Stagewise pseudo-value regression for time-varying effects on the cumulative incidence.
In a competing risks setting, the cumulative incidence of an event of interest describes the absolute risk for this event as a function of time. For regression analysis, one can either choose to model all competing events by separate cause-specific hazard models or directly model the association between covariates and the cumulative incidence of one of the events. With a suitable link function, direct regression models allow for a straightforward interpretation of covariate effects on the cumulative incidence. In practice, where data can be right-censored, these regression models are implemented using a pseudo-value approach. For a grid of time points, the possibly unobserved binary event status is replaced by a jackknife pseudo-value based on the Aalen-Johansen method. We combine a stagewise regression technique with the pseudo-value approach to provide variable selection while allowing for time-varying effects. This is implemented by coupling variable selection between the grid times, but determining estimates separately. The effect estimates are regularized to also allow for model fitting with a low to moderate number of observations. This technique is illustrated in an application using clinical cancer registry data from hepatocellular carcinoma patients. The results are contrasted with traditional hazard-based modeling. In addition to a more straightforward interpretation, when using the proposed technique, the identification of time-varying effect patterns on the cumulative incidence is seen to be feasible with a moderate number of observations.
Institute of Medical Biostatistics, Epidemiology and Informatics, University Medical Center, Johannes Gutenberg University Mainz, 55101, Mainz, Germany.
Daniela
D
Zöller
Institute of Medical Biostatistics, Epidemiology and Informatics, University Medical Center, Johannes Gutenberg University Mainz, 55101, Mainz, Germany.
Irene
I
Schmidtmann
Internal Medicine I, University Medical Center, Johannes Gutenberg University Mainz, 55101, Mainz, Germany.
Arndt
http://orcid.org/0000-0003-1198-1716
A
Weinmann
Department of Public Health, University of Copenhagen, 1014, Copenhagen, Denmark.
Thomas A
TA
Gerds
Institute of Medical Biostatistics, Epidemiology and Informatics, University Medical Center, Johannes Gutenberg University Mainz, 55101, Mainz, Germany.
Harald
http://orcid.org/0000-0002-5666-8662
H
Binder
D000465:Algorithms; D056808:Biostatistics; D006528:Carcinoma, Hepatocellular / Q000401:mortality / Q000628:therapy; D003198:Computer Simulation; D006801:Humans; D015994:Incidence; D008113:Liver Neoplasms / Q000401:mortality / Q000628:therapy; D015233:Models, Statistical; D012042:Registries / Q000706:statistics & numerical data; D012044:Regression Analysis; D012307:Risk Factors; D013997:Time Factors
competing risks; cumulative incidence; pseudo-values; stagewise regression; time-varying effects