The investigators used physicians' prescribing preferences as instrumental variables, as described in Section 1, for the physicians' prescriptions of varenicline or nicotine replacement products. In the conventional observational analysis, after adjustment for a wide range of observable patient characteristics, patients prescribed varenicline had a 51% lower risk of all-cause mortality than those prescribed other nicotine replacement products in the nine months after their first prescription, (hazard ratio=0.49, 95% confidence interval (95%CI): 0.40 to 0.61). However, the investigators found little evidence of a reduction in all-cause mortality using instrumental variable analysis (risk difference per 1,000 prescriptions=0.7, 95% CI: -3.3 to 4.7). This suggests that the conventional multivariable-adjusted regression may have suffered from bias due to unmeasured confounding, as the effect sizes are implausible.