Semiparametric regression and risk prediction with competing risks data under missing cause of failure

Abstract

The cause of failure in cohort studies that involve competing risks is frequently incompletely observed. To address this, several methods have been proposed for the semiparametric proportional cause-specific hazards model under a missing at random assumption. However, these proposals provide inference for the regression coefficients only, and do not consider the infinite dimensional parameters, such as the covariate-specific cumulative incidence function. Nevertheless, the latter quantity is essential for risk prediction in modern medicine. In this paper we propose a unified framework for inference about both the regression coefficients of the proportional cause-specific hazards model and the covariate-specific cumulative incidence functions under missing at random cause of failure. Our approach is based on a novel computationally efficient maximum pseudo-partial-likelihood estimation method for the semiparametric proportional cause-specific hazards model. Using modern empirical process theory we derive the asymptotic properties of the proposed estimators for the regression coefficients and the covariate-specific cumulative incidence functions, and provide methodology for constructing simultaneous confidence bands for the latter. Simulation studies show that our estimators perform well even in the presence of a large fraction of missing cause of failures, and that the regression coefficient estimator can be substantially more efficient compared to the previously proposed augmented inverse probability weighting estimator. The method is applied using data from an HIV cohort study and a bladder cancer clinical trial.

Censored count data regression with missing censoring information

“…[44] and [52] estimate the linear regression and partially linear single-index models for survival data with missing censoring indicators. A similar issue arises in competing risks data analysis with missing cause of failure, see for example [2,3,51,28].…”

Semiparametric Marginal Regression for Clustered Competing Risks Data with Missing Cause of Failure

“…With informative cluster size, the standard methods for clustered data lead to bias, since larger clusters are over-represented in the sample and have a larger influence on the parameter estimates. In addition, cause of failure is frequently incompletely observed in real-world settings due to nonresponse/missingness or by the study design (Bakoyannis et al, 2020). A complete case analysis which discards observations with missing event types is expected to lead to bias and efficiency loss (Lu and Tsiatis, 2001;Bakoyannis et al, 2010).…”

“…The issue of missing cause of failure with independent competing risks data has received considerable attention in the literature (Goetghebeur and Ryan, 1995;Lu and Tsiatis, 2001;Craiu and Duchesne, 2004;Gao and Tsiatis, 2005;Lu and Liang, 2008;Bakoyannis et al, 2010;Hyun et al, 2012;Bordes et al, 2014;Nevo et al, 2018;Bakoyannis et al, 2020). Recently, Bakoyannis et al (2020) proposed a unified framework for semiparametric regression and risk prediction for competing risks data with missing at random (MAR) cause of failure, under the proportional cause-specific hazards model. Unlike previous methods, the approach by Bakoyannis et al (2020) provides inference for both regression and functional parameters such as the cumulative incidence function.…”

“…Recently, Bakoyannis et al (2020) proposed a unified framework for semiparametric regression and risk prediction for competing risks data with missing at random (MAR) cause of failure, under the proportional cause-specific hazards model. Unlike previous methods, the approach by Bakoyannis et al (2020) provides inference for both regression and functional parameters such as the cumulative incidence function. The latter quantity is key for risk prediction in modern medicine.…”

“…The latter quantity is key for risk prediction in modern medicine. Moreover, simulation studies have shown that the approach by Bakoyannis et al (2020) provides substantially more efficient regression parameter estimates compared to augmented inverse probability weighting estimators (Gao and Tsiatis, 2005;Hyun et al, 2012) and the multiple-imputation estimator (Lu and Tsiatis, 2001). However, all the aforementioned methods did not consider a potential within-cluster dependence and are thus expected to lead to invalid inferences with clustered data.…”