Corbett, Philip (2001) Accuracy of logistic models and receiver operating characteristic curves. PhD thesis, University of Warwick.

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Abstract

The accuracy of prediction is a commonly studied topic in modern statistics. The
performance of a predictor is becoming increasingly more important as real-life
decisions axe made on the basis of prediction. In this thesis we investigate the
prediction accuracy of logistic models from two different approaches.
Logistic regression is often used to discriminate between two groups or populations
based on a number of covariates. The receiver operating characteristic
(ROC) curve is a commonly used tool (especially in medical statistics) to assess
the performance Of such a score or test. By using the same data to fit the logistic
regression and calculate the ROC curve we overestimate the performance that
the score would give if validated on a sample of future cases. This overestimation
is studied and we propose a correction for the ROC curve and the area under the
curve. The methods axe illustrated through way of two medical examples and a
simulation study, and we show that the overestimation can be quite substantial
for small sample sizes.
The idea of shrinkage pertains to the notion that by including some prior information
about the data under study we can improve prediction. Until now,
the study of shrinkage has almost exclusively been concentrated on continuous
measurements. We propose a methodology to study shrinkage for logistic regression
modelling of categorical data with a binary response. Categorical data
with a large number of levels is often grouped for modelling purposes, which
discards useful information about the data. By using this information we can
apply Bayesian methods to update model parameters and show through examples
and simulations that in some circumstances the updated estimates are better
predictors than the model.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Receiver operating characteristic curves, Logistic regression analysis
Official Date:	August 2001
Dates:	Date Event August 2001 Submitted
Institution:	University of Warwick
Theses Department:	Department of Statistics
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Copas, John B.
Sponsors:	Engineering and Physical Sciences Research Council (EPSRC)
Extent:	x, 180 p.
Language:	eng

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