# A flexible semiparametric transformation model for recurrent event data

## Abstract

In this article, we propose a class of semiparametric transformation models for recurrent event data, in which the baseline mean function is allowed to depend on covariates through an additive model, and some covariate effects are allowed to be time-varying. For inference on the model parameters, estimating equation approaches are developed, and the asymptotic properties of the resulting estimators are established. In addition, a lack-of-fit test is presented to assess the adequacy of the model. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer study is illustrated.

## Keywords

Estimating equation Marginal model Model checking Recurrent events Time-varying effects Transformation model## Notes

### Acknowledgments

The authors thank the Editor, Professor Mei-Ling Ting Lee, an Associate Editor, and two referees for their insightful comments and suggestions that greatly improved the article. The second author’ research was partly supported by the National Natural Science Foundation of China Grants (No. 11231010, 11171330 and 11021161) and Key Laboratory of RCSDS, CAS (No.2008DP173182).

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