The Instrumental Variable Method to Study Self-Selection Mechanism: A Case of Influenza Vaccination


Byung-Kwang Yoo, Centers for Disease Control and Prevention, NCBDDD, 1600 Clifton Road, MS E-87, Atlanta, GA 30333, USA. E-mail:


Objective:  To assess whether estimates of the effectiveness of influenza vaccination in reducing rates of hospitalizations and all-cause mortality derived from cross-sectional data could be improved by applying the instrumental variable (IV) method to data representing the community-dwelling elderly population in the United States in order to adjust for self-selection bias.

Methods:  Secondary data analysis, using the 1996–97 Medicare Current Beneficiary Survey data. First, using single-equation probit regressions this study analyzed influenza-related hospitalization and death due to all causes predicted by vaccination status, which was measured by claims or survey data. Second, to adjust for potential self-selection of the vaccine receipt, for example, higher vaccination rates among high-risk individuals, bivariate probit (BVP) models and two-stage least squares (2SLS) models were employed. The IV was having either arthritis or gout.

Results:  In single-equation probit models, vaccination appeared to be ineffective or even to increase the probability of adverse outcomes. Based on BVP and 2SLS models, vaccination was demonstrated to be effective in reducing influenza-related hospitalization by at least 31%. The BVP model results implied significant self-selection in the single-equation probit models.

Conclusions:  Adjusting for self-selection, BVP analyses yielded vaccine effectiveness estimates for a nationally representative cross-sectional sample of the community-dwelling elderly population that are consistent with previous estimates based on randomized controlled trials, prospective cohort studies, and meta-analyses. This result suggests that analyses with 2SLS and BVP in particular may be useful for the analysis of observational data regarding prevention in which self-selection is an important potential source of bias.