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Abstract:
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Multivariate failure time data are frequently analyzed using the marginal proportional hazards models and the frailty models. When the sample size is extraordinarily large, using either approach could face computational challenges. In this paper, we focus on the marginal model approach and propose a divide-and-combine method to analyze large-scale multivariate failure time data. We propose to randomly divide the full data into multiple subsets and propose a weighted method to combine these estimators obtained from individual subsets using three weights. Under mild conditions, we show that the combined estimator is asymptotically equivalent to the estimator obtained from the full data as if the data were analyzed all at once. In addition, to screen out risk factors with weak signals, we propose to perform the regularized estimation on the combined estimator using its combined confidence distribution. Theoretical properties, such as consistency, oracle properties, and asymptotic equivalence between the divide-and-combine approach and the full data approach are studied. Performance of the proposed method is investigated using simulation studies and a real big data example.
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