In several types of study we may want to examine the consistency of an observed relation across two or more subgroups of the individuals studied. For example, in a clinical trial we might want to know if the observed treatment difference is the same for young and old patients or for different stages of disease at presentation. In an epidemiological study we might want to know whether the observed relation between an exposure and disease is different among smokers and non-smokers

In such cases we are interested in examining whether one effect is modified by the value of another variable. This may be viewed as the examination of the heterogeneity of an observed effect, such as treatment benefit in a clinical trial, across subsets of individuals. The statistical term for heterogeneity of this type is …