Accelerated failure time model under general biased sampling scheme: Table 1.

Abstract

SUMMARYRight-censored time-to-event data are sometimes observed from a (sub)cohort of patients whose survival times can be subject to outcome-dependent sampling schemes. In this paper, we propose a unified estimation method for semiparametric accelerated failure time models under general biased estimating schemes. The proposed estimator of the regression covariates is developed upon a bias-offsetting weighting scheme and is proved to be consistent and asymptotically normally distributed. Large sample properties for the estimator are also derived. Using rank-based monotone estimating functions for the regression parameters, we find that the estimating equations can be easily solved via convex optimization. The methods are confirmed through simulations and illustrated by application to real datasets on various sampling schemes including length-bias sampling, the case-cohort design and its variants.

Combining case-control studies for identifiability and efficiency improvement in logistic regression

“…The estimation and inference of case-cohort data with Cox's proportional hazards model, transformation models and other semiparametric models are studied by Prentice (1986), Lu and Tsiatis (2006), Cai andZeng (2004, 2007), Liu et al (2010), Zeng and Lin (2014), Ni et al (2016), Tao, Zeng and Lin (2017), etc. Unified estimations for semiparametric linear transformation models, the accelerated failure time model and quantile regression under general biased sampling schemes were studied by Kim, Lu, Sit and Ying (2013), Kim, Sit and Ying (2016) and Xu et al (2017). In fact, earlier work on nonparametric inference were developed for recovering the distribution function in two-sample problem in the presence of selection bias under known selection bias weight function; see Vardi (1982Vardi ( , 1985, Qin (1993) and Qin and Zhang (1997).…”

Censored quantile regression model with time‐varying covariates under length‐biased sampling

“…To take the covariate effect into account, extensive research efforts have also been devoted to the corresponding treatments under the regression context. Models including Cox proportional hazards model (see, for example, Wang, 1996; Tsai, 2009; Qin and Shen, 2010) and accelerated failure time (AFT) model (see Shen et al ., 2009; Kim et al ., 2016; Chiou and Xu, 2017) are actively studied.…”