Tree-based modeling of time-varying coefficients in discrete time-to-event models
Hazard models are popular tools for the modeling of discrete time-to-event data. In particular two approaches for modeling time dependent effects are in common use. The more traditional one assumes a linear predictor with effects of explanatory variables being constant over time. The more flexible approach uses the class of semiparametric models that allow the effects of the explanatory variables to vary smoothly over time. The approach considered here is in between these modeling strategies. It assumes that the effects of the explanatory variables are piecewise constant. It allows, in particular, to evaluate at which time points the effect strength changes and is able to approximate quite complex variations of the change of effects in a simple way. A tree-based method is proposed for modeling the piecewise constant time-varying coefficients, which is embedded into the framework of varying-coefficient models. One important feature of the approach is that it automatically selects the relevant explanatory variables and no separate variable selection procedure is needed. The properties of the method are investigated in several simulation studies and its usefulness is demonstrated by considering two real-world applications.
KeywordsDiscrete time-to-event data Time-varying coefficients Recursive partitioning Semiparametric regression Survival analysis
This paper uses data from the German Family Panel pairfam, coordinated by Josef Brüderl, Karsten Hank, Johannes Huinink, Bernhard Nauck, Franz Neyer, and Sabine Walper. Pairfam is funded as long-term project by the German Research Foundation (DFG).
The work was supported by the German Research Foundation (DFG), Grant SCHM 2966/2-1.
- Brüderl J, Drobnic̆ S, Hank K, Huinink J, Nauck B, Neyer F, Walper S, Alt P, Borschel E, Bozoyan C, Buhr P, Finn C, Garrett M, Greischel H, Hajek K, Herzig M, Huyer-May B, Lenke R, Müller B, Peter T, Schmiedeberg C, Schütze P, Schumann N, Thönnissen C, Wetzel M, Wilhelm B (2018) The German family panel (pairfam). GESIS Data Archive, Cologne. ZA5678 Data file Version 9.1.0. https://doi.org/10.4232/pairfam.56184.108.40.206.
- Heim N, Berger M, Wiedemeyer V, Reich RH, Martini M (2018) A mathematical approach improves the predictability of length of hospitalization due to acute odontogenic infection. A retrospective investigation of 303 patients. J Cranio-Maxillofac Surg 47:334–340. https://doi.org/10.1016/jjcms201812002 CrossRefGoogle Scholar
- Huininik J (2014) Alter der Mütter bei Geburt des ersten und der nachfolgenden Kinder - europäischer Vergleich. In: Deutsche Familienstiftung (Hrsg) Wenn Kinder - wann Kinder? Ergebnisse der ersten Welle des Beziehungs- und Familienpanels. Parzellers Buchverlag, Fulda, pp 13–26Google Scholar
- Huinink J, Brüderl J, Nauck B, Walper S, Castiglioni L, Feldhaus M (2011) Panel analysis of intimate relationships and family dynamics (pairfam): conceptual framework and design. J Fam Res 23:77–101Google Scholar
- Klein J, Möschberger M (2003) Survival analysis: statistical methods for censored and truncated data. Springer, New YorkGoogle Scholar
- Van den Berg GJ (2001) Duration models: specification, identification and multiple durations. In: Heckman JJ, Leamer E (eds) Handbook of econometrics. North Holland, AmsterdamGoogle Scholar
- Welchowski T, Schmid M (2018) discSurv: discrete time survival analysis. R package version 1.3.4. http://CRAN.R-project.org/package=discSurv
- Wood SN (2018) mgcv: mixed GAM computation vehicle with GCV/AIC/REML smoothness estimation. R package version 1.8-15. https://CRAN.R-project.org/package=mgcv
- Yee TW (2017) VGAM: vector generalized linear and additive models. R package version 1.0-4. https://CRAN.R-project.org/package=VGAM