title: A joint frailty-copula model between tumour progression and death for meta-analysis.
abstract: Dependent censoring often arises in biomedical studies when time to tumour progression (e.g., relapse of cancer) is censored by an informative terminal event (e.g., death). For meta-analysis combining existing studies, a joint survival model between tumour progression and death has been considered under semicompeting risks, which induces dependence through the study-specific frailty. Our paper here utilizes copulas to generalize the joint frailty model by introducing additional source of dependence arising from intra-subject association between tumour progression and death. The practical value of the new model is particularly evident for meta-analyses in which only a few covariates are consistently measured across studies and hence there exist residual dependence. The covariate effects are formulated through the Cox proportional hazards model, and the baseline hazards are nonparametrically modeled on a basis of splines. The estimator is then obtained by maximizing a penalized log-likelihood function. We also show that the present methodologies are easily modified for the competing risks or recurrent event data, and are generalized to accommodate left-truncation. Simulations are performed to examine the performance of the proposed estimator. The method is applied to a meta-analysis for assessing a recently suggested biomarker CXCL12 for survival in ovarian cancer patients. We implement our proposed methods in R joint.Cox package.
authors.affiliation: 1 Graduate Institute of Statistics, National Central University, Jhongli City, Taoyuan, Taiwan.
authors.forename: Takeshi
authors.initials: T
authors.lastname: Emura
authors.affiliation: 2 Center for Advanced Medicine and Clinical Research, Nagoya University Hospital, Japan.
authors.forename: Masahiro
authors.initials: M
authors.lastname: Nakatochi
authors.affiliation: 2 Center for Advanced Medicine and Clinical Research, Nagoya University Hospital, Japan.
authors.forename: Kenta
authors.initials: K
authors.lastname: Murotani
authors.affiliation: 3 INSERM CR897 (Biostatistic), Université Bordeaux Segalen, Bordeaux Cedex, France.
authors.forename: Virginie
authors.initials: V
authors.lastname: Rondeau
mesh_terms: D014408:Biomarkers, Tumor / Q000378:metabolism; D056808:Biostatistics / Q000379:methods; D054377:Chemokine CXCL12 / Q000378:metabolism; D016000:Cluster Analysis; D003198:Computer Simulation; D018450:Disease Progression; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D015201:Meta-Analysis as Topic; D015233:Models, Statistical; D009369:Neoplasms / Q000209:etiology* / Q000401:mortality*; D010051:Ovarian Neoplasms / Q000378:metabolism / Q000401:mortality; D016016:Proportional Hazards Models; D012307:Risk Factors; D012984:Software; D018709:Statistics, Nonparametric; D016019:Survival Analysis; D013997:Time Factors
chemical_list: D014408:Biomarkers, Tumor; C515255:CXCL12 protein, human; D054377:Chemokine CXCL12
keywords: Dependent censoring; dynamic prediction; semicompeting risk; spline; surrogate endpoint; survival analysis