In IyarLin/segmenTree: Find sub groups (segments) with heterogenuus treatment effect in Randomised Controlled Trial data.

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The 'segmenTree' algorithm is a decision tree based algorithm for discovery of heterogeneous treatment effects in randomized controlled trial (RCT) data.

What follows below is a light intro to the algorithm specifics.

Problem setup

We observe a RCT data ${y_i,x_i,t_i}_{i=1}^{N}$ where $y_i \in {0,1}$ is a binary outcome of interest, $t_i \in {0,1}$ is a binary treatment and $x_i \in \mathbb{R}^p$ is a vector of observation covariates. Since our data was generated in a RCT we can assume that the treatment assignment is independent of the covariates such that: $P(T_i = 1|x_i) = P(T_i = 1)$, meaning: $P(Y|do(T=1)) = P(Y|T=1)$.

In RCTs one usually estimates the average treatment effect $ATE$ using:

$$\hat{ATE} = \mathbb{E}(Y|T=1) - \mathbb{E}(Y|T=0) = \frac{\sum_{i=1}^N {y_i=1,t_i=1}}{\sum_{i=1}^N{t_i=1}} - \frac{\sum_{i=1}^N {y_i=1,t_i=0}}{\sum_{i=1}^N{t_i=0}}$$ We'd like to go a step further and partition the data to $k$ segments ${l_j}_{j=1}^k$ such that we maximize the associated segment average treatment effect ${ATE_j}$ heterogeneity. More on what that means later.

These segment $ATE_j$ are known in the literature as conditional treatment effect (AKA $CATE$): $\tau(x) = ATE_j \,\, \forall x \in l_j = \mathbb{E}(Y|T = 1, X = x) - \mathbb{E}(Y|T = 0, X = x)$ where in our case. We can estimate the $ATE_j$ with:

$$\hat{ATE}j = \frac{\sum{i=1}^N {y_i=1,t_i=1,x_i \in l_j}}{\sum_{i=1}^N{t_i=1,x_i \in l_j}} - \frac{\sum_{i=1}^N {y_i=1,t_i=0,x_i \in l_j}}{\sum_{i=1}^N{t_i=0,x_i \in l_j}}$$

IyarLin/segmenTree documentation built on July 24, 2020, 7:35 p.m.