As a guide to practitioners, we describe a variety of methods for obtaining standard errors and confidence intervals for subsample and 2-sample IV estimators. When the IV is strong, the SUR/delta method used in this work is appropriate and produces quite similar confidence intervals compared with the other methods examined. However, for moderate and weaker IVs, the Fieller, bootstrap, and Bayesian confidence intervals are considerably larger than those derived from the SUR/delta methods and sequential regression. The SUR/delta and sequential regression methods are problematic for weak IV scenarios, since they do not adequately account for the error that accompanies estimation of the effect of the IV on the exposure, and they assume that the sampling distribution of the IV estimate is normal. Thus, in the presence of a weaker IV, more robust methods for confidence interval calculation may be needed, such as bootstrapping. Unfortunately, bootstrapping was not computationally feasible for the simulation-based work presented here. Fieller's theorem is a straightforward alternative strategy for confidence interval calculation without the assumption of a normal distribution for the IV estimate; details on how
