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. Author manuscript; available in PMC: 2013 Nov 5.
Published in final edited form as: Ann Appl Stat. 2013 Sep 1;7(3):10.1214/13-AOAS634SUPP. doi: 10.1214/13-AOAS634SUPP

Table 3.

Efficiency of other estimators (using data from the target population or based on the combined-data analysis) relative to the constrained maximum likelihood estimator calculated using data only from the target population. Standard errors of entries do not exceed 3% of the value.

Population 1 Population 2
Pop-Specific Combined-data Pop-Specific Combined-data
EML PSL EML CML PSL EML PSL EML CML PSL
β
β0 = −3.8 0.98 0.94 1.81 1.89 1.77 0.98 1.00 2.24 2.34 2.20
β1 = 1.2 0.99 0.92 1.81 1.87 1.73 0.99 0.99 2.27 2.35 2.18
β2 = 1.5 0.99 0.91 1.80 1.85 1.70 0.99 0.98 2.35 2.42 2.23
ROC(t)
t = .1 0.96 0.95 1.75 1.84 1.76 0.99 1.01 2.16 2.28 2.18
t = .3 0.99 0.98 1.77 1.81 1.77 1.00 1.01 2.25 2.31 2.25
t = .5 0.99 0.98 1.71 1.75 1.71 0.99 0.99 2.33 2.38 2.33
t = .7 0.98 0.95 1.66 1.71 1.62 0.98 0.97 2.33 2.39 2.27
t = .9 0.97 0.92 1.66 1.72 1.59 0.98 0.96 2.31 2.39 2.21
CDFRx(p)
p = (.22, .12) 0.99 1.01 1.14 1.15 1.17 1.00 1.02 1.28 1.29 1.32
p = (.30, .16) 0.98 0.95 1.31 1.35 1.26 0.99 0.97 1.39 1.43 1.36
p = (.43, .23) 0.96 0.96 1.20 1.24 1.19 0.99 0.98 1.35 1.40 1.34
p = (.56, .35) 0.98 0.96 1.37 1.38 1.35 0.99 0.98 1.44 1.46 1.42
p = (.67, .48) 0.98 1.00 1.24 1.25 1.25 0.99 1.01 1.26 1.28 1.26
Risk(y|x)
y = (−1.1, −1.2) 1.00 0.96 1.51 1.53 1.47 0.99 0.97 1.98 2.00 1.91
y = (−.24, −.36) 0.99 0.95 1.32 1.32 1.29 1.00 1.00 1.51 1.55 1.49
y = (.33, .20) 0.99 0.92 1.16 1.14 1.13 0.99 0.98 1.35 1.40 1.32
y = (.88, .75) 1.00 0.99 1.08 1.08 1.08 0.99 1.00 1.10 1.12 1.10
y = (1.6, 1.5) 1.00 0.93 1.40 1.45 1.34 0.99 0.98 1.53 1.53 1.50

the values separated by commas correspond to population 1 and population 2 respectively.