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Estimating Smooth Rates from Interval-Censored Data
Jutta Gampe, Hein Putter (Leiden University Medical Center, Niederlande), Paul Eilers (Erasmus Medical Center, Niederlande)
When observations are made only at particular points in time (as in panel surveys), then the resulting data are interval-censored. As a consequence, neither the exact event times nor the times during which individuals are at risk of experiencing the event are available. Parametric models for the hazard allow for the rather straightforward handling of such data, but they imply a prespecified shape of the unknown rates. If more flexible hazard modeling is sought, then a methodology for estimating the missing data (as provided by the EM algorithm) is a natural candidate. However, nonparametric estimation has its own complications in this setting.
Imposing the modest assumption of smooth hazards fundamentally facilitates the problem. It considerably speeds up the convergence of the EM algorithm. Also, incorporating left-truncated data is straightforward.
Technically, the problem is solved by expanding the log of the hazard function as a linear combination of B-splines with coefficients constrained by a roughness penalty. In the EM algorithm, a smoothing step is introduced in each iteration and the optimal smoothing parameter is estimated automatically by Schall's algorithm. Additionally, covariates can be included in a proportional hazards setting. An R-package that implements this approach is being developed.
Extensions to additive and varying coefficient models and to multistate models are possible.
Gampe, J.; Putter, H.; Eilers, P. H. C.:
In: Proceedings of the 30th International Workshop on Statistical Modelling, Linz, Austria, 6-10 July 2015, 181–186. Linz: Johannes Kepler University. (2015)