Journal ArticleDOI
A solution to the problem of separation in logistic regression
Georg Heinze,Michael Schemper +1 more
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A procedure by Firth originally developed to reduce the bias of maximum likelihood estimates is shown to provide an ideal solution to separation and produces finite parameter estimates by means of penalized maximum likelihood estimation.Abstract:
The phenomenon of separation or monotone likelihood is observed in the fitting process of a logistic model if the likelihood converges while at least one parameter estimate diverges to +/- infinity. Separation primarily occurs in small samples with several unbalanced and highly predictive risk factors. A procedure by Firth originally developed to reduce the bias of maximum likelihood estimates is shown to provide an ideal solution to separation. It produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald tests and confidence intervals are available but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. The clear advantage of the procedure over previous options of analysis is impressively demonstrated by the statistical analysis of two cancer studies.read more
Citations
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Journal ArticleDOI
Bradley-Terry Models in R: The BradleyTerry2 Package
Heather Turner,David Firth +1 more
TL;DR: This is a short overview of the R add-on package BradleyTerry2, which facilitates the specification and fitting of Bradley-Terry logit, probit or cauchit models to paircomparison data.
Journal ArticleDOI
Two distinct patterns of treatment resistance: clinical predictors of treatment resistance in first-episode schizophrenia spectrum psychoses
John Lally,Olesya Ajnakina,M. Di Forti,Antonella Trotta,Arsime Demjaha,Anna Kolliakou,Valeria Mondelli,T. Reis Marques,Carmine M. Pariante,Paola Dazzan,S. S. Shergil,Oliver D. Howes,Anthony S. David,James H. MacCabe,Fiona Gaughran,Robin M. Murray +15 more
TL;DR: For the majority of the TR group, antipsychotic TR is present from illness onset, necessitating increased consideration for the earlier use of clozapine.
Journal ArticleDOI
Bias reduction in exponential family nonlinear models
Ioannis Kosmidis,David Firth +1 more
TL;DR: In this article, a more general family of bias-reducing adjustments is developed for a broad class of univariate and multivariate generalized nonlinear models, and a necessary and sufficient condition is given for the existence of a penalized likelihood interpretation of the method.
Journal ArticleDOI
A framework for the comparison of maximum pseudo-likelihood and maximum likelihood estimation of exponential family random graph models
TL;DR: This paper uses a methodology to enable estimators of ERG model parameters to be compared and shows the superiority of the likelihood-based estimators over those based on pseudo- likelihood, with the bias-reduced pseudo-likelihood out-performing the general pseudo-Likelihood.
Journal ArticleDOI
Risk factors for chronic thromboembolic pulmonary hypertension
TL;DR: Identification of CTEPH, followed by early referral for evaluation and treatment by an experienced PEA centre, is recommended, as an estimated 10–15% of patients are at risk for residual pulmonary hypertension following PEA surgery, due to significant concomitant small-vessel disease.
References
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Book
Regression Diagnostics: Identifying Influential Data and Sources of Collinearity
TL;DR: In this article, the authors present a method for detecting and assessing Collinearity of observations and outliers in the context of extensions to the Wikipedia corpus, based on the concept of Influential Observations.
Journal ArticleDOI
Regression Diagnostics: Identifying Influential Data and Sources of Collinearity
TL;DR: This chapter discusses Detecting Influential Observations and Outliers, a method for assessing Collinearity, and its applications in medicine and science.
Journal Article
Statistical methods in cancer research. Volume I - The analysis of case-control studies.
N. E. Breslow,N. E. Day +1 more
Journal ArticleDOI
Bias reduction of maximum likelihood estimates
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.
Book
Modelling Survival Data in Medical Research
TL;DR: This paper discusses the design of clinical trials, use of computer software in survival analysis, and some non-parametric procedures for modelling survival data.