Association, Regression and Diagnostic Accuracy Analyses of Competing Risks Data

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Competing risks commonly occur in analyzing time-to-event outcomes with composite endpoints. Due to dependent censoring imposed by competing events, standard methods for dealing with usual independent censoring, such as censoring imposed by time limits on the duration of observation, may not be applicable. In this proposal, the investigator discusses two projects that address challenges arising from the analyses of competing risks data. The first project aims to quantify the association between two lung infection times using the Cystic Fibrosis Foundation registry data, where the event times are left truncated and competing-risk censored. Conditional cause-specific hazard (CSH) functions and conditional cumulative incidence function (CIFs) are considered to incorporate left truncation. An extended Dabrowska method is proposed to estimate the bivariate conditional survival function, and then used to estimate the bivariate conditional CIF. Nonparametric association analysis is subsequently carried out based on association measures that are quantified through conditional cumulative CSH functions and CIFs. The goal of the second project is to explore an important intrinsic relationship between CIFs in a regression setting, and propose a flexible parametric regression model that explicitly takes into account the additivity constraint on the CIFs. The parametric model adopts a modified logistic model as baseline CIFs and a generalized odds-rate model for covariate effects. This model explicitly takes into account the constraint that a subject with any given prognostic factors should eventually fail from one of the causes so the asymptotes of the CIFs should add up to one. There is limited research on association analysis of bivariate competing risks data and no prior work for left-truncated competing risks data, a common situation when registry data are used to quantify the association between two events of interest. Regression models based on CIFs have been well studied to evaluate covariate effects on the event of interest in the presence of competing-risk censoring. However, existing methods do not explicitly account for the additivity constraint on CIFs, resulting in interpretation issues. The proposed two projects address each of these methodological gaps and are expected to enhance our understanding of the two areas. The proposed projects have been motivated by real problems that the PI encountered in collaborations with researchers from other areas, and are designed to address those practical issues. The projects can be applied in such diverse fields as medicine, public health, reliability studies in engineering, actuarial sciences and finance. The PI is actively working with graduate students and expects some of them will get involved with the proposed research for their dissertations. Hence the proposed work will be naturally integrated with education through graduate student advising and training.