Discovering Effect Modification in an Observational Study of Surgical   Mortality at Hospitals with Superior Nursing
  There is effect modification if the magnitude or stability of a treatment effect varies systematically with the level of an observed covariate. A larger or more stable treatment effect is typically less sensitive to bias from unmeasured covariates, so it is important to recognize effect modification when it is present. We illustrate a recent proposal for conducting a sensitivity analysis that empirically discovers effect modification by exploratory methods, but controls the family-wise error rate in discovered groups. The example concerns a study of mortality and use of the intensive care unit in 23,715 matched pairs of two Medicare patients, one of whom underwent surgery at a hospital identified for superior nursing, the other at a conventional hospital. The pairs were matched exactly for 130 four-digit ICD-9 surgical procedure codes and balanced 172 observed covariates. The pairs were then split into five groups of pairs by CART in its effort to locate effect modification. The evidence of a beneficial effect of magnet hospitals on mortality is least sensitive to unmeasured biases in a large group of patients undergoing rather serious surgical procedures, but in the absence of other life-threatening conditions, such as a comorbidity of congestive heart failure or an emergency admission leading to surgery. 
Kwonsang Lee, Dylan S. Small, Jesse Y. Hsu, Jeffrey H. Silber and Paul   R. Rosenbaum
stat.AP