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Maximum likelihood estimator for cumulative incidence functions under proportionality constraint

Abstract

This paper deals with a model of possibly dependent competing risks in the presence of additional independent censoring. Under the assumption that the cumulative incidence functions are proportional or equivalently that the cause-specific cumulative hazard functions are proportional, we derive a maximum likelihood estimator for the cumulative incidence functions. Asymptotic results are derived for our estimator namely strong consistency, convergence rate, weak convergence and strong approximation. Pointwise confidence bands are then constructed. Simulation results are carried out to assess the accuracy of the pointwise confidence bands and to investigate the effect of model misspecification. We also briefly consider the case of independent competing risks with proportional net cumulative hazard functions in the presence of independent censoring.

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Correspondence to Ségolen Geffray.

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Geffray, S., Guilloux, A. Maximum likelihood estimator for cumulative incidence functions under proportionality constraint. Sankhya A 73, 303–328 (2011). https://doi.org/10.1007/s13171-011-0013-1

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  • DOI: https://doi.org/10.1007/s13171-011-0013-1

AMS (2000) subject classification

  • Primary 62-02,62N01,62N02,62G05,62G20

Keywords and phrases

  • Competing risks
  • censoring
  • proportionality constraint
  • cumulative incidence functions
  • asymptotic theory