Unobserved heterogeneity: The odd effects of frailty

Individuals differ. This is a basic observation of life and also of statistics. Some die old and some die young. Some are tall and some are small. In medicine one will find that a treatment that is useful for one person may be much less so for another person. And one person’s risk factor may be less risky for another one. This variation is found everywhere in biology and other fields, like in reliability studies of technical devices. Even between genetically inbred laboratory animals one observes a considerable variation.

One aim of a statistical analysis may be precisely to understand the factors determining such variation. For instance one might perform a regression analysis with some covariates. However, it is a general observation that such analyses always leave an unexplained rest. There is some variation that cannot be explained by observable covariates, and sometimes this remaining variation may be large and important. Traditionally, this is considered an error variance, something that creates uncertainty but can otherwise be handled in the statistical analysis, and usually one would not worry too much about it. However, in some cases there are reasons to worry.