brier.RdCompute the Brier score, for a coxph model
brier(fit, times, newdata, ties = TRUE, detail = FALSE, timefix = TRUE,
efron = FALSE)result of a coxph fit
time points at which to create the score
optional, used to validate a prior fit with new data
if TRUE, treate tied event/censoring times properly
if TRUE, the returned object has more detail. This can be useful for debugging or for instruction.
deal with near ties in the data. See the tied times vignette.
use the same survival estimate for the NULL model as was used in the coxph call
Far more details are found in the vignette. At any time point tau, the scaled Brier score is essentially the R-squared statistic where y = the 0/1 variable "event at or before tau", yhat is the probability of an event by tau, as predicted by the model, and the ybar is the predicted probablity without covariate, normally from a Kaplan-Meier. If \(R^2= 1- \sum(y- \hat y)^2/\sum (y- \mu)^2\), the Brier score is formally only the numerator of the second term. The rescaled value is much more useful, however.
Many, perhaps even most algorithms do not properly deal with a tied
censoring time/event time pair. The tied option is present
mostly verify that we get the same answer, when we make the same
mistake. The numerical size of the inaccuracy is very small; just large
enough to generate concern that this function is incorrect.
A sensible argument can be made that the NULL model should be a
coxph call with no covariates, rather than the Kaplan-Meier;
but it turns out that the effect is very slight.
This is allowed by the efron argument.
a list with components
the \(R^2\) value, a scaled Brier score. This will be a vector with one entry for each time point.
the brier score, a vector with one entry per time point
the time points at which the score was computed
cfit <- coxph(Surv(rtime, recur) ~ age + meno + size + pmin(nodes,11),
data= rotterdam)
round(cfit$concordance["concordance"], 3) # some predictive power
#> concordance
#> 0.675
brier(cfit, times=c(4,6)*365.25) # values at 4 and 6 years
#> $rsquared
#> [1] 0.1501931 0.1514488
#>
#> $brier
#> [1] 0.1952731 0.2097106
#>
#> $times
#> [1] 1461.0 2191.5
#>