Add IJMPR replication (#1436)

README.md

@@ -161,6 +161,10 @@ Imke Mayer, Erik Sverdrup, Tobias Gauss, Jean-Denis Moyer, Stefan Wager and Juli
 [<a href="https://projecteuclid.org/euclid.aoas/1600454872">paper</a>,
 <a href="https://arxiv.org/pdf/1910.10624.pdf">arxiv</a>]
 
+Erik Sverdrup, Maria Petukhova, and Stefan Wager.
+<b>Estimating Treatment Effect Heterogeneity in Psychiatry: A Review and Tutorial with Causal Forests.</b> 2024.
+[<a href="https://arxiv.org/abs/2409.01578">arxiv</a>]
+
 Stefan Wager and Susan Athey.
 <b>Estimation and Inference of Heterogeneous Treatment Effects using Random Forests.</b>
 <i>Journal of the American Statistical Association</i>, 113(523), 2018.

experiments/README.md

@@ -12,6 +12,8 @@ This directory contains replication code for
 
 * Mayer, Sverdrup, Gauss, Moyer, Wager, and Josse (2020): This is available at https://github.com/imkemayer/causal-inference-missing
 
+* Sverdrup, Petukhova, and Wager (2024): `ijmpr`
+
 * Wager and Athey (2018): This paper is not based on GRF, but on the deprecated `causalForest`. For replication code see https://github.com/swager/causalForest
 
 * Yadlowsky, Fleming, Shah, Brunskill, and Wager (2021): The method is available in the GRF function `rank_average_treatment_effect`. For replication code see https://github.com/som-shahlab/RATE-experiments
@@ -46,6 +48,10 @@ Imke Mayer, Erik Sverdrup, Tobias Gauss, Jean-Denis Moyer, Stefan Wager and Juli
 [<a href="https://projecteuclid.org/euclid.aoas/1600454872">paper</a>,
 <a href="https://arxiv.org/pdf/1910.10624.pdf">arxiv</a>]
 
+Erik Sverdrup, Maria Petukhova, and Stefan Wager.
+<b>Estimating Treatment Effect Heterogeneity in Psychiatry: A Review and Tutorial with Causal Forests.</b> 2024.
+[<a href="https://arxiv.org/abs/2409.01578">arxiv</a>]
+
 Stefan Wager and Susan Athey.
 <b>Estimation and Inference of Heterogeneous Treatment Effects using Random Forests.</b>
 <i>Journal of the American Statistical Association</i>, 113(523), 2018.

experiments/ijmpr/README.md

@@ -0,0 +1,14 @@
+_This folder has replication files for the paper "Estimating Treatment Effect Heterogeneity in Psychiatry: A Review and Tutorial with Causal Forests" by Sverdrup, Petukhova, and Wager._
+
+The file `analysis.R` contains example code to run the type of analysis described in the paper using synthetic data. This script relies on the packages `"grf", "maq", "ggplot2"`.
+
+The file `synthetic_data.csv` was generated using the following code and is not intended to bear resemblance to the Army STARRS-LS data used in the paper.
+
+```R
+n = 4000
+X = cbind(round(matrix(rnorm(n * 5), n, 5), 2), matrix(rbinom(n * 4, 1, 0.5), n, 4))
+W = rbinom(n, 1, 1 / (1 + exp(-X[, 1] - X[, 2])))
+Y = 1 - rbinom(n, 1, 1 / (1 + exp((pmax(2 * X[, 1], 0) * W + 1))))
+colnames(X) = make.names(1:ncol(X))
+write.csv(cbind(outcome = Y, treatment = W, X), "synthetic_data.csv", row.names = FALSE)
+```

experiments/ijmpr/analysis.R

@@ -0,0 +1,267 @@
+rm(list = ls())
+set.seed(42)
+
+library(grf)
+library(maq) # For Qini curves.
+library(ggplot2)
+
+# Read in data and specify outcome Y, treatment W, and (numeric) matrix of covariates X.
+data = read.csv("https://raw.githubusercontent.com/grf-labs/grf/master/experiments/ijmpr/synthetic_data.csv")
+Y = data$outcome
+W = data$treatment
+X = data[, -c(1, 2)]
+
+
+# This script assumes the covariates X have named columns.
+# If not provided, we make up some default names.
+if (is.null(colnames(X))) colnames(X) = make.names(1:ncol(X))
+
+
+# *** Estimating an average treatment effect (ATE) ***
+
+# A simple difference in means estimate ignoring non-random assignment.
+summary(lm(Y ~ W))
+
+# A doubly robust ATE estimate (forest-based AIPW).
+cf.full = causal_forest(X, Y, W)
+average_treatment_effect(cf.full)
+
+# A histogram of the estimated propensity scores.
+# Overlap requires that these don't get too close to either 0 or 1.
+hist(cf.full$W.hat, xlab = "Estimated propensity scores", main = "")
+
+
+# *** Estimating CATEs ***
+
+# Split data into a train and test sample.
+train = sample(nrow(X), 0.6 * nrow(X))
+test = -train
+
+# Fit a CATE function on training data.
+cate.forest = causal_forest(X[train, ], Y[train], W[train])
+
+# Predict CATEs on test set.
+X.test = X[test, ]
+tau.hat.test = predict(cate.forest, X.test)$predictions
+
+# A histogram of CATE estimates.
+hist(tau.hat.test, xlab = "Estimated CATEs", main = "")
+
+# On their own, the CATE point estimates are noisy.
+# What we often care about is whether they capture meaningful heterogeneity.
+
+# Here we construct groups according to which quartile of the predicted CATEs the unit belongs.
+# Then, we calculate ATEs in each of these groups and see if they differ.
+num.groups = 4 # 4 for quartiles, 5 for quintiles, etc.
+quartile = cut(tau.hat.test,
+               quantile(tau.hat.test, seq(0, 1, by = 1 / num.groups)),
+               labels = 1:num.groups,
+               include.lowest = TRUE)
+# Create a list of test set samples by CATE quartile.
+samples.by.quartile = split(seq_along(quartile), quartile)
+
+# Look at ATEs in each of these quartiles. To calculate these we fit a separate evaluation forest.
+eval.forest = causal_forest(X.test, Y[test], W[test])
+
+# Calculate doubly robust ATEs for each group.
+ate.by.quartile = lapply(samples.by.quartile, function(samples) {
+  average_treatment_effect(eval.forest, subset = samples)
+})
+
+# Plot group ATEs along with 95% confidence bars.
+df.plot.ate = data.frame(
+  matrix(unlist(ate.by.quartile), num.groups, byrow = TRUE, dimnames = list(NULL, c("estimate","std.err"))),
+  group = 1:num.groups
+)
+
+ggplot(df.plot.ate, aes(x = group, y = estimate)) +
+  geom_point() +
+  geom_errorbar(aes(ymin = estimate - 1.96 * std.err, ymax = estimate + 1.96 * std.err, width = 0.2)) +
+  xlab("Estimated CATE quantile") +
+  ylab("Average treatment effect")
+
+
+# *** Evaluate heterogeneity via TOC/AUTOC ***
+
+# In the previous section we split the data into quartiles.
+# The TOC is essentially a continuous version of this exercise.
+
+# Use eval.forest to form a doubly robust estimate of TOC/AUTOC.
+rate.cate = rank_average_treatment_effect(
+  eval.forest,
+  tau.hat.test,
+  q = seq(0.05, 1, length.out = 100)
+)
+# Plot the TOC.
+plot(rate.cate)
+
+# An estimate and standard error of AUTOC.
+print(rate.cate)
+
+# Get a 2-sided p-value Pr(>|t|) for RATE = 0 using a t-value.
+2 * pnorm(-abs(rate.cate$estimate / rate.cate$std.err))
+
+# [For alternatives to perform these tests without performing train/test splits,
+# including relying on one-sided tests, see the following vignette for more details
+# https://grf-labs.github.io/grf/articles/rate_cv.html]
+
+
+# *** Policy evaluation with Qini curves ****
+
+# We can use the `maq` package for this exercise. This package is more general
+# and accepts CATE estimates from multiple treatment arms along with costs that
+# denominate what we spend by assigning a unit a treatment. In this application
+# we can simply treat the number of units we are considering deploying as the cost.
+
+# Form a doubly robust estimate of a CATE-based Qini curve (using eval.forest).
+num.units = nrow(X)
+qini = maq(tau.hat.test,
+           num.units,
+           get_scores(eval.forest) * num.units,
+           R = 200)
+
+# Form a baseline Qini curve that assigns treatment uniformly.
+qini.baseline = maq(tau.hat.test,
+                    num.units,
+                    get_scores(eval.forest) * num.units,
+                    R = 200,
+                    target.with.covariates = FALSE)
+
+# Plot the Qini curve along with 95% confidence lines.
+plot(qini, ylab = "PTSD cases prevented", xlab = "Units held back from deployment", xlim = c(0, num.units))
+plot(qini.baseline, add = TRUE, ci.args = NULL)
+
+# Get estimates from the curve, at for example 500 deployed units.
+average_gain(qini, 500)
+
+# Compare the benefit of targeting the 500 units predicted to benefit the most with the baseline.
+difference_gain(qini, qini.baseline, 500)
+
+
+# [The paper shows Qini curves embellished with ggplot. We could have retrieved
+# the data underlying the curves and customized our plots further.
+# For more details we refer to https://github.com/grf-labs/maq]
+
+
+# *** Describing the fit CATE function ****
+
+# Our `cate.forest` has given us some estimated function \tau(x).
+# Let's have a closer look at how this function stratifies our sample in terms of "covariate" profiles.
+# One way to do so is to look at histograms of our covariates by for example low / high CATE predictions.
+
+# First, we'll use a simple heuristic to narrow down the number of predictors to look closer at.
+# Here we use the variable importance metric of the fit CATE function to select 4 predictors to look closer at.
+varimp.cate = variable_importance(cate.forest)
+ranked.variables = order(varimp.cate, decreasing = TRUE)
+top.varnames = colnames(X)[ranked.variables[1:4]]
+print(top.varnames)
+
+# Select the test set samples predicted to have low/high CATEs.
+# [We could also have used the full sample for this exercise.]
+low = samples.by.quartile[[1]]
+high = samples.by.quartile[[num.groups]]
+
+# Make some long format data frames for ggplot.
+df.lo = data.frame(
+  covariate.value = unlist(as.vector(X.test[low, top.varnames])),
+  covariate.name = rep(top.varnames, each = length(low)),
+  cate.estimates = "Low"
+)
+df.hi = data.frame(
+  covariate.value = unlist(as.vector(X.test[high, top.varnames])),
+  covariate.name = rep(top.varnames, each = length(high)),
+  cate.estimates = "High"
+)
+df.plot.hist = rbind(df.lo, df.hi)
+
+# Plot overlaid histograms of the selected covariates by low/high classification.
+ggplot(df.plot.hist, aes(x = covariate.value, fill = cate.estimates)) +
+  geom_histogram(alpha = 0.7, position = "identity") +
+  facet_wrap(~ covariate.name, scales = "free", ncol = 2)
+
+
+# *** Best linear projections (BLP) ****
+
+# Select some potential effect modifier(s) we are interested in.
+blp.vars = c("X1", "X2", "X3")
+
+# Estimate the best linear projection on our variables.
+best_linear_projection(cf.full, X[, blp.vars])
+
+
+# *** Risk vs CATE-based targeting ***
+
+# In our application it was reasonable to hypothesize that soldiers with high
+# "risk" of developing PTSD also has a high treatment effect (i.e. low resilience).
+
+# Train a risk model on the training set. First, select units with high combat stress.
+train.hi = train[W[train] == 0]
+
+# Use a regression forest to estimate P[develops PTSD | X, high combat stress]
+# (We recorded Y = 1 if healthy and so 1 - Y is 1 if the outcome is PTSD)
+rf.risk = regression_forest(X[train.hi, ], 1 - Y[train.hi])
+risk.hat.test = predict(rf.risk, X.test)$predictions
+
+# Compare risk vs CATE-based targeting using the AUTOC.
+rate.risk = rank_average_treatment_effect(
+  eval.forest,
+  cbind(tau.hat.test, risk.hat.test)
+)
+plot(rate.risk)
+print(rate.risk)
+
+# Construct a 95% confidence interval for the AUTOCs as well as for AUTOC(cate.hat) - AUTOC(risk.hat).
+rate.risk$estimate + data.frame(lower = -1.96 * rate.risk$std.err,
+                                upper = 1.96 * rate.risk$std.err,
+                                row.names = rate.risk$target)
+
+
+# *** Appendix: Evaluate CATE models via the AUTOC ***
+
+# Causal forest is a two-step algorithm that first accounts for confounding and baseline effects
+# via the propensity score e(x) and a conditional mean model m(x), then in the second step estimates
+# treatment effect heterogeneity. In some settings we may want to try using different covariates (or
+# possibly models) for e(x), m(x), and CATE predictions.
+
+# Estimate m(x) = E[Y | X = x] using a regression forest.
+Y.forest = regression_forest(X[train, ], Y[train], num.trees = 500)
+Y.hat = predict(Y.forest)$predictions
+
+# Estimate e(x) = E[W | X = x] using a regression forest.
+W.forest = regression_forest(X[train, ], W[train], num.trees = 500)
+W.hat = predict(W.forest)$predictions
+
+# Select the covariates X with, for example, m(x) variable importance in the top 25%.
+varimp.Y = variable_importance(Y.forest)
+selected.vars = which(varimp.Y >= quantile(varimp.Y, 0.75))
+print(colnames(X)[selected.vars])
+
+if (length(selected.vars) <= 1) stop("You should really try and use more than just one predictor variable with forests.")
+
+# Try and fit a CATE model using this smaller set of potential heterogeneity predictors.
+X.subset = X[, selected.vars]
+cate.forest.restricted = causal_forest(X.subset[train, ], Y[train], W[train],
+                                       Y.hat = Y.hat, W.hat = W.hat)
+# Predict CATEs on test set.
+tau.hat.test.restricted = predict(cate.forest.restricted, X.test[, selected.vars])$predictions
+
+# Compare CATE models with AUTOC.
+rate.cate.compare = rank_average_treatment_effect(
+  eval.forest,
+  cbind(tau.hat.test, tau.hat.test.restricted)
+)
+# Get an estimate of the AUTOCs, as well as difference in AUTOC.
+print(rate.cate.compare)
+
+# Get a p-value for the AUTOCs and difference in AUTOCs.
+data.frame(
+  p.value = 2 * pnorm(-abs(rate.cate.compare$estimate / rate.cate.compare$std.err)),
+  target = rate.cate.compare$target
+)
+
+# Or equivalently, we could construct a 2-sided confidence interval.
+rate.cate.compare$estimate + data.frame(lower = -1.96 * rate.cate.compare$std.err,
+                                        upper = 1.96 * rate.cate.compare$std.err,
+                                        row.names = rate.cate.compare$target)
+
+# [In this synthetic example the restricted CATE model does not do much better.]