Bayesian classification of tumours by using gene expression data

Summary. Precise classification of tumours is critical for the diagnosis and treatment of cancer. Diagnostic pathology has traditionally relied on macroscopic and microscopic histology and tumour morphology as the basis for the classification of tumours. Current classification frameworks, however, cannot discriminate between tumours with similar histopathologic features, which vary in clinical course and in response to treatment. In recent years, there has been a move towards the use of complementary deoxyribonucleic acid microarrays for the classi‐fication of tumours. These high throughput assays provide relative messenger ribonucleic acid expression measurements simultaneously for thousands of genes. A key statistical task is to perform classification via different expression patterns. Gene expression profiles may offer more information than classical morphology and may provide an alternative to classical tumour diagnosis schemes. The paper considers several Bayesian classification methods based on reproducing kernel Hilbert spaces for the analysis of microarray data. We consider the logistic likelihood as well as likelihoods related to support vector machine models. It is shown through simulation and examples that support vector machine models with multiple shrinkage parameters produce fewer misclassification errors than several existing classical methods as well as Bayesian methods based on the logistic likelihood or those involving only one shrinkage parameter.