We define subsample and 2-sample IV estimation as follows. Assuming that data on the IV (G) are available for all participants, subsample IV estimation can occur when data on the exposure (X) are available for only a subset of participants but outcome data (Y) are available for all participants. The samples with data on X and Y have sample sizes defined as nX and nY, respectively. Subsample IV estimation could also occur when data on Y are available for a subset of participants but data on X are available for all participants, although this strategy is not considered further here. Two-sample IV estimation occurs when data on G and X are available for one sample and data on G and Y are available on an independent sample, such that no participants have data on both X and Y.
