. Author manuscript; available in PMC: 2019 May 20.

Published in final edited form as: Stat Med. 2018 Mar 6;37(11):1767–1787. doi: 10.1002/sim.7623

Algorithm 1.

PTO forest.

Require: Data (X_i, T_i, Y_i). estimated propensity function

\hat{π} (\cdot)

Z_{i} \leftarrow T_{i} \frac{Y_{i}}{\hat{π} (X_{i})} + (1 - T_{i}) \frac{- Y_{i}}{1 - \hat{π} (X_{i})}

1. (TO forest) Build a depth-controlled random forest F on X to predict Z.

2. (Pollination) For each tree in the forest F, replace the node estimates

\bar{Z}

with

{\bar{Y}}_{1} - {\bar{Y}}_{0}

. This entails sending each observation down each tree to get the mean response in treatment and control groups for each leaf, replacing the mean TO. This yields treatment effect estimates

{\hat{τ}}_{i}

3. (Optional) Build an additional random forest G on X to predict

\hat{τ}

. This adds a layer of regularization and interpretability (through variable importance) of the results.