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. Author manuscript; available in PMC: 2014 Jan 7.
Published in final edited form as: Stat Med. 2011 Dec 5;30(30):10.1002/sim.4412. doi: 10.1002/sim.4412

Table 4.

Performance of estimators when p1q1 ≠ (1−q1)(p2q2). Coverage is the empirical coverage of the nominal 95% confidence interval and length is the average length of the 95% confidence interval. Allocation a = 0.35.

p1 = .4, q1 = .2, p2 = .4, q2 = .1 p1 = .4, q1 = .2, p2 = .3, q2 = .1

n Estimator Bias Variance MSE Coverage Length Bias Variance MSE Coverage Length
50 MLE -.002 .022 .022 92 0.555 .008 .024 .024 93 0.554
CMLE .042 .013 .014 89 0.402 .002 .011 .011 92 0.388
O .021 .010 .011 94 0.382 -.023 .009 .009 95 0.366
EST .019 .011 .012 90 0.366 -.027 .010 .010 90 0.347
WA .021 .010 .011 92 0.370 -.022 .009 .009 92 0.353
Range SE .003- .0005- .0005- .8- .0000- .003- .0004- .0004- .7- .0000-
.005 .0010 .0010 .10 .0013 .005 .0011 .0011 1.0 .0013

100 MLE .001 .010 .010 93 0.391 .001 .010 .010 93 0.391
CMLE .043 .006 .008 89 0.287 .000 .006 .006 94 0.279
O .021 .005 .005 93 0.270 -.024 .005 .005 93 0.259
EST .020 .005 .006 92 0.265 -.025 .005 .005 91 0.253
WA .021 .005 .005 93 0.266 -.024 .005 .005 92 0.255
Range SE .002- .0002- .0002- .8- .0000- .002- .0002- .0002- .7- .0000-
.003 .0005 .0004 1.0 .0005 .003 .0005 .0005 .9 .0005

200 MLE -.002 .005 .005 93 0.279 -.003 .005 .005 95 0.279
CMLE .045 .003 .005 85 0.204 .001 .003 .003 94 0.199
O .021 .002 .003 93 0.191 -.023 .002 .003 92 0.183
EST .021 .003 .003 92 0.189 -.023 .002 .003 91 0.182
WA .022 .002 .003 93 0.189 -.023 .002 .003 91 0.182
Range SE .002- .0001- .0001- .8- .0000 .002- .0001- .0001- .7- .0000-
.002 .0002 .0002 1.1 .0003 .002 .0002 .0002 .9 .0003

400 MLE -.001 .003 .003 95 0.198 .000 .002 .002 94 0.198
CMLE .044 .001 .003 79 0.145 .000 .001 .001 96 0.141
O .021 .001 .002 92 0.135 -.024 .001 .002 89 0.130
EST .021 .001 .002 92 0.135 -.025 .001 .002 88 0.129
WA .022 .001 .002 92 0.135 -.024 .001 .002 89 0.129
Range SE .001- <.0001- <.0001- .7- .0000- .001- <.0001- <.0001- .7- .0000-
.002 .0001 .0001 1.3 .0001 .002 .0001 .0001 1.0 .0001