grf (version 2.0.1)

compute_eta: Compute pseudo outcomes (based on the influence function of tau(X) for each unit) used for CART splitting.

Description

We compute: eta = [sum (W - W.hat)^2 (1 / C.hat - integral_0^Y_i (lambdaC / C.hat) dt)]^(-1) ("denominator") * sum (Gamma / C.hat - integral_0^Y_i (lambdaC / C.hat)(W - W.hat)(Q(t) - m.hat)dt) ("numerator")

Usage

compute_eta(S.hat, C.hat, lambda.C.hat, Y.grid, Y, D, m.hat, W.centered)

Arguments

S.hat

Estimates of the conditional survival function S(t, x, w).

C.hat

Estimates of the conditional survival function for the censoring process S_C(t, x, w).

lambda.C.hat

Estimates of the conditional hazard function for the censoring process S_C(t, x, w).

Y.grid

The time values corresponding to S.hat and C.hat.

Y

The event times.

D

The censoring indicator.

m.hat

Estimates of m(X).

W.centered

W - W.hat.

Value

A list with the numerator and denominator of eta.

Details

where Gamma = (W - W.hat)(Y - m.hat) if D == 1 else (W - W.hat)(Q(Y) - m.hat) Q(t) - E[T | X, W, Y >= t] m(x) = e(X) E[T | X, W = 1] + (1 - e(X)) E[T | X, W = 0] lambda.C = -d/dt log(C.hat(t, x, w)) is the conditional hazard function of the censoring process.

Some useful properties: The expected survival time E[T] is the integral of the survival function S(t). The conditional expected survival time E[T | T >= y] is y + the integral of S(t + y) / S(y).