title: Tests of calibration and goodness-of-fit in the survival setting.
abstract: To access the calibration of a predictive model in a survival analysis setting, several authors have extended the Hosmer-Lemeshow goodness-of-fit test to survival data. Grønnesby and Borgan developed a test under the proportional hazards assumption, and Nam and D'Agostino developed a nonparametric test that is applicable in a more general survival setting for data with limited censoring. We analyze the performance of the two tests and show that the Grønnesby-Borgan test attains appropriate size in a variety of settings, whereas the Nam-D'Agostino method has a higher than nominal Type 1 error when there is more than trivial censoring. Both tests are sensitive to small cell sizes. We develop a modification of the Nam-D'Agostino test to allow for higher censoring rates. We show that this modified Nam-D'Agostino test has appropriate control of Type 1 error and comparable power to the Grønnesby-Borgan test and is applicable to settings other than proportional hazards. We also discuss the application to small cell sizes.
authors: Division of Preventive Medicine, Brigham and Women's Hospital Harvard Medical School, 900 Commonwealth Ave., East Boston, MA, 02215, U.S.A.
authors: Olga V
authors: OV
authors: Demler
authors: Nina P
authors: NP
authors: Paynter
authors: Nancy R
authors: NR
authors: Cook
mesh_terms: D000328:Adult; D000368:Aged; D015982:Bias; D002138:Calibration; D003198:Computer Simulation; D003327:Coronary Disease / Q000453:epidemiology / Q000209:etiology; D005260:Female; D006801:Humans; D008137:Longitudinal Studies; D008875:Middle Aged; D008962:Models, Theoretical; D016016:Proportional Hazards Models; D018570:Risk Assessment / Q000379:methods; D018401:Sample Size; D018709:Statistics, Nonparametric; D016019:Survival Analysis
keywords: calibration; goodness-of-fit; survival analysis