Accelerated failure time model for data from outcome-dependent sampling
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Accelerated failure time model for data from outcome-dependent sampling Jichang Yu1
· Haibo Zhou2 · Jianwen Cai2
Received: 26 December 2019 / Accepted: 29 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Outcome-dependent sampling designs such as the case–control or case–cohort design are widely used in epidemiological studies for their outstanding cost-effectiveness. In this article, we propose and develop a smoothed weighted Gehan estimating equation approach for inference in an accelerated failure time model under a general failure time outcome-dependent sampling scheme. The proposed estimating equation is continuously differentiable and can be solved by the standard numerical methods. In addition to developing asymptotic properties of the proposed estimator, we also propose and investigate a new optimal power-based subsamples allocation criteria in the proposed design by maximizing the power function of a significant test. Simulation results show that the proposed estimator is more efficient than other existing competing estimators and the optimal power-based subsamples allocation will provide an ODS design that yield improved power for the test of exposure effect. We illustrate the proposed method with a data set from the Norwegian Mother and Child Cohort Study to evaluate the relationship between exposure to perfluoroalkyl substances and women’s subfecundity. Keywords Accelerated failure time model · Induced smoothing · Outcome-dependent sampling · Wald statistic · Survival data Mathematics Subject Classification 62D05 · 62N01
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10985020-09508-y) contains supplementary material, which is available to authorized users.
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Jianwen Cai [email protected]
1
School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, Hubei, China
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Department of Biostatistics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA
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J. Yu et al.
1 Introduction Cost of exposure assessment is often a limiting factor for the size of the study in many epidemiological and biomedical studies. As such, cost-effective study designs are desirable by investigators with a limited budget. Those designs provide investigators an alternative to the simple random sampling design for the same overall cost but with bigger statistical power. Outcome-dependent sampling (ODS) refers to such a costeffective sampling scheme where one observes the exposure with a probability that depends on the value of the outcome (e.g., Zhou et al. 2002; Weaver and Zhou 2005). The case–control study is the most well-known outcome-dependent sampling design with the outcome being a binary variable (e.g., Prentice and Pyke 1979; Breslow and Cain 1988; Weinberg and Wacholder 1993; Breslow and Holubkov 1997; Wang and Zhou 2010). While a case–control study over-samples the cases, recently developed ODS with a continuous outcome over-samples from the two tail regions of the dist
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