Using interactions of area dose and individual exposure to estimate effects of population health interventions

Evaluations of natural experiments in population health studies typically construct and compare exposed and unnexposed populations classified by area or individual exposure. Populations are often dichotomised on one of these dimensions, even if the underlying dose of exposure is graded. We propose that effects of population health interventions can be estimated more accurately by using both dimensions, using an interaction of a continuous measure of dose at area level and the probability of exposure at the individual level. This is particularly useful when receipt of treatment by individuals is either unknown or endogenous. This dose-exposure interaction can be integrated into many common natural experiment designs and we propose it as a verification test. Furthermore, this interaction term can be calibrated to be a predicted probability of exposure and then used to ensure the magnitude of the estimated treatment effect is plausible. We describe how to use this approach and demonstrate its application in two examples: the effects of introducing social prescribing link workers on whether people feel supported by local services; and the effects of a welfare reform on the mental health of benefit claimants. In both cases and in a simulation study, the interactions approach produces more specific, precise and interpretable estimates of intervention effects. We suggest that researchers evaluating population health interventions that are expected to impact on some populations more than others should consider using a dose-exposure interaction design.