scholarly journals Role of ocular perfusion pressure in glaucoma: the issue of multicollinearity in statistical regression models

2016 ◽  
Vol 1 (2) ◽  
pp. 89-96
Author(s):  
Alessandra Guglielmi ◽  
Giovanna Guidoboni ◽  
Alon Harris
Keyword(s):  
Blood Pressure ◽  
Regression Models ◽  
Goodness Of Fit ◽  
Perfusion Pressure ◽  
Logistic Models ◽  
Statistical Regression ◽  
Ocular Perfusion Pressure ◽  
Logistic Regression Models ◽  
Ocular Perfusion ◽  
Clinical Dataset

Purpose: Intraocular pressure (IOP), mean arterial pressure (MAP), systolic blood pressure (SYS), diastolic blood pressure (DIA), ocular perfusion pressure (OPP) are important factors for clinical considerations in glaucoma. The existence of linear relationships among these factors, referred to as multicollinearity in statistics, makes it difficult to determine the contribution of each factor to the overall glaucoma risk. The aim of thiswork is to describe howto account for multicollinearity when applying statistical methods to quantify glaucoma risk.Methods: Logistic regression models including multicollinear covariates are reviewed, and statistical techniques for the selection of non-redundant covariates are discussed. A meaningful statistical model including IOP, OPP and SYS as non-redundant covariates is obtained from a clinical dataset including 84 glaucoma patients and 73 healthy subjects, and is used to predict the probability that new individuals joining the study may have glaucoma, based on the values of their covariates.Results: Logistic models with satisfactory goodness-of-fit to the clinical dataset include age, gender, heart rate and either one of the following triplets as covariates: (i)(SYS, DIA, OPP); (ii) (IOP, SYS, OPP); (iii) (IOP, SYS, DIA); or (iv) (IOP, SYS, MAP). Choosing triplet (ii), higher disease probabilities are predicted for higher IOP levels. Similar predictions in terms of disease probability can be obtained for dierent combinations of OPP, SYS and IOP.Conclusion: Multicollinearity does not allow to clearly estimate the single eect of an individual covariate on the overall glaucoma risk. Instead, statistically assessing the combined eects of IOP, OPP, and blood pressure provide useful predictions of disease probability.

Heterogeneity in arterial hypertension and ocular perfusion pressure definitions: Towards a consensus on blood pressure‐related parameters for glaucoma studies

2018 ◽  
Vol 97 (4) ◽  
pp. e487-e492 ◽  
Author(s):  
João Barbosa‐Breda ◽  
Luis Abegão‐Pinto ◽  
Karel Van Keer ◽  
Danilo A. Jesus ◽  
Sophie Lemmens ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Arterial Hypertension ◽  
Perfusion Pressure ◽  
Ocular Perfusion Pressure ◽  
Ocular Perfusion

On Graphically Checking Goodness-of-fit of Binary Logistic Regression Models

2009 ◽  
Vol 48 (03) ◽  
pp. 306-310 ◽  
Author(s):  
C. E. Minder ◽  
G. Gillmann
Keyword(s):  
Logistic Regression ◽  
Regression Analysis ◽  
Regression Models ◽  
Goodness Of Fit ◽  
Graphical Method ◽  
Logistic Models ◽  
Binary Logistic Regression ◽  
Logistic Regression Models ◽  
Logistic Analysis ◽  
Viable Solution

Summary Objectives: This paper is concerned with checking goodness-of-fit of binary logistic regression models. For the practitioners of data analysis, the broad classes of procedures for checking goodness-of-fit available in the literature are described. The challenges of model checking in the context of binary logistic regression are reviewed. As a viable solution, a simple graphical procedure for checking goodness-of-fit is proposed. Methods: The graphical procedure proposed relies on pieces of information available from any logistic analysis; the focus is on combining and presenting these in an informative way. Results: The information gained using this approach is presented with three examples. In the discussion, the proposed method is put into context and compared with other graphical procedures for checking goodness-of-fit of binary logistic models available in the literature. Conclusion: A simple graphical method can significantly improve the understanding of any logistic regression analysis and help to prevent faulty conclusions.

scholarly journals Blood Pressure, Ocular Perfusion Pressure, and Body Mass Index in Glaucoma Patients

2013 ◽  
Vol 23 (5) ◽  
pp. 664-669 ◽  
Author(s):  
Sandra Ngo ◽  
Alon Harris ◽  
Brent A. Siesky ◽  
Anne Schroeder ◽  
George Eckert ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Body Mass Index ◽  
Body Mass ◽  
Perfusion Pressure ◽  
Ocular Perfusion Pressure ◽  
Ocular Perfusion

scholarly journals How to Test for Goodness of Fit in Ordinal Logistic Regression Models

2017 ◽  
Vol 17 (3) ◽  
pp. 668-686 ◽  
Author(s):  
Morten W. Fagerland ◽  
David W. Hosmer
Keyword(s):  
Regression Models ◽  
Goodness Of Fit ◽  
Logistic Models ◽  
Ratio Test ◽  
Response Variable ◽  
Logistic Regression Models ◽  
Explanatory Variables ◽  
Goodness Of Fit Tests ◽  
Interaction Terms ◽  
Different Types

Ordinal regression models are used to describe the relationship between an ordered categorical response variable and one or more explanatory variables. Several ordinal logistic models are available in Stata, such as the proportional odds, adjacent-category, and constrained continuation-ratio models. In this article, we present a command (ologitgof) that calculates four goodness-of-fit tests for assessing the overall adequacy of these models. These tests include an ordinal version of the Hosmer–Lemeshow test, the Pulkstenis–Robinson chi-squared and deviance tests, and the Lipsitz likelihood-ratio test. Together, these tests can detect several different types of lack of fit, including wrongly specified continuous terms, omission of different types of interaction terms, and an unordered response variable.

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