Finding the best treatment under heavy censoring and hidden bias

We analyse male survival duration after hospitalization following an acute myocardial infarction with a large (N = 11024) Finnish data set to find the best performing hospital district (and to disseminate its treatment protocol).This is a multiple-treatment problem with 21 treatments (i.e. 21 hospital districts).The task of choosing the best treatment is difficult owing to heavy right censoring (73%), which makes the usual location measures (the mean and median) unidentified; instead, only lower quantiles are identified. There is also a sample selection issue that only those who made it to a hospital alive are observed (54%); this becomes a problem if we wish to know their potential survival duration after hospitalization, if they had survived to a hospital contrary to the fact. The data set is limited in its covariates - only age is available - but includes the distance to the hospital, which plays an interesting role. Given that only age and distance are observed, it is likely that there are unobserved confounders. To account for them, a sensitivity analysis is conducted following pair matching. All estimators employed point to a clear winner and the sensitivity analysis indicates that the finding is fairly robust.