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On comparing competing risks using the ratio of their cumulative incidence functions

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  • Hammou Barmi

    (Baruch College, The City University of New York)

Abstract

For $$ 1\le i \le r$$ 1 ≤ i ≤ r , let $$F_i$$ F i be the cumulative incidence function (CIF) corresponding to the ith risk in an r-competing risks model. We assume a discrete or a grouped time framework and obtain the maximum likelihood estimators (m.l.e.) of these CIFs under the restriction that $$F_i(t)/F_{i+1}(t)$$ F i ( t ) / F i + 1 ( t ) is nondecreasing, $$1 \le i \le r-1.$$ 1 ≤ i ≤ r - 1 . We also derive the likelihood ratio tests for testing for and against this restriction and obtain their asymptotic distributions. The theory developed here can also be used to investigate the association between a failure time and a discretized or ordinal mark variable that is observed only at the time of failure. To illustrate the applicability of our results, we give examples in the competing risks and the mark variable settings.

Suggested Citation

  • Hammou Barmi, 2022. "On comparing competing risks using the ratio of their cumulative incidence functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(6), pages 1067-1083, December.
    • Handle: RePEc:spr:aistmt:v:74:y:2022:i:6:d:10.1007_s10463-022-00823-9
    DOI: 10.1007/s10463-022-00823-9
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    References listed on IDEAS

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    1. Peter Gilbert & Ian McKeague & Yanqing Sun, 2004. "Tests for Comparing Mark-Specific Hazards and Cumulative Incidence Functions," UW Biostatistics Working Paper Series 1032, Berkeley Electronic Press.
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