Semiparametric regression on cumulative incidence function with interval‐censored competing risks data

Abstract

Many biomedical and clinical studies with time-to-event outcomes involve competing risks data. These data are frequently subject to interval censoring. This means that the failure time is not precisely observed, but is only known to lie between two observation times such as clinical visits in a cohort study. Not taking into account the interval censoring may result in biased estimation of the cause-specific cumulative incidence function, an important quantity in the competing risk framework, used for evaluating interventions in populations, for studying the prognosis of various diseases and for prediction and implementation science purposes. In this work we consider the class of semiparametric generalized odds-rate transformation models in the context of sieve maximum likelihood estimation based on B-splines. This large class of models includes both the proportional odds and the proportional subdistribution hazard models (i.e., the Fine-Gray model) as special cases. The estimator for the regression parameter is shown to be semiparametrically efficient and asymptotically normal. Simulation studies suggest that the method performs well even with small sample sizes. As an illustration we use the proposed method to analyze data from HIV-infected individuals obtained from a large cohort study in sub-Saharan Africa. We also provide the R function that implements the proposed method and present an illustrative example.

Sieve Estimation of a Class of Partially Linear Transformation Models With Interval-Censored Competing Risks Data

“…Note, the link functions are allowed to vary with varying causes of failure. These authors assumed that the true link functions are known (Scharfstein et al, 1998;Fine and Gray, 1999;Fine, 2001;Mao and Wang, 2010;Bakoyannis et al, 2017), which we also adopt. This assumption facilitates our estimation, given that estimation of α = (α 1 , .…”

“…Our main contributions in this paper are as follows. First, we present a class of partially linear GOR transformation models for interval-censored competing risk data, which extends the linear GOR transformation models (Mao et al, 2017;Bakoyannis et al, 2017) and the nonparametric additive transformation models. Second, our sieve-ML proposal is a pragmatic compromise between a purely B-spline approach with a faster convergence rate under the same smoothness conditions for different nonparametric functions and a purely Bernstein polynomial approach with better computability and shape preserving property.…”

“…Finally, regarding theoretical contributions, our proofs of almost sure consistency, rate of convergence and asymptotic normality utilizes the theory of empirical processes and functional analysis, and are established using new techniques, such as the symmetrization inequality (Panchenko, 2003), Hoeffding's inequality and the Riesz representation theorem (Goodrich, 1970). These are more challenging than the techniques used for the linear transformation model used in Mao et al (2017) and Bakoyannis et al (2017).…”

“…For example, Li (2016) considered a sieve maximum likelihood approach (sieve-ML) for the Fine-Gray model (Fine and Gray, 1999) under interval censoring and possible left-truncation, while Mao et al (2017) proposed a broad class of semiparametric regression models accommodating both proportional and nonproportional sub-distribution hazards, and devised a fast and stable EMtype estimation framework. Recently, Bakoyannis et al (2017) considered a class of semiparametric generalized odds rate (GOR) transformation models (Scharfstein et al, 1998) via the sieve-ML approach based on B-splines, and showed that estimator for the (finite-dimensional) regression parameter is semiparametrically efficient. In all these work, the covariates were assumed to be related linearly to the time-to-event responses, which precludes as-1.…”

Incidence Estimation in Post-ICU Populations: Challenges and Possible Solutions When Using Claims Data

“…If so, these outcomes' incidence could be measured by the exact date of the physician visit with the delivered EBM-code and not only by the time frame spanned by multiple physician visits. There are new statistical methods allowing to model competing risk data in combination with interval censoring [43]. These techniques can provide more exact dates for a relevant part of the sample.…”