Supervised and unsupervised latent class models for high-dimensional data

High-dimensional data are becoming quite common in biomedical applications. Examples of such data include histological, genetic, and microarray data. Often, in cancer research, new diseases are not well-characterized and nonclinical presentations may be subject to inter-observer variability. In the presence of a large number of observed variables, researchers are often interested in clustering or classification based on these variables, in order to ascertain diagnosis or prognosis. Latent class analysis summarizes correlated variables by estimating a few unobservable latent classes, and is a useful technique for data reduction and classification. This work considers latent class methods for high-dimensional data, in order to elucidate clinical subsets and prognosis of cancer patients. Chapter 1 presents a penalized latent class model for ordinal data. Ordinal data are common when assessing cancer histology, as many histological variables are measured on an ordinal scale. The methodology is illustrated on a study of schwannoma, a tumor of the nerve sheath, and elucidates a few features that are useful in predicting latent class membership. Chapter 2 considers a supervised approach to latent class analysis for high-dimensional data. In this approach, survival informs the latent class structure. Two models are considered: one that incorporates a variable selection procedure in order to discriminate variables that are predictive of survival, and one that incorporates smoothing of class-specific probabilities. The methodologies are compared and illustrated on a study of a promising glioma gene, YKL-40. Both methods are successful in uncovering classes of glioma patients that correlate with survival. The analysis demonstrates immunohistochemical measurements of YKL-40 predict survival, even in the presence of clinical diagnosis. Chapter 3 considers latent class methods for the analysis of aCGH data. The methodology developed in this chapter leads to the classification of cancer patients into clinical subsets, allowing researchers to characterize the genomic profiles of these subsets. This is achieved by considering a latent class analysis that accounts for correlation in DNA copy number across the chromosome. Based on copy number profiles, the methodology characterizes distinct classes of glioma patients that correlate with diagnosis and prognosis.