## The Annals of Applied Statistics

### Partially time-varying coefficient proportional hazards models with error-prone time-dependent covariates—an application to the AIDS Clinical Trial Group 175 data

#### Abstract

Due to cost and time considerations, interest has focused on identifying surrogate markers that could be substituted for the clinical endpoint, time to an event of interest, in evaluation of treatment efficacy. Joint models are often used to assess the effect of surrogate markers and treatment. Motivated by recent works studying the AIDS Clinical Trial Group (ACTG) 175 data, we propose a partially time-varying coefficient proportional hazards model for modeling the relationship between the hazard of failure and time-dependent and time-independent covariates. The time-varying coefficients are approximated by polynomial splines, and the corrected score and conditional score approaches are adopted to estimate the regression coefficients. The proposed estimators are consistent, and the asymptotic normality is established for the constant coefficients, which enables us to construct confidence intervals and permits joint inference. The finite-sample performance of the proposed method is assessed by Monte Carlo simulation studies. The proposed model is applied to ACTG 175 data to assess the temporal dynamics of the effect of treatment and CD4 count on time to AIDS or death.

#### Article information

Source
Ann. Appl. Stat., Volume 11, Number 1 (2017), 274-296.

Dates
Revised: November 2016
First available in Project Euclid: 8 April 2017

https://projecteuclid.org/euclid.aoas/1491616881

Digital Object Identifier
doi:10.1214/16-AOAS1003

Mathematical Reviews number (MathSciNet)
MR3634324

Zentralblatt MATH identifier
1366.62241

#### Citation

Song, Xiao; Wang, Li. Partially time-varying coefficient proportional hazards models with error-prone time-dependent covariates—an application to the AIDS Clinical Trial Group 175 data. Ann. Appl. Stat. 11 (2017), no. 1, 274--296. doi:10.1214/16-AOAS1003. https://projecteuclid.org/euclid.aoas/1491616881

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#### Supplemental materials

• Supplementary materials for Partially time-varying coefficient proportional hazards models with error-prone time-dependent covariates—an application to the AIDS Clinical Trial Group 175 data. This supplement consists of four web appendices. Web Appendix A gives the asymptotic properties, the regularity conditions and the proofs of the asymptotic properties. Web Appendix B lists the lemmas used in the proofs. Web Appendix C derives the convergence result when the Hazard model is misspecified. Web Appendix D shows the analysis results of the ACTG 175 data including both $\log(\mathrm{CD}4)$ and $\log(\mathrm{CD}8)$.