Introduction

Abstract

Isotonic inference concerns situations in which a set of parameters is assumed, a priori, to satisfy certain order restrictions. In the most common case, where populations are arranged in ordered groups, the parameter of interest is assumed to change monotonically with the ordering of the groups. It is then reasonable to take account of the order restrictions in making inferences about the group parameters, such as point or interval estimations or significance tests. Isotonic inference represents a statistical tool of great value in many areas of applied research, especially within the fields of genetic epidemiology and molecular genetics. The purpose of this book is to illustrate a new statistical approach to test allelic association and genotype-specific effects in the genetic study of a disease. We deal with population-based association studies via permutation testing and some likelihood-based tests, but comparisons with other methods will also be performed, analysing advantages and disadvantages of each one, particularly with regard to power properties with small sample sizes. We will focus on case-control analyses to study allelic association between marker, disease-gene and environmental factors. Permutation tests, in particular, will be extended to multivariate and more complex studies where we deal with several genes and several alleles together.