Table 1.

Analytical techniques included in Medical Research Council guidance on natural experimental studies ¹

Analytical technique	Brief description
Controlling for observable characteristics
Matching	Involves finding unexposed individuals (or clusters of individuals) which are similar to those receiving the intervention, and comparing outcomes in the two groups
Regression adjustment2	Measured characteristics that differ between those receiving the intervention and others can be taken into account in multiple regression analyses
Propensity scores	An estimate of the likelihood of being exposed given a set of covariates, propensity scores are usually estimated by logistic regression, and can be used to match exposed with unexposed units (which may be individuals or clusters of some kind) using values of the propensity score rather than the covariates themselves
Controlling for unobservable characteristics
Difference in differences	Involves comparison of change over time in exposed and unexposed groups, which enables control of unobserved individual differences and common trends
Instrumental variables	An instrumental variable is a factor associated with exposure to an intervention, but independent of other factors associated with exposure, and associated with outcomes only via its association with exposure
Regression discontinuity	This approach exploits a step change or ‘cutoff’ in a continuous variable used to assign treatment, or otherwise determine exposure to an intervention. The assumption is that units (individuals, areas, etc.) just below and just above this threshold will otherwise be similar in terms of characteristics that may influence outcomes

¹Source: Medical Research Council [9].

²For the purposes of the review, cross sectional studies that used single equation regression adjustment were excluded since they feature extensively in existing reviews.