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Book Summary:
This thesis investigates different statistical problems that appear in a clinical trial conducted to evaluate a diagnostic test. In particular, it examines methods that can be used to draw valid conclusions regarding test performance. This is because in clinical practice sometimes test accuracy is estimated based on a data set which is not representative of the whole population. In such cases, the test performance estimates are not accurate because of the so-called verification bias. Recent studies such as Kosinski and Barnhart (2003) treat verification bias as a missing data problem and apply frequentist approaches such as the EM algorithm. In this thesis I propose a Bayesian approach to verification bias correction. Moreover, I study how valuable the statistical findings are from the point of view of clinical decision making. In addition, this thesis introduces a method of designing clinical trials for test evaluation based on Bayesian decision theory. The proposed methodology is a Bayesian experimental design approach. It involves specifying a utility function that models the purpose of the experiment, namely the selection of patients for some risky diagnostic procedure. Also, a criterion for comparing experiments is calculated using Monte Carlo methods. The best set of experimental patients is selected by maximizing this criterion over the design space. This optimization problem poses computational difficulties due to a high dimensional discrete design space and, also, to an optimality criterion formula of high complexity. Recently, many such complicated design problems have appeared in clinical sciences and other fields, so that developing new optimal design methods represents an active area of research today. In particular simulation-based techniques are proposed in Clyde at al. (1995a), Bielza et al. (1999), Müller (1999). Novel deterministic algorithms are introduced in this thesis to perform a more systematic search over the design space and to address the computational difficulties. |
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