A beginner’s guide to selection priors to test MNAR mechanisms
When embarking on a sensitivity analysis with pattern-mixture models, researchers should first decide whether they are interested in testing the impact of a range of additive and/or multiplicative offset terms. When analyzing a categorical outcome, only multiplicative terms should be used. When analyzing a continuous outcome, either could be used and so the researcher must apply local and expert knowledge to decide which type of offset most plausibly reflects the MNAR mechanism.
Each researcher will employ their own decision process to select a range of plausible offset values, depending on the data and knowledge they have available. These data may also guide your decision to choose an additive (\(delta\)) or multiplicative (\(c\)) offset parameter. Three sources of information we recommend exploring for selecting these values are:
Relevant scientific or gray literature
Local stakeholders who may have been involved in study implementation
Expert knowledge from individuals who implemented the study or studies similar, or who hold knowledge about the study population
To assess threats to causal inference from unmeasured confounders, Vanderweele and colleagues introduced the “E-Value”: “the minimum strength of association on the risk ratio scale that an unmeasured confounder would need to have with both the exposure and the outcome, conditional on the measured covariates, to fully explain away a specific exposure-outcome association.”
In the same vein, we propose that sensitivity analysis of MNAR mechanisms is fundamentally concerned with “At what direction and magnitude, would an MNAR mechanisms need to operate in order to wash out the causal effect I estimated under an MCAR or MAR assumption?”. In the absence of any relevant information on which to base your priors, we propose testing a very wide range of offset parameter values (using both additive and multiplicative offsets) and then reporting the magnitude of the offset at which your study conclusions would change.