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Loss Function Based Ranking Methods with Applications to Health Services Research and Gene Expression

 Rongheng Lin, PhD Candidate, Johns Hopkins Department of Biostatistics

Ranking methods are important in performance comparison of a group of units and in identifying outlying units. Examples of the this former are to rank health services providers or educational institutions; the examples of this later are to identify the areas with elevated disease incidence and to identify the differential expressed genes. When (posterior) distributions of the parameters of interest are stochastically ordered, all reasonable ranking methods should lead to same result. However, when these distributions are not stochastically ordered, the performance of ranks based on traditional statistics (e.g., Maximum likelihood estimates, Bayes Posterior Means, hypothesis test statistics) is usually not optimal, since these statistics were not designed for the ranking goal.

In this thesis, we consider the loss function based ranking approach. With loss functions as guides, we use both parametric and semi-parametric hierarchical models to produce ranks and evaluate them by both mathematical analysis and simulation. Estimates that minimize Squared Error Loss for ranks (e.g, the posterior mean ranks) are effective, but in many applications interest focuses on identifying the relatively good (e.g., in the upper 10%) or relatively poor performers. We construct loss functions and optimizing rank estimates that address these goals and evaluate these and other candidate estimates. We apply our new ranking methods to two applications, in comparison with other ranking methods; the analysis of standardized mortality ratios computed from the U.S Renal Data System and the analysis of differential gene expression levels in two groups of lung cancer patients.

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