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

Alessandra Guglielmi, Giovanna Guidoboni, Alon Harris

Abstract


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.


Keywords


glaucoma, generalized linear models, logistic regression, multicollinearity, statistical methods, disease probability

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