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Efficient allocation of scarce resources to health programs involves measuring the economic benefits of life saving and/or improvement in health status. While several attempts have been made to quantify individual preferences for life, only a few, if any, have attempted to measure individual preferences for quality of life. In this thesis, we develop a methodology based on the estimation of individual preference functions to arrive at monetary measures of the value of marginal improvements in health status. / The first chapter reviews conventional methodologies for estimating the value of human life, and points out many theoretical and empirical propositions related to our own concerns. The second chapter analyzes various procedures used to quantify variations in health status. We distinguish non-monetary procedures, which combine recent psychometric techniques and research on health level scaling to obtain estimates of the relative desirability of a state of health, and monetary procedures which, we conclude, still need to be developed. / The third chapter presents a new methodology based on the direct estimation of bivariate welfare function of income and level of health. The theoretical basis of our approach and the data source are described in this chapter. Various functional forms were tried but we have finally retained the log-normal specification to derive estimates of the monetary value of a marginal change in the state of health for different subgroups of individuals. / We conclude with critical discussion of our results. Some improvements over the approach used are suggested in the fifth chapter.

A clinical trial is considered in which two treatments are to be compared. Treatment allocation schemes are usually designed to assign approximately equal numbers of patients to each treatment. The purpose of this thesis is to investigate the efficiency of estimation and the effect of instability in the response variable for allocation schemes which are aimed at reducing the number of patients who receive the inferior treatment. The general background to outcome-dependent allocation schemes is described in Chapter 1. A discussion of ethical and practical problems associated with these methods is presented together with brief details of actual trials conducted. In Chapter 2, the response to treatment is Bernoulli and the trial size is fixed. A simple method for estimating the treatment difference is proposed. Simulation results for a selection of allocation schemes indicate that the effect of instability upon the performance of the schemes can sometimes be substantial. A decision-theory approach is taken in Chapter 3. The trial is conducted in a number of stages and the interests of both the patients in the trial and those who will be treated after the end of the trial are taken into account. Using results for conditional normal distributions, analytical results are derived for estimation of the treatment difference for both a stable and an unstable normal response variable for three allocation schemes. Some results for estimation are also given for other responses. The problem of sequential testing is addressed in Chapter 4. With instability in the response variable, it is shown that the error probabilities for the test for a stable response variable can be approximately preserved by using a modified test statistic with appropriately-widened stopping boundaries. In addition, some recent results for estimation following sequential tests are outlined. Finally, the main conclusions of the thesis are highlighted in Chapter 5.

The intent of this research is to identify through various statistical analyses any features, attributes, or characteristics of Madison points from Albee Phase context that could be used to distinguish them from Madison points made and used by other contemporaneous prehistoric groups. Descriptive statistics for an assemblage of Albee points will be generated to establish baseline data that theoretically characterizes a modal behavior for Albee Phase flint knappers. The Albee Phase data will be combined with comparable data for Yankeetown points and Angel Phase points. This combined data set will constitute the research universe, which will be subjected to discriminant function analysis. Discriminant function analysis is envisioned as a tool to: 1) Identify variables or a combination of variables that are unique to Albee Phase triangular points, 2) Produce a linear function to define an Albee Phase Madison point, and 3) Test that function by successfully allocating the points in the research universe to their appropriate, archaeologically defined cultural group. / Department of Anthropology

Microarray technology allows researchers to monitor the mRNA transcription levels of thousands of genes in parallel which opens the door for more advanced cancer research. This thesis focuses on a case study of papillary thyroid carcinoma data. Fourteen publicly available Affymetrix microarray data sets were used where seven samples were collected from normal thyroid tissue and the remaining seven were collected from papillary thyroid carcinoma tissue. The present study compared the results obtained from three different normalization processes: MAS5.0, RMA and GCRMA in detecting differentially expressed genes under two conditions. Internal consistencies within the methods as well as the results across three methods were compared. Statistical packages 82.5.1 and Bioconductor 2.08 are used to perform the data analysis. Each step of normalization with MAS5.0 and RMA is described. Statistical package Limma is used to fit a linear model. Finally an empirical Bayes method is used to detect the significantly differentially expressed genes. First, considering all genes a comparison is made among the three normalization methods where RMA and GCRMA showed the maximum agreement in detecting differentially expressed genes. Then using unspecified filtering process a set of genes was selected and the whole process was replicated where the top fifty differentially expressed genes did not show any overlap with each other. / Department of Mathematical Sciences