


Open accessBook
01 Apr 1988-
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.

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Topics: Matrix (mathematics) (58%), Jacobian matrix and determinant (53%), Hessian matrix (52%) ... show more

2,774 Citations


Open access
12 Nov 2013-
Abstract: Categorical data analysis , Categorical data analysis , کتابخانه الکترونیک و دیجیتال - آذرسا

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2,145 Citations


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