Performance of two formal tests based on martingales residuals to check the proportional hazard assumption and the functional form of the prognostic factors in flexible parametric excess hazard models.
Net survival, the one that would be observed if the disease under study was the only cause of death, is an important, useful, and increasingly used indicator in public health, especially in population-based studies. Estimates of net survival and effects of prognostic factor can be obtained by excess hazard regression modeling. Whereas various diagnostic tools were developed for overall survival analysis, few methods are available to check the assumptions of excess hazard models. We propose here two formal tests to check the proportional hazard assumption and the validity of the functional form of the covariate effects in the context of flexible parametric excess hazard modeling. These tests were adapted from martingale residual-based tests for parametric modeling of overall survival to allow adding to the model a necessary element for net survival analysis: the population mortality hazard. We studied the size and the power of these tests through an extensive simulation study based on complex but realistic data. The new tests showed sizes close to the nominal values and satisfactory powers. The power of the proportionality test was similar or greater than that of other tests already available in the field of net survival. We illustrate the use of these tests with real data from French cancer registries.
Hospices Civils de Lyon, Service de Biostatistique-Bioinformatique, F-69003, Lyon, France, and CNRS, UMR5558, Laboratoire de Biométrie et Biologie Evolutive, Equipe Biostatistique-Santé, Université Lyon 1, F-69100, Villeurbanne, France and McGill University Health Center, Department of Epidemiology, Biostatistics and Occupational Health, H3A 1A2, Montreal, QC, Canada.
Coraline
C
Danieli
Hospices Civils de Lyon, Service de Biostatistique-Bioinformatique, F-69003, Lyon, France and CNRS, UMR5558, Laboratoire de Biométrie et Biologie Evolutive, Equipe Biostatistique-Santé, Université Lyon 1, F-69100, Villeurbanne, France.
Nadine
N
Bossard
Hospices Civils de Lyon, Service de Biostatistique-Bioinformatique, F-69003, Lyon, France and CNRS, UMR5558, Laboratoire de Biométrie et Biologie Evolutive, Equipe Biostatistique-Santé, Université Lyon 1, F-69100, Villeurbanne, France.
Laurent
L
Roche
Cancer Research UK Cancer Survival Group, Faculty of Epidemiology and Population Health, Department of NonCommunicable Disease Epidemiology, London School of Hygiene and Tropical Medicine, London WC1E 7HT, UK.
Aurelien
A
Belot
Department of Chronic Diseases and Injuries, The French Public Health Agency, 94410, Saint Maurice, France and Hospices Civils de Lyon, Service de Biostatistique-Bioinformatique, F-69003, Lyon, France and CNRS, UMR5558, Laboratoire de Biométrie et Biologie Evolutive, Equipe Biostatistique-Santé, Université Lyon 1, F-69100, Villeurbanne, France.
Zoe
Z
Uhry
Prevention Division, Center for Public Health Sciences, National Cancer Center, Tokyo, 104-0045, Japan.
Hadrien
H
Charvat
Hospices Civils de Lyon, Service de Biostatistique-Bioinformatique, F-69003, Lyon, France and CNRS, UMR5558, Laboratoire de Biométrie et Biologie Evolutive, Equipe Biostatistique-Santé, Université Lyon 1, F-69100, Villeurbanne, France THE CENSURWORKING SURVIVAL GROUP.
Laurent
L
Remontet
D006801:Humans; D009369:Neoplasms; D011379:Prognosis; D016016:Proportional Hazards Models; D011634:Public Health; D012042:Registries; D012107:Research Design; D016019:Survival Analysis
Checking model assumptions; Flexible parametric excess hazard model; Functional form; Martingale residuals; Net survival; Proportional hazard assumption