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#### Statistical Methods for High Throughput Screening Drug Discovery Data

(University of Waterloo, 2005)

High Throughput Screening (HTS) is used in drug discovery to screen large numbers of compounds against a biological target. Data on activity against the target are collected for a representative sample of compounds selected from a large library. The goal of drug discovery is to relate the activity of a compound to its chemical structure, which is quantified by various explanatory variables, and hence to identify further active compounds. Often, this application has a very unbalanced class distribution, with a rare active class. <br /><br /> Classification methods are commonly proposed as solutions to this problem. However, regarding drug discovery, researchers are more interested in ranking compounds by predicted activity than in the classification itself. This feature makes my approach distinct from common classification techniques. <br /><br /> In this thesis, two AIDS data sets from the National Cancer Institute (NCI) are mainly used. Local methods, namely K-nearest neighbours (KNN) and classification and regression trees (CART), perform very well on these data in comparison with linear/logistic regression, neural networks, and Multivariate Adaptive Regression Splines (MARS) models, which assume more smoothness. One reason for the superiority of local methods is the local behaviour of the data. Indeed, I argue that conventional classification criteria such as misclassification rate or deviance tend to select too small a tree or too large a value of

**k**(the number of nearest neighbours). A more local model (bigger tree or smaller**k**) gives a better performance in terms of drug discovery. <br /><br /> Because off-the-shelf KNN works relatively well, this thesis takes this promising method and makes several novel modifications, which further improve its performance. The choice of**k**is optimized for each test point to be predicted. The empirically observed superiority of allowing**k**to vary is investigated. The nature of the problem, ranking of objects rather than estimating the probability of activity, enables the**k**-varying algorithm to stand out. Similarly, KNN combined with a kernel weight function (weighted KNN) is proposed and demonstrated to be superior to the regular KNN method. <br /><br /> High dimensionality of the explanatory variables is known to cause problems for KNN and many other classifiers. I propose a novel method (subset KNN) of averaging across multiple classifiers based on building classifiers on subspaces (subsets of variables). It improves the performance of KNN for HTS data. When applied to CART, it also performs as well as or even better than the popular methods of bagging and boosting. Part of this improvement is due to the discovery that classifiers based on irrelevant subspaces (unimportant explanatory variables) do little damage when averaged with good classifiers based on relevant subspaces (important variables). This result is particular to the ranking of objects rather than estimating the probability of activity. A theoretical justification is proposed. The thesis also suggests diagnostics for identifying important subsets of variables and hence further reducing the impact of the curse of dimensionality. <br /><br /> In order to have a broader evaluation of these methods, subset KNN and weighted KNN are applied to three other data sets: the NCI AIDS data with Constitutional descriptors, Mutagenicity data with BCUT descriptors and Mutagenicity data with Constitutional descriptors. The**k**-varying algorithm as a method for unbalanced data is also applied to NCI AIDS data with Constitutional descriptors. As a baseline, the performance of KNN on such data sets is reported. Although different methods are best for the different data sets, some of the proposed methods are always amongst the best. <br /><br /> Finally, methods are described for estimating activity rates and error rates in HTS data. By combining auxiliary information about repeat tests of the same compound, likelihood methods can extract interesting information about the magnitudes of the measurement errors made in the assay process. These estimates can be used to assess model performance, which sheds new light on how various models handle the large random or systematic assay errors often present in HTS data....#### Convex duality in constrained mean-variance portfolio optimization under a regime-switching model

(University of Waterloo, 2008-09-23)

In this thesis, we solve a mean-variance portfolio optimization problem with portfolio constraints under a regime-switching model. Specifically, we seek a portfolio process which minimizes the variance of the terminal ...

#### Multivariate First-Passage Models in Credit Risk

(University of Waterloo, 2008-10-17)

This thesis deals with credit risk modeling and related mathematical issues. In particular we study first-passage models for credit risk, where obligors default upon first passage of a ``credit quality" process to ...

#### Statistical Learning in Drug Discovery via Clustering and Mixtures

(University of Waterloo, 2007-09-20)

In drug discovery, thousands of compounds are assayed to detect activity against a
biological target. The goal of drug discovery is to identify compounds that are active against the target (e.g. inhibit a virus). Statistical ...

#### Efficient Procedure for Valuing American Lookback Put Options

(University of Waterloo, 2007-05-22)

Lookback option is a well-known path-dependent option where its
payoff depends on the historical extremum prices. The thesis focuses
on the binomial pricing of the American floating strike lookback put
options with ...

#### Robust Estimation of Mean Functions and Treatment Effects for Recurrent Events Under Event-Dependent Censoring and Termination: Application to Skeletal Complications in Cancer Metastatic to Bone

(Taylor & Francis, 2009)

In clinical trials featuring recurrent clinical events, the definition and estimation of treatment
effects involves a number of interesting issues, especially when loss to follow-up may be eventrelated
and when terminal ...

#### A Multistate Model for Bivariate Interval-Censored Failure Time Data

(Wiley, 2008-12)

Interval-censored life-history data arise when the events of interest are only detectable at periodic assessments. When interest lies in the occurrence of two such events, bivariate-interval censored event time data are ...

#### Interval Censoring and Longitudinal Survey Data

(University of Waterloo, 2007-09-11)

Being able to explore a relationship between two life events is of great interest to scientists from different disciplines. Some issues of particular concern are, for example, the connection between smoking cessation and ...

#### Topics in Delayed Renewal Risk Models

(University of Waterloo, 2007-08-03)

Main focus is to extend the analysis of the ruin related
quantities, such as the surplus immediately prior to ruin, the
deficit at ruin or the ruin probability, to the delayed renewal
risk models.
First, the background ...

#### Efficient Kernel Methods for Statistical Detection

(University of Waterloo, 2008-03-28)

This research is motivated by a drug discovery problem -- the AIDS anti-viral database from the National Cancer Institute. The objective of the study is to develop effective statistical methods to model the relationship ...