From ba9f993c8446d107fa9123cd99a053c54c07c202 Mon Sep 17 00:00:00 2001 From: Erik Sverdrup Date: Tue, 3 Sep 2024 20:50:03 -0700 Subject: [PATCH] Add IJMPR replication (#1436) --- README.md | 4 + experiments/README.md | 6 + experiments/ijmpr/README.md | 14 + experiments/ijmpr/analysis.R | 267 ++ experiments/ijmpr/synthetic_data.csv | 4001 ++++++++++++++++++++++++++ 5 files changed, 4292 insertions(+) create mode 100644 experiments/ijmpr/README.md create mode 100644 experiments/ijmpr/analysis.R create mode 100644 experiments/ijmpr/synthetic_data.csv diff --git a/README.md b/README.md index 9ffce3a16..3a3f795d6 100755 --- a/README.md +++ b/README.md @@ -161,6 +161,10 @@ Imke Mayer, Erik Sverdrup, Tobias Gauss, Jean-Denis Moyer, Stefan Wager and Juli [paper, arxiv] +Erik Sverdrup, Maria Petukhova, and Stefan Wager. +Estimating Treatment Effect Heterogeneity in Psychiatry: A Review and Tutorial with Causal Forests. 2024. +[arxiv] + Stefan Wager and Susan Athey. Estimation and Inference of Heterogeneous Treatment Effects using Random Forests. Journal of the American Statistical Association, 113(523), 2018. diff --git a/experiments/README.md b/experiments/README.md index 97ca78371..079dae593 100644 --- a/experiments/README.md +++ b/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 [paper, arxiv] +Erik Sverdrup, Maria Petukhova, and Stefan Wager. +Estimating Treatment Effect Heterogeneity in Psychiatry: A Review and Tutorial with Causal Forests. 2024. +[arxiv] + Stefan Wager and Susan Athey. Estimation and Inference of Heterogeneous Treatment Effects using Random Forests. Journal of the American Statistical Association, 113(523), 2018. diff --git a/experiments/ijmpr/README.md b/experiments/ijmpr/README.md new file mode 100644 index 000000000..b922df31b --- /dev/null +++ b/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) +``` diff --git a/experiments/ijmpr/analysis.R b/experiments/ijmpr/analysis.R new file mode 100644 index 000000000..a3544c67f --- /dev/null +++ b/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.] diff --git a/experiments/ijmpr/synthetic_data.csv 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