Analysis of twophase sampling data with semiparam

Authors: Yanqing Sun Xiyuan Qian Qiong Shou Peter B Gilbert

Publish Date: 2016/03/19

Volume: 23, Issue: 3, Pages: 377-399

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Abstract

Under the casecohort design introduced by Prentice Biometrica 731–11 1986 the covariate histories are ascertained only for the subjects who experience the event of interest ie the cases during the followup period and for a relatively small random sample from the original cohort ie the subcohort The casecohort design has been widely used in clinical and epidemiological studies to assess the effects of covariates on failure times Most statistical methods developed for the casecohort design use the proportional hazards model and few methods allow for timevarying regression coefficients In addition most methods disregard data from subjects outside of the subcohort which can result in inefficient inference Addressing these issues this paper proposes an estimation procedure for the semiparametric additive hazards model with casecohort/twophase sampling data allowing the covariates of interest to be missing for cases as well as for noncases A more flexible form of the additive model is considered that allows the effects of some covariates to be time varying while specifying the effects of others to be constant An augmented inverse probability weighted estimation procedure is proposed The proposed method allows utilizing the auxiliary information that correlates with the phasetwo covariates to improve efficiency The asymptotic properties of the proposed estimators are established An extensive simulation study shows that the augmented inverse probability weighted estimation is more efficient than the widely adopted inverse probability weighted completecase estimation method The method is applied to analyze data from a preventive HIV vaccine efficacy trialThe authors thank Richard Wyatt David Montefiori and John Mascola for measuring the immune response data for the VaxGen 004 trial The authors thank the reviewers for their constructive comments that have improved the paper Sun’s research was partially supported by NSF Grants DMS1208978 and DMS1513072 NIH Grant R37 AI054165 and the Reassignment of Duties fund provided by the University of North Carolina at Charlotte Gilbert’s research was partially supported by NIH Grant R37 AI054165Let ft be a function abrightarrow R Given any finite partition Gamma =a=t 0cdots t K=b of a b the variation of f over a b is Vfab=sup sum k=1K ft kft k1 Gamma mathrmis a partition of ab The function f has bounded variation on a b if Vfabinfty A vector f of functions has bounded variation if each component of f has bounded variation and in this case Vf a b is the vector of the variations of the component functionsThe processes X it Z it and W it 0le tle tau have bounded second moments their sample paths are left continuous and of bounded variation The variations of the processes U icdot Z icdot and W icdot satisfy the conditions EVert VU i stVert 21/2 le Ctsalpha EVert VZ i stVert 21/2 le Ctsalpha and EVert VW i stVert 21/2 le Ctsalpha for stin 0tau where alpha 0 and C0 are constants and Vert cdot Vert is the Euclidean normThe censoring is independent in the sense that the censoring does not alter the risk of failure This assumption is described by EdtildeN it X i0t Z i0t tildeT ige t=EdN it X i0t Z i0t T ige t where tildeN it=ItildeT ile t N it=IT ile t and X i0t=X is 0le sle t and Z i0t=Z is 0le sle t are the covariate histories up to time tThe function pi varOmega ipsi is twice differentiable with respect to psi the compact set varTheta psi pi prime psi varOmega ipsi =partial pi varOmega ipsi /partial psi is uniformly bounded and there is a varepsilon 0 such that pi varOmega ipsi ge varepsilon 0 for all i=1ldots nThe functions mu 1varOmega ivarphi 1 and mu 2varOmega ivarphi 2 are twice differentiable with respect to varphi 1 and varphi 2 on the compact sets varTheta varphi 1 and varTheta varphi 2 respectively

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