Causal attribution fractions for epidemiological studies, applied to a UK Biobank study of smoking and BMI
Epidemiological studies often use proportional hazard models to estimate associations between potential risk factors and disease risk. It is emphasised that when the "backdoor criteria" from causal-inference applies, if diseases are sufficiently rare, then the proportional hazard model can be used to estimate causal associations. When the "frontdoor criteria" applies (allowing causal estimates with unmeasured confounders), similar estimates are found to mediation analyses with measured confounders. Reasons for this are discussed. An attribution fraction is constructed using the average causal effects (ACE) of exposures on the population, and simple methods for its evaluation are suggested. It differs from the attribution fraction used by the World Health Organisation (WHO), except for specific circumstances where the latter can agree or provide a bound. A counterfactual argument determines an individual's attribution fraction Af in terms of proportional hazard estimates, as Af = 1 − 1/R, where R is an individual's relative risk. Causally meaningful attribution fractions cannot be constructed for all known risk factors or confounders, but there are important cases where they can. As an example, systematic proportional hazards studies with UK Biobank data estimate the attribution fractions of smoking and BMI for 226 diseases. The attribution of risk is characterised in terms of disease chapters from the International Classification of Diseases (ICD-10), and the diseases most strongly attributed to smoking and BMI are identified. The result is a quantitative characterisation of the causal influence of smoking and BMI on the landscape of disease incidence in the UK Biobank population.