Abstract
Causal inference from observational data is notoriously difficult, and relies upon many unverifiable assumptions, including no confounding or selection bias. Here, we demonstrate how to apply a range of sensitivity analyses to examine whether a causal interpretation from observational data may be justified. These methods include: testing different confounding structures (as the assumed confounding model may be incorrect), exploring potential residual confounding and assessing the impact of selection bias due to missing data. We aim to answer the causal question 'Does religiosity promote cooperative behaviour?' as a motivating example of how these methods can be applied. We use data from the parental generation of a large-scale (n = approximately 14,000) prospective UK birth cohort (the Avon Longitudinal Study of Parents and Children), which has detailed information on religiosity and potential confounding variables, while cooperation was measured via self-reported history of blood donation. In this study, there was no association between religious belief or affiliation and blood donation. Religious attendance was positively associated with blood donation, but could plausibly be explained by unmeasured confounding. In this population, evidence that religiosity causes blood donation is suggestive, but rather weak. These analyses illustrate how sensitivity analyses can aid causal inference from observational research.