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An algorithm for estimating survival under a copula-based dependent truncation model

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Abstract

Traditional analysis with truncated survival data has been developed under the assumption that the lifetime variable of interest is statistically independent of the truncation variable. However, empirical evidence has shown that the truncation variable may depend on the lifetime of interest in many real-world examples. The lack of independence can lead to seriously biased analysis. In this article, we revisit an existing estimation procedure for survival under a copula-based dependent truncation model. Here, the same estimating equation is adopted but a different algorithm to solve the equation is proposed. We compare the new algorithm with the existing one and discuss its theoretical and practical usefulness. Real data examples are analyzed for illustration. We implemented the proposed algorithm in an R “depend.truncation” package, available from CRAN.

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Notes

  1. One can replace the estimating equation of Chaieb et al. (2006) by the estimating equation of Emura et al. (2011). We refer the detailed results under the estimating equation of Emura et al. (2011) to the Supplemental Materials. Although we found some numerical difference between the two approaches of Chaieb et al. (2006) and Emura et al. (2011), the substantive conclusions on the resident’s lifetime distribution are similar. Please refer to the Supplemental Materials for the detailed comparison.

  2. One can replace the estimating equation of Chaieb et al. (2006) by the estimating equation of Emura et al. (2011). Although the two estimating equations are different, there is virtually no numerical difference between the two estimates. This phenomenon occurs in the absence of censoring (Emura et al. 2011).

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Acknowledgments

We are grateful to Professor Weijing Wang for raising the main idea of the method. We also thank the associate editor and the reviewer for their careful reading of our manuscript and their helpful comments that substantially improve the manuscript. This work is supported by the research grant funded by the National Science Council of Taiwan (NSC 101-2118-M-008-002-MY2), the Ministry of Science and Technology of Taiwan (MOST 103-2118-M-008-MY2) and MEXT KAKENHI, Grant-in-Aid for Scientific Research (C) 13203524 of Japan.

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Authors and Affiliations

  1. Graduate Institute of Statistics, National Central University, Jhongli, Taiwan

    T. Emura

  2. Center for Advanced Medicine and Clinical Research, Nagoya University Hospital, Nagoya, Japan

    K. Murotani

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  1. T. Emura
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  2. K. Murotani
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Correspondence to T. Emura.

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Emura, T., Murotani, K. An algorithm for estimating survival under a copula-based dependent truncation model. TEST 24, 734–751 (2015). https://doi.org/10.1007/s11749-015-0432-8

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