. Author manuscript; available in PMC: 2023 Jun 30.

Published in final edited form as: Stat Med. 2023 Apr 5;42(14):2496–2520. doi: 10.1002/sim.9734

Table 4.

Naive, unconditionally and conditionally unbiased / bias-adjusted estimates calculated using the observed data and O’Brien-Fleming efficacy stopping boundaries from the MUSEC trial. Standard errors (SEs) are calculated using a parametric bootstrap approach with 10⁵ replicates, assuming that the true difference in proportions is equal to 0.14.

Type of estimator	Estimator	Difference in proportions (SE)	Relative difference to overall MLE
MLE/naive	MLE (overall)	0.1370 (0.054)	-
Unconditionally unbiased/bias-adjusted	MLE (stage 1)	0.1436 (0.057)	+5%
	Median unbiased estimator (MUE)	0.1341 (0.054)	-2%
	UMVUE	0.1278 (0.054)	-7%
	Bias-corrected MLE (UBC-MLE)	0.1328 (0.055)	-3%
Conditionally unbiased/bias-adjusted	MLE (stage 2)	0.1139 (0.111)	-17%
	Conditional MUE (CMUE)	0.1851 (0.080)	+35%
	UMVCUE	0.1724 (0.071)	+26%
	Bias-corrected MLE (CBC-MLE)	0.1909 (0.073)	+39%