Adjusting for unmeasured confounding using validation data:simplified two-stage calibration for survival and dichotomous outcomes

In epidemiology, one typically wants to estimate the risk of an outcome associated with an exposure after adjusting for confounders. Sometimes, outcome and exposure and maybe some confounders are available in a large data set, whereas some important confounders are only available in a validation data set that is typically a subset of the main data set. A generally applicable method in this situation is the two-stage calibration (TSC) method. We present a simplified easy-to-implement version of the TSC for the case where the validation data are a subset of the main data. We compared the simplified version to the standard TSC version for incidence rate ratios, odds ratios, relative risks, and hazard ratios using simulated data, and the simplified version performed better than our implementation of the standard version. The simplified version was also tested on real data and performed well.