| compute_eta {grf} | R Documentation |
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")
compute_eta(S.hat, C.hat, lambda.C.hat, Y.grid, Y, D, m.hat, W.centered)
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. |
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).
A list with the numerator and denominator of eta.