Cluster analysis of microarray data using the in-group proportion

The cDNA microarray revolutionized the field of biology and ushered in the era of genomics and proteomics. In addition, it has the potential to change the field of statistics because the data generated from microarray experiments are very different from traditional data structures. In statistics, a typical dataset has more observations than features. A typical microarray dataset, however, has many more features than observations. Therefore, methods for analyzing this type of data are required.; A new statistic, the in-group proportion (IGP), is designed to do just that. In this dissertation it is introduced, its properties are described, and two cluster analysis methods that use the in-group proportion are presented. Although both methods may be applied to low-dimensional or high-dimensional data, they are designed specifically for microarray datasets. One method is for estimating the number of clusters present in a dataset. The other method is for statistically validating clusters found in one dataset using an independent dataset. Both methods are shown to be effective when applied to simulated and real datasets. Moreover, the latter method is applied to an extensive cDNA microarray dataset to discover and statistically validate three subtypes of breast cancer that are subsequently shown to also be biologically valid.; These methods and the results are somewhat crude. They are intended to be a starting point upon which more sophisticated procedures and analyses are to be based. Nevertheless, as shown in this dissertation, the in-group proportion and these generally-applicable methods can play important roles, especially prior to the development of more theoretically rigorous statistics and tests.