Right censoring destroys the conjugacy that makes the DP posterior a
DP: what survives is a product-limit form in which each risk set
contributes one Beta-posterior factor. That product is the Bayesian
analogue of Kaplan-Meier, and the prior enters only through the
prior-mean survival S0 attached to each factor.
Usage
Ghosalsurvdppost(times, events, t_query, alpha = 2)
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.
- alpha
DP concentration, positive.
Value
List with estimate, survival_at_t,
method.
Details
Formula: S(t) = prod over events t_j <= t of
(alpha S0(t_j) + R_j - 1) / (alpha S0(t_j) + R_j),
with S0 the unit-exponential survival and R_j the risk set size.
References
Ghosal & van der Vaart (2017), Fundamentals of
Nonparametric Bayesian Inference, CUP, section 13.2.
Examples
times <- c(2, 3, 3, 5, 6, 8, 9, 12); events <- c(1, 1, 0, 1, 0, 1, 1, 0)
Ghosalsurvdppost(times, events, t_query = 6, alpha = 2)$survival_at_t
#> [1] 0.6046202
