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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Journal ArticleDOI
Peripheral blood AKAP7 expression as an early marker for lymphocyte-mediated post-stroke blood brain barrier disruption
Grant C. O’Connell,Madison B. Treadway,Ashley B Petrone,Connie S. Tennant,Noelle Lucke-Wold,Paul D. Chantler,Taura L. Barr +6 more
TL;DR: Results suggest that AKAP7 expression levels may have clinical utility as a prognostic biomarker for post-stroke BBB complications, and are likely elevated early in patients who later develop post- stroke BBB disruption due to the presence of an invasive lymphocyte population in the peripheral blood.
Journal ArticleDOI
On the existence of maximum likelihood estimates for presence-only data
Trevor J. Hefley,Mevin B. Hooten +1 more
TL;DR: In this paper, the authors demonstrate the issue with conventional maximum likelihood mathematically, using a data example, and a simulation experiment and show alternative estimation methods, such as penalized likelihood and Bayesian methods.
Journal ArticleDOI
Telemedicine and Outpatient Subspecialty Visits Among Pediatric Medicaid Beneficiaries
TL;DR: Use overall was low, and results indicated that early telemedicine policies and implementation did not close disparities in subspecialty visit rates by child geographic and sociodemographic characteristics.
Journal ArticleDOI
Performance of Waist-To-Height Ratio, Waist Circumference, and Body Mass Index in Discriminating Cardio-Metabolic Risk Factors in a Sample of School-Aged Mexican Children.
Ibiza Aguilar-Morales,Eloisa Colin-Ramirez,Susana Rivera-Mancía,Maite Vallejo,Clara A Vázquez-Antona +4 more
TL;DR: WHtR performed similarly to WC and z-BMI in predicting lipidic and non-lipidic cardio-metabolic risk factors; however, a WHtR ≥ 0.5 was superior in detecting an increased risk of elevated LDL-c.
Book ChapterDOI
Overview of Maximum Likelihood Estimation
TL;DR: In this paper, the authors propose a general objective function for least square multiple regression, where the objective is to find the values of unknown parameters that minimize the sum of squared errors of prediction.
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.