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Keywords:

  • competing risks;
  • conditional probability;
  • dependence structures;
  • subsurvival functions;
  • U-statistics

Abstract.  Dependence structures between the failure time and the cause of failure are expressed in terms of the monotonicity properties of the conditional probabilities involving the cause of failure and the failure time. These properties of the conditional probabilities are used for testing four types of departures from the independence of the failure time and the cause of failure and tests based on U-statistics are proposed. In the process, a concept of concordance and discordance between a continuous and a binary variable is introduced to propose a statistical test. The proposed tests are applied to two illustrative applications.