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Non-parametric maximum likelihood estimation of the cause specific failure probability, and of its standard error, in the presence of competing risks is discussed with reference to some contraceptive use dynamics data from Bangladesh. The cause specific incidence function provides an intuitively appealing summary curve for failure rates and probabilities, such as probabilities of discontinuation of different kinds of contraception, based on right-censored data of the particular event. Dinse and Larson's formula can be utilized to calculate the standard error of the cause specific probability for the failure type of interest, and to construct pointwise confidence intervals. The accuracy of these intervals, as well as those based on the log(-log) transformation and the arcsine transformation, are compared by simulations. We find that Dinse and Larson's formula, used in conjuction with a log(-log) transform, yields reliable standard error estimates and accurate coverage in samples of small and large size, and can be recommended for use in this situation.
Jahar B. Choudhury (Wed,) studied this question.