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Test for detecting heterogeneity in the conditional treatment effect (CATE)

Source: R/hte.R
hte_test_conditional.Rd

For binary treatment \(T\), covariates \(Z\) and outcome \(Y\), it tests the hypothesis $$H_0^c(S): \tau(Z) \text{ only depends on } Z \text{ through } Z_{S^c},$$ where \(S\) is a subset of covariates and \(\tau(Z)=\mathbb{E}[Y | T=1, Z] - \mathbb{E}[Y | T=0, Z]\) is the CATE. When \(S\) is the full set, this amounts to testing \(\tau(Z)\) is a constant; when \(S\) is a proper subset, this amounts to testing \(Z_S\) has no further effect modification while holding \(Z_{S^c}\) fixed.

Usage

hte_test_conditional(
  y,
  Tr,
  Z,
  S = 1:ncol(Z),
  hunt.style = "optimal",
  folds.crossfit = 5,
  trim.outlier.hunt = TRUE,
  splits = c(0.5, 0.5),
  arg.hunt_grf = list(honesty = FALSE, tune.parameters = "all"),
  verbose = FALSE,
  randomized = FALSE
)

Arguments

y

Numeric response vector of length n.

Tr

Binary (0/1) treatment vector of length n.

Z

Numeric covariate matrix of dimension n x p.

S

A subset of 1:ncol(Z) giving the covariates whose effect modification is tested (they have none under the null, given the rest). Default 1:ncol(Z) tests for any heterogeneity (constant CATE under the null); S = NULL leaves the CATE unrestricted.

hunt.style

One of "optimal" (default), "wls" or "vanilla", selecting the hunting algorithm in dScoreTest. The hunted alternative is a grf outcome model fitted separately for the treated and control arms (T-learner).

folds.crossfit

Number of cross-fitting folds passed to fit_CATE when estimating the CATE. Default 5.

trim.outlier.hunt, splits, verbose

Passed through to dScoreTest; see there for details.

arg.hunt_grf

Arguments passed to grf::regression_forest() for hunting.

randomized

If FALSE (default), the propensity \(e(Z) = \mathbb{E}[T \mid Z]\) used by fit_CATE and by the debiasing step is estimated with grf::probability_forest. If TRUE, T is assumed randomized (independent of Z), so \(e(Z)\) is taken to be the constant mean(T), fitted upfront without cross-fitting.

Value

An object of class "dScoreTest": a list whose key elements are the debiased test statistic t.stat and the one-sided p-value p.val (right tail of the standard normal), along with the test-set score residuals, the hunted direction, and the call. It has print, summary and plot methods.

See also

fit_CATE, dScoreTest

Examples

 set.seed(1)
 n <- 600
 Z  <- matrix(rnorm(n * 3), n, 3)
 Tr <- rbinom(n, 1, plogis(Z[, 1]))
 y  <- Z[, 2] + Z[, 3] + Tr * (1 + Z[, 1]) + rnorm(n)  # CATE varies with Z1
 # \donttest{
 # allow modification by Z1 (S = {2,3}): well-specified, should not reject
 hte_test_conditional(y, Tr, Z, S = c(2, 3))
#> Debiased score test: 
#> y ~ X, with X consists of T, Z1, Z2, Z3.
#> (hunt.style = optimal, hunt.method = grf.hte, debias.method = hte.conditional)
#> n = 600, two-way split: hunt = 300, debias & test = 300
#> 
#> T = 0.5666, p-value = 0.285481
 # forbid all modification (constant CATE): misspecified, should reject
 hte_test_conditional(y, Tr, Z, S = 1:3)
#> Debiased score test: 
#> y ~ X, with X consists of T, Z1, Z2, Z3.
#> (hunt.style = optimal, hunt.method = grf.hte, debias.method = hte.conditional)
#> n = 600, two-way split: hunt = 300, debias & test = 300
#> 
#> T = 3.8425, p-value = 6.08863e-05
 # }