Risk in health: more information and more uncertainty

Risk is a major factor in health, with a strong focus on minimising risk wherever possible. The mathematical starting point is probability. Reliable or relevant data is often missing or hard to get. Moreover, the results of studies are all too easily interpreted wrongly – even by medical experts. Usually it is seen as useful to have more information in making decisions. As we show below this is not always true; we will use the exemplar of breast cancer and screening as an illustration throughout this paper to explain circumstances where there is ‘more information and more uncertainty’ following Knight and type 2 errors. We identify the different stakeholders and parts of their internal criteria that form their ‘rationality’, which may well be idiosyncratic. The intention is to pave the way for a ‘shared’ decision which is best for individuals and for society simultaneously. Statistics educators will find an important field of research and teaching.