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.

Dependent censoring arises in biomedical studies when the survival outcome of interest is censored by competing risks. In survival data with microarray gene expressions, gene selection based on the univariate Cox regression analyses has been used extensively in medical research, which however, is only valid under the independent censoring assumption.In this paper, we first consider a copula-based framework to investigate the bias caused by dependent censoring on gene selection. Then, we utilize the copula-based dependence model to develop an alternative gene selection procedure. Simulations show that the proposed procedure adjusts for the effect of dependent censoring and thus outperforms the existing method when dependent censoring is indeed present. The non-small-cell lung cancer data is analyzed to demonstrate the usefulness of our proposal. We implemented the proposed method in an R "compound.Cox" package.

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A surrogate endpoint can be used instead of the most relevant clinical endpoint to assess the efficiency of a new treatment. Before being used, a surrogate endpoint must be validated based on appropriate methods. Numerous validation approaches have been proposed with the most popular used in a context of meta‐analysis, based on a two‐step analysis strategy. For two failure‐time endpoints, two association measurements are usually used, Kendall's τ at the individual level and the adjusted coefficient of determination ( ) at the trial level. However, is not always available due to model estimation constraints. We propose a one‐step validation approach based on a joint frailty model, including both individual‐level and trial‐level random effects. Parameters have been estimated using a semiparametric penalized marginal log‐likelihood method, and various numerical integration approaches were considered. Both individual‐ and trial‐level surrogacy were evaluated using a new definition of Kendall's τ and the coefficient of determination. Estimators' performances were evaluated using simulation studies and satisfactory results were found. The model was applied to individual patient data meta‐analyses in gastric cancer to assess disease‐free survival as a surrogate for overall survival, as part of the evaluation of adjuvant therapy.

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a b s t r a c tQuasi-independence is a common assumption for analyzing truncated data. To verify this condition, we propose a class of weighted log-rank type statistics that include existing tests proposed by Tsai (1990) and Martin and Betensky (2005) as special cases. To choose an appropriate weight function that may lead to a more power test, we derive a score test when the dependence structure under the alternative hypothesis is modeled via the odds ratio function proposed by Chaieb, Rivest and Abdous (2006). Asymptotic properties of the proposed tests are established based on the functional delta method which can handle more general situations than results based on rank-statistics or U-statistics. Extension of the proposed methodology under two different censoring settings is also discussed. Simulations are performed to examine finite-sample performances of the proposed method and its competitors. Two datasets are analyzed for illustrative purposes.