Bayesian Information Criterion (BIC) for comparison of flexsurvreg models
# S3 method for flexsurvreg
BIC(object, cens = TRUE, ...)The BIC of the fitted model. This is minus twice the log likelihood plus p*log(n), where
p is the number of parameters and n is the sample
size of the data. If weights was supplied to
flexsurv, the sample size is defined as the sum of the
weights.
Fitted model returned by flexsurvreg
(or flexsurvspline).
Include censored observations in the sample size term
(n) used in the calculation of BIC.
Other arguments (currently unused).
There is no "official" definition of what the sample size should be for the use of BIC in censored survival analysis. BIC is based on an approximation to Bayesian model comparison using Bayes factors and an implicit vague prior. Informally, the sample size describes the number of "units" giving rise to a distinct piece of information (Kass and Raftery 1995). However censored observations provide less information than observed events, in principle. The default used here is the number of individuals, for consistency with more familiar kinds of statistical modelling. However if censoring is heavy, then the number of events may be a better represent the amount of information. Following these principles, the best approximation would be expected to be somewere in between.
AIC and BIC are intended to measure different things. Briefly, AIC measures predictive ability, whereas BIC is expected to choose the true model from a set of models where one of them is the truth. Therefore BIC chooses simpler models for all but the tiniest sample sizes (\(log(n)>2\), \(n>7\)). AIC might be preferred in the typical situation where "all models are wrong but some are useful". AIC also gives similar results to cross-validation (Stone 1977).
Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90(430), 773-795.
Stone, M. (1977). An asymptotic equivalence of choice of model by cross‐validation and Akaike's criterion. Journal of the Royal Statistical Society: Series B (Methodological), 39(1), 44-47.