\(U_n(t,\beta) = n^{-1}\sum_i \int_0^t [Z_i - E_n(s,\beta)]
dN_i(s)\) with \(E_n\) the risk-set weighted average covariate
(Eq. 1.4, p. 5). Indexed by t, so it is a stochastic PROCESS whose
weak convergence – not merely asymptotic normality of the
endpoint – licenses Cox inference. Its root defines the
estimator, which makes this a Z-estimation problem. Mirrors
morie.fn.ksr023.
Usage
morie_cox_score_process(beta, z, time, event, t_grid = NULL)
Arguments
- beta
coefficients.
- z
covariates.
- time
follow-up times.
- event
binary 0/1 event indicators.
- t_grid
times to report at; the event times when NULL.
Value
list: t_grid, U, U_final, E_bar, is_process,
root_defines_estimator, n_events, n, method.
References
Kosorok, Ch. 1, Eq. (1.4), p. 5.
Examples
set.seed(1)
z <- rnorm(60)
tt <- rexp(60) / exp(0.7 * z)
morie_cox_score_process(0.7, z, tt, rep(1, 60))$is_process
#> [1] TRUE
