Regression Analysis for the Additive Hazards Model with General Biased Survival Data
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Acta Mathemacae Applicatae Sinica, English Series The Editorial Office of AMAS & Springer-Verlag GmbH Germany 2020
Regression Analysis for the Additive Hazards Model with General Biased Survival Data Xiao-lin CHEN School of Statistics, Qufu Normal University, Qufu 273165, China (E-mail: [email protected])
Abstract
In survival analysis, data are frequently collected by some complex sampling schemes, e.g., length
biased sampling, case-cohort sampling and so on. In this paper, we consider the additive hazards model for the general biased survival data. A simple and unified estimating equation method is developed to estimate the regression parameters and baseline hazard function. The asymptotic properties of the resulting estimators are also derived. Furthermore, to check the adequacy of the fitted model with general biased survival data, we present a test statistic based on the cumulative sum of the martingale-type residuals. Simulation studies are conducted to evaluate the performance of proposed methods, and applications to the shrub and Welsh Nickel Refiners datasets are given to illustrate the methodology. Keywords data
additive hazards model; estimating equation; general biased sampling; model checking; survival
2000 MR Subject Classification
1
62N02; 62N03
Introduction
In survival analysis, great majority of data are collected by the simple random sampling scheme, and hence the sampling probability is independent of data. So data come from the same distribution which is the target population of interest. However, for a variety of reasons, survival data are sometimes sampled by several complex sampling schemes, which produce biased survival data. One important feature of biased data is that they represent different population as the target one. For example, in the length biased design, subjects represent the population with probability proportional to the target one by their underlying length. Other frequently encountered biased sampling schemes include the left truncation, the case-cohort design and some variants of the case-cohort designs[9] . There is already a great deal of literature on biased survival data from various complex sampling designs under different semiparametric survival models. As the most prevalent model, study on Cox’s proportional hazards model is the most abundant. For the length-biased data, Wang [26] developed a pseudo-likelihood method based on a bias-adjusted risk set sampling; Ghosh [6] suggested an estimating equation approach under the assumption that the cross-sectional data have no follow-up. The method was improved by Qin and Shen [21]. As an effective method to save time and cost, case-cohort design is applied widely and studied extensively. Work includes Prentice [20], Self and Prentice [22], Chen and Lo [4], [10] and so on. For the left truncation, [27] considered the statistical analysis of prevalent cohort data, which produces the left truncation automatically. Accelerated failure time model and transformation model are another two important semiparametric survival mode
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