Journal ArticleDOI
A solution to the problem of separation in logistic regression
Georg Heinze,Michael Schemper +1 more
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TLDR
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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Reducing the Impact of Bias in Likelihood Inference for Prominent Model Settings
TL;DR: This thesis proposes a convenient way to refine Wald-type inference in regression settings through asymptotic bias correction of the $z$-statistic, and suggests a strategy to extend the current range of applications of the modified profile likelihood.
Exact Approaches for Bias Detection and Avoidance with Small, Sparse, or Correlated Categorical Data
TL;DR: In this article, the authors present an approach for bias detection and avoidance with small, sparse, or correlated categorical data using small, Sparse, or Correlated Categorical Data.
Journal ArticleDOI
Ocean acidification causes mortality in the medusa stage of the cubozoan Carybdea xaymacana.
TL;DR: This study investigates the effect of 2300 OA projections on the mortality rate of the medusa-stage of the cubozoan species Carybdea xaymacana, compared to ambient seawater pH conditions and represents the first evidence of the potential lethal effects of post-2050 OA projection on jellyfish.
Journal ArticleDOI
Life-history transitions of the coral-reef fish Elacatinus lori.
A. J. Rickborn,Peter M. Buston +1 more
TL;DR: This study provides the first comprehensive description of these life-history transitions for a species within the genus Elacatinus, the most speciose genus of fishes on Caribbean coral reefs.
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Oral Cyanobacteria and Hepatocellular Carcinoma
TL;DR: The role of the oral microbiome in liver cancer development has not been widely investigated as discussed by the authors , however, the role of 16S rRNA sequences in the development of liver cancer has been investigated.
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.