Probability and likelihood in genetic counselling

The aim of this paper is to clarify some of the concepts used in the calculation of risk in genetic counselling. The use of probability as a measure of risk in a particular case is reviewed, with special reference to the Fisher-Neyman controversy. The technical concept of likelihood is then introduced and applied to risk probabilities themselves. The difficulties of interpretation are discussed, with a distinction drawn between calculating the risk for a child and inferring the genotype of his mother, even though the risk is wholly determined by the genotype. Fiducial inference is briefly mentioned, and the paper ends with a discussion of the problem which arises when the functional relationship between an unknown parameter and the unknown risk is not 1:1. The conclusion is tentatively reached that risk can only be gauged by probability and thus that prior probabilities must sometimes be assumed, but the paper is primarily intended as a guide and catalyst for the informed discussion of some of the difficulties, which may involve ethical dilemmas.