Statistical models are often used for the prediction of
future random variables. There are two types of prediction, point
prediction and probabilistic prediction. The prediction accuracy is
quantified by performance measures, which are typically based on
loss functions. We study the estimators of these performance
measures, the prediction error and performance scores, for point and
probabilistic predictors, respectively. The focus of this thesis is
to assess the prediction performance of survival models that analyze
censored survival times. To accommodate censoring, we extend the
inverse probability censoring weighting (IPCW) method, thus
arbitrary loss functions can be handled. We also develop confidence
interval procedures for these performance measures.
We compare model-based, apparent loss based and cross-validation
estimators of prediction error under model misspecification and
variable selection, for absolute relative error loss (in chapter 3)
and misclassification error loss (in chapter 4). Simulation results
indicate that cross-validation procedures typically produce reliable
point estimates and confidence intervals, whereas model-based
estimates are often sensitive to model misspecification. The methods
are illustrated for two medical contexts in chapter 5. The apparent
loss based and cross-validation estimators of performance scores for
probabilistic predictor are discussed and illustrated with an
example in chapter 6. We also make connections for performance.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/3974 |
| Date | January 2008 |
| Creators | Yuan, Yan |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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