Abstract:
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The recently developed beta product confidence procedure (BPCP) provides non-asymptotic confidence intervals for a survival distribution at a fixed time with right censored data. With no censoring the BPCP reduces to an exact binomial confidence interval. With censoring it is known to guarantee coverage in the progressive Type II censoring case, and simulations imply at least nominal coverage for the independence censoring case. The problem is that because of discreteness and censoring the interval coverage may be larger than needed. We modify the BPCP, to create a mid-p version, that reduces to the mid-p confidence interval for a binomial parameter when there is no censoring. We show through extensive simulations that like other mid-p confidence intervals, this mid-p BPCP has coverage closer to the nominal level, and generally has at least nominal coverage except in very low censoring scenarios. In contrast, the two asymptotically-based approximations have lower than nominal coverage. This poor coverage is due to the extreme inflation of the lower error rates, although the upper limits are very conservative. Both BPCP and its mid-p version are available in the bpcp R package.
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