Regression Diagnostics of the Semiparametric Proportional Rate Model for Irregularly Spaced Repeated Measurements

Abstract

Counting process techniques have been successfully introduced to semiparametric inference of repeated measurements. Cheng and Wei (2000) proposed a simple inference procedure for the semiparametric proportional rate model, which reduces to relative risk regression models for binary data. While the baseline mean functions are completely unspecified, it still requires several assumptions for valid inference. In this article, a goodness-of-fit test for it is proposed based on cumulative residuals. Theoretical justification is provided and an illustration with a dataset from a clinical trial is given. Results of simulation studies to evaluate finite sample performance are also provided.

Keywords:

• Counting process
• Cumulative residuals
• Gaussian process
• Relative risk

Mathematics Subject Classification:

• Primary 62N03
• Secondary 62H15

Acknowledgments

The author is grateful to a reviewer for the helpful suggestions, which improved the presentation of the article. This research was partly supported by grant from the Ishibashi Foundation for the Promotion of Science and the Ministry of Education, Science, Sports, and Culture Grant-in-Aid for Young Scientists (B), #18700280, Japan.