Letting alpha tend to zero in the censored-data DP posterior gives
Lo's censored Bayesian bootstrap, and its product-limit factors reduce
to the Kaplan-Meier factors (R_j - d_j) / R_j exactly. The
vanishing-prior limit of the Bayesian procedure IS the classical
estimator, which is the cleanest statement of why Kaplan-Meier needs
no Bayesian apology.
Usage
Ghosalbbcensored(times, events, t_query)
Arguments
- times
Observed follow-up times.
- events
Event indicators, 1 for an event and 0 for censoring.
- t_query
Time at which the survival is reported.
Value
List with estimate, km_survival,
method.
Details
Formula: S(t) = prod over events t_j <= t of (R_j - 1) / R_j.
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 13.7.1.
Examples
times <- c(2, 3, 3, 5, 6, 8, 9, 12); events <- c(1, 1, 0, 1, 0, 1, 1, 0)
Ghosalbbcensored(times, events, t_query = 6)[c("estimate", "km_survival")]
#> $estimate
#> [1] 0.6
#>
#> $km_survival
#> [1] 0.6
#>
