Skip to contents

Semiparametric Bernstein-von Mises for the Cox model

Source: R/gh_c13_15.R
Ghosalcoxbvm.Rd

sqrt(n)(beta_n - beta0) tends to N(0, I_eff^(-1)) where I_eff is the EFFICIENT information – the information for beta after projecting out the infinite-dimensional baseline hazard. Two consequences carry the practical content: Bayesian credible intervals for beta are asymptotically valid CONFIDENCE intervals, which is not automatic in semiparametric problems and does fail for other functionals; and nothing is lost by not knowing the baseline hazard.

Usage

Ghosalcoxbvm(x, time = NULL, event = NULL, beta_grid = NULL)

Arguments

x

Covariates, a vector or a matrix with one row per time.

time

Follow-up times; required.

event

Event indicators 0/1; all events when NULL.

beta_grid

Grid for the normal approximation of the first coefficient; a 4-standard-error window when NULL.

Value

List with beta, se, efficient_information, beta_grid, posterior_normal, efficient, credible_equals_confidence, caveat, n_events, n, method.

Details

Formula: Newton on the Cox partial likelihood, with grad_i = x_i - xbar_i and hess -= (weighted second moment

  • outer(xbar_i, xbar_i)) over each risk set; se = sqrt(diag(pinv(I))).

References

Ghosal & van der Vaart (2017), Fundamentals of Nonparametric Bayesian Inference, CUP, sections 13.6.2 and 13.7.2.

Examples

set.seed(7)
x <- rnorm(150)
time <- rexp(150, exp(0.5 * x))
g <- Ghosalcoxbvm(x, time = time, event = rbinom(150, 1, 0.8))
c(g$beta, g$se)
#> [1] 0.4992095 0.1110526