City Research Online

Abstract

We consider an extension of Aalen’s additive regression model allowing covariates to have effects that vary on two different time-scales. The two time-scales considered are equal up to a constant that varies for each individual, such as for example follow-up time and age in medical studies or calendar time and age in longitudinal studies. The model has been introduced in Scheike (2001) where it was solved via smoothing techniques. We present a new backfitting 20 algorithm estimating the structured model without having to use smoothing. Estimators of the cumulative regression functions on the two time-scales are suggested by solving local estimating equations jointly on the two time-scales. We provide large sample properties and simultaneous confidence bands. The model is applied to data on myocardial infarction providing a separation of the two effects stemming from time since diagnosis and age.

Publication Type:	Article
Additional Information:	This is a pre-copyedited, author-produced version of an article accepted for publication in Bibometrika following peer review. The version of record Hiabu, M., Nielsen, J. P. and Scheike, T. (2020). Non-Smooth Backfitting for Excess Risk Additive Regression Model with Two Survival Time-Scales. Biometrika, is available online at: https://doi.org/10.1093/biomet/asaa058
Publisher Keywords:	Aalen model, counting process, disability model, illness-death model, generalized additive models, multiple time-scales, non-parametric estimation, varying-coefficient models
Subjects:	H Social Sciences > HF Commerce > HF5601 Accounting
Departments:	Bayes Business School > Actuarial Science & Insurance
SWORD Depositor:	Symplectic Administrator

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