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Default Priors for the Intercept Parameter in Logistic Regressions.

ABSTRACT: In logistic regression, separation occurs when a linear combination of predictors perfectly discriminates the binary outcome. Because finite-valued maximum likelihood parameter estimates do not exist under separation, Bayesian regressions with informative shrinkage of the regression coefficients offer a suitable alternative. Classical studies of separation imply that efficiency in estimating regression coefficients may also depend upon the choice of intercept prior, yet relatively little focus has been given on whether and how to shrink the intercept parameter. Alternative prior distributions for the intercept are proposed that downweight implausibly extreme regions of the parameter space, rendering regression estimates that are less sensitive to separation. Through simulation and the analysis of exemplar datasets, differences across priors stratified by established statistics measuring the degree of separation are quantified. Relative to diffuse priors, these proposed priors generally yield more efficient estimation of the regression coefficients themselves when the data are nearly separated. They are equally efficient in non-separated datasets, making them suitable for default use. Modest differences were observed with respect to out-of-sample discrimination. These numerical studies also highlight the interplay between priors for the intercept and the regression coefficients: findings are more sensitive to the choice of intercept prior when using a weakly informative prior on the regression coefficients than an informative shrinkage prior.

SUBMITTER: Boonstra PS

PROVIDER: S-EPMC6748335 | biostudies-literature | 2019 May

REPOSITORIES: biostudies-literature

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Default Priors for the Intercept Parameter in Logistic Regressions.

Boonstra Philip S PS Barbaro Ryan P RP Sen Ananda A

Computational statistics & data analysis 20181105

In logistic regression, separation occurs when a linear combination of predictors perfectly discriminates the binary outcome. Because finite-valued maximum likelihood parameter estimates do not exist under separation, Bayesian regressions with informative shrinkage of the regression coefficients offer a suitable alternative. Classical studies of separation imply that efficiency in estimating regression coefficients may also depend upon the choice of intercept prior, yet relatively little focus h ...[more]

PMID: 31530966

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Project description:BackgroundGeneralized regression neural network (GRNN) and logistic regression (LR) are extensively used in the medical field; however, the better model for predicting stroke outcome has not been established. The primary goal of this study was to compare the accuracies of GRNN and LR models to identify the most optimal model for the prediction of acute stroke outcome, as well as explore useful biomarkers for predicting the prognosis of acute stroke patients.MethodIn a single-center study, 216 (80% for the training set and 20% for the test set) acute stroke patients admitted to the Shenzhen Second People's Hospital between December 2019 to June 2021 were retrospectively recruited. The functional outcomes of the patients were measured using Barthel Index (BI) on discharge. A training set was used to optimize the GRNN and LR models. The test set was utilized to validate and compare the performances of GRNN and LR in predicting acute stroke outcome based on the area under the receiver operating characteristic curve (AUROC), accuracy, sensitivity, and the Kappa value.ResultThe LR analysis showed that age, the National Institute Health Stroke Scale score, BI index, hemoglobin, and albumin were independently associated with stroke outcome. After validating in test set using these variables, we found that the GRNN model showed a better performance based on AUROC (0.931 vs 0.702), sensitivity (0.933 vs 0.700), specificity (0.889 vs 0.722), accuracy (0.896 vs 0.729), and the Kappa value (0.775 vs 0.416) than the LR model.ConclusionOverall, the GRNN model demonstrated superior performance to the LR model in predicting the prognosis of acute stroke patients. In addition to its advantage in not affected by implicit interactions and complex relationship in the data. Thus, we suggested that GRNN could be served as the optimal statistical model for acute stroke outcome prediction. Simultaneously, prospective validation based on more variables of the GRNN model for the prediction is required in future studies.

Dataset Information

Default Priors for the Intercept Parameter in Logistic Regressions.

Publications

Default Priors for the Intercept Parameter in Logistic Regressions.

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