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
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Phthalate exposure and prostate cancer in a population-based nested case-control study.
Shu-Chun Chuang,Hui-Chi Chen,Chien-Wen Sun,Yuh-An Chen,Yin-Han Wang,Chun-Ju Chiang,Chu-Chih Chen,Shu-Li Wang,Shu-Li Wang,Shu-Li Wang,Chien-Jen Chen,Chao A. Hsiung +11 more
TL;DR: DEHP, BBzP, and DiBP exposure were associated with prostate cancer occurrence in abdominally obese men, and the main limitation remains the lack of mechanistic experiments and comparable toxicological data.
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Additionality in U.S. Agricultural Conservation Programs
TL;DR: The authors found that more than 95% of off-field structural practices (filter strips, riparian buffers) supported by payments are additional but less than 50% of conservation tillage payments yield additional adoption.
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Identification of risk factors for self-injurious behavior in male prisoners
TL;DR: Conditional logistic regression revealed that a combination of risk factors from domains defined by developmental, offense history, mental health, and institutional functioning factors correctly classified 93% of the prisoners in the sample.
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Impact of real-time traffic characteristics on crash occurrence: Preliminary results of the case of rare events.
TL;DR: The method and findings of the study attempt to provide insights on the mechanism of crash occurrence and also to overcome data considerations for the first time in safety evaluation of motorways.
Journal ArticleDOI
Fixed effects in rare events data: a penalized maximum likelihood solution
TL;DR: This article proposed a penalized maximum likelihood fixed effects (PML-FE) estimator, which retains the complete sample by providing finite estimates of the fixed effects for each unit and explored the small sample performance of PML-FE versus common alternatives via Monte Carlo simulations, evaluating the accuracy of both parameter and effects estimates.
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.