Augmented inverse probability weighted estimation and prediction for cause-specific proportional hazards regression with missing covariates

Abstract

This paper describes estimation of the regression parameters and prediction of the cumulative incidence functions under the cause-specific proportional hazards model when some of covariates are not fully observed. Assuming that missingness mechanism is missing at random, we propose the augmented inverse probability weighted method for estimation and inference procedures. A nonparametric regression approach is adapted for estimating selection probabilities and conditional expectations of missing covariates in the augmented estimating function. We establish the asymptotic properties of the predicted cumulative incidence functions under the cause-specific proportional hazards model with missing covariates and derive consistent variance estimators of the predicted cumulative incidence functions. Simulation studies show that the procedures perform well. The proposed methods are illustrated with stage IV breast cancer data obtained from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute.

Keywords:

• Augmented estimating equation
• competing risks
• cumulative incidence function
• missing covariates
• proportional hazards model

2020 Mathematics Subject classification:

• 62N02

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The details about where to access to the SEER data can be found at: https://seer.cancer.gov/data/

Additional information

Funding

This work was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07041070, NRF-2022R1F1A1065153).