Adjustment for missing confounders in studies based on observational databases: 2-stage calibration combining propensity scores from primary and validation data.

Bias caused by missing or incomplete information on confounding factors constitutes an important challenge in observational studies. The incorporation of external data on more detailed confounding information into the main study data may help remove confounding bias. This work was motivated by a study of the association between chronic obstructive pulmonary disease and herpes zoster. Analyses were based on administrative databases in which information on important confounders-cigarette smoking and alcohol consumption-was lacking. We consider adjusting for the confounding bias arising from missing confounders by incorporating a validation sample with data on smoking and alcohol consumption obtained from a small-scale National Health Interview Survey study. We propose a 2-stage calibration (TSC) method, which summarizes the confounding information through propensity scores and combines the analysis results from the main and the validation study samples, where the propensity score adjustment from the main sample is crude and that from the validation sample is more precise. Unlike the existing methods, the validity of the TSC approach does not rely on any specific measurement error model. When applying the TSC method to the motivating study above, the odds ratio of herpes zoster associated with chronic obstructive pulmonary disease is 1.91 (95% confidence interval: 1.62, 2.26) after adjustment for cumulative smoking and alcohol consumption.