Estimating the expectation of the log-likelihood with censored data for estimator selection.
A criterion for choosing an estimator in a family of semi-parametric estimators from incomplete data is proposed. This criterion is the expected observed log-likelihood (ELL). Adapted versions of this criterion in case of censored data and in presence of explanatory variables are exhibited. We show that likelihood cross-validation (LCV) is an estimator of ELL and we exhibit three bootstrap estimators. A simulation study considering both families of kernel and penalized likelihood estimators of the hazard function (indexed on a smoothing parameter) demonstrates good results of LCV and a bootstrap estimator called ELL(bboot). We apply the ELL(bboot) criterion to compare the kernel and penalized likelihood estimators to estimate the risk of developing dementia for women using data from a large cohort study.
Liquet
Benoit
B
INSERM E0338, Université Victor Segalen Bordeaux 2, 146 rue Léo Saignat, 33076 Bordeaux Cedex, France.
Commenges
Daniel
D
D015982:Bias; D015331:Cohort Studies; D003627:Data Interpretation, Statistical; D003704:Dementia / Q000453:epidemiology*; D006801:Humans; D015994:Incidence; D016013:Likelihood Functions; D015233:Models, Statistical; D011237:Predictive Value of Tests; D016016:Proportional Hazards Models; D012680:Sensitivity and Specificity