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. Author manuscript; available in PMC: 2022 May 1.
Published in final edited form as: Epidemiology. 2021 May 1;32(3):393–401. doi: 10.1097/EDE.0000000000001332

Figure 1: General double cross-fit procedure for doubly robust estimators.

Figure 1:

Step 0) The exposure (X), outcome (Y), and necessary set of confounders for identification (Z) are identified and collected.

Step 1) The data is partitioned into three approximately equal sized sample splits.

Step 2) The treatment nuisance model and the outcome nuisance model are fit in each sample split.

Step 3) Predicted outcomes under each treatment are estimated using the nuisance models estimated using discordant data sets. For example, sample split 1 uses the treatment nuisance model from sample split 3 and the outcome nuisance model from sample split 2.

Step 4) The target parameter is calculated from the mean of the predictions across all splits. The variance for the particular split is calculated as the mean of variance of each split.

Steps 1-4 are repeated a number of times to reduce sensitivity to particular sample splits. The overall point estimate is calculated as the median of the point estimates for all of the different splits. The estimated variance consists of two parts: the variability of the ACE within a particular split and the variance of the ACE point estimate between each split.