In this work, we propose a single nucleotide polymorphism (SNP) set association test for censored phenotypes in the presence of a family-based design. The proposed test is valid for both common and rare variants. A proportional hazards Cox model is specified for the marginal distribution of the trait and the familial dependence is modeled via a Gaussian copula. Censored values are treated as partially missing data and a multiple imputation procedure is proposed in order to compute the test statistics. The P-value is then deduced analytically. The finite-sample empirical properties of the proposed method are evaluated and compared to existing competitors by simulations and its use is illustrated using a breast cancer data set from the Consortium of Investigators of Modifiers of BRCA1 and BRCA2.
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