Semiparametric regression and risk prediction with competing risks data under missing cause of failure
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Semiparametric regression and risk prediction with competing risks data under missing cause of failure Giorgos Bakoyannis1
· Ying Zhang2 · Constantin T. Yiannoutsos1
Received: 17 December 2018 / Accepted: 16 January 2020 © The Author(s) 2020
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 covariatespecific 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. Keywords Cause-specific hazard · Cumulative incidence function · Confidence band
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10985020-09494-1) contains supplementary material, which is available to authorized users.
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Giorgos Bakoyannis [email protected]
1
Department of Biostatistics, Indiana University Fairbanks School of Public Health and School of Medicine, 410 West 10th Street, Suite 3000, Indianapolis, IN 46202, USA
2
Department of Biostatistics, University of Nebraska Medical Center, Omaha, USA
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Bakoyannis et al.
Mathematics Subject Classification 62N01 · 62N02
1 Introduction There is an increasing frequency of epidemiological studies and clinical trials that involve a large number of subjects, longer observation periods and multiple outcomes or competing risks (Ness et al. 2009). The basic identifiable quantities from studies with competing risks are the cause-specific hazard and the cumulative incidence function (Putter et al. 2007; Bakoyannis and Touloumi 2012). Choosing the most relevant estimand in a given study depends on the scientific question of interest: if the goal of the study
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