Variable selection in modelling clustered data via within‐cluster resampling

In many biomedical applications, there is a need to build risk‐adjustment models based on clustered data. However, methods for variable selection that are applicable to clustered discrete data settings with a large number of candidate variables and potentially large cluster sizes are lacking. We develop a new variable selection approach that combines within‐cluster resampling techniques with penalized likelihood methods to select variables for high‐dimensional clustered data. We derive an upper bound on the expected number of falsely selected variables, demonstrate the oracle properties of the proposed method and evaluate the finite sample performance of the method through extensive simulations. We illustrate the proposed approach using a colon surgical site infection data set consisting of 39,468 individuals from 149 hospitals to build risk‐adjustment models that account for both the main effects of various risk factors and their two‐way interactions.