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. Author manuscript; available in PMC: 2010 May 25.
Published in final edited form as: Biometrics. 2009 Apr 13;66(1):131–139. doi: 10.1111/j.1541-0420.2009.01238.x

Table 1.

Results of Simulation Experiment A: Small versus large sample performance of the 2-Stage Estimator, Robins’ G-Estimator with bt = 0, and Robins’ G-Estimator relying on starting guesses for bt from the 2-Stage Estimator. Parameters have true value βtj = 0.45 for all t = 1, 2, 3 and j = 0, 1.

True 2-Stage Estimator
 Robins’ G-Estimator with bt = 0 for all t
 Robins’ G-Estimator using 2-Stage Guesses
PMTR AVG EST SD AVG SE 95% COV MSE AVG EST SD AVG SE 95% COV REL MSE AVG EST SD AVG SE 95% COV REL MSE
n = 50
β1,0 0.458 0.515 0.471 91.8 0.265 0.412 0.658 0.604 92.2 1.6 0.444 0.633 0.553 89.6 1.5
β1,1 0.453 0.580 0.532 91.0 0.337 0.413 0.870 0.768 91.3 2.3 0.463 0.846 0.704 86.4 2.1
β2,0 0.441 0.536 0.455 89.4 0.287 0.413 0.603 0.557 92.9 1.3 0.457 0.564 0.422 83.9 1.1
β2,1 0.412 0.739 0.637 90.0 0.547 0.393 0.990 0.841 90.4 1.8 0.402 0.863 0.637 84.7 1.4
β3,0 0.475 0.489 0.381 87.0 0.240 0.409 0.683 0.562 93.0 2.0 0.442 0.496 0.311 77.1 1.0
β3,1 0.430 0.634 0.493 85.8 0.402 0.404 1.155 0.893 91.7 3.3 0.483 0.688 0.422 73.7 1.2
n = 300
β1,0 0.451 0.175 0.169 93.2 0.031 0.430 0.242 0.232 94.6 1.9 0.438 0.236 0.225 94.1 1.8
β1,1 0.452 0.197 0.186 93.5 0.039 0.463 0.314 0.297 92.8 2.6 0.468 0.310 0.292 93.4 2.5
β2,0 0.441 0.164 0.170 96.4 0.027 0.435 0.209 0.216 95.6 1.6 0.445 0.182 0.184 95.4 1.2
β2,1 0.456 0.229 0.222 93.8 0.053 0.449 0.336 0.330 94.7 2.2 0.454 0.279 0.266 94.1 1.5
β3,0 0.451 0.158 0.148 93.3 0.025 0.457 0.204 0.200 94.5 1.7 0.447 0.162 0.149 92.5 1.0
β3,1 0.439 0.184 0.182 93.4 0.034 0.429 0.326 0.314 94.4 3.1 0.444 0.207 0.201 92.3 1.3
n = 1000
β1,0 0.452 0.089 0.092 95.3 0.008 0.446 0.129 0.127 94.9 2.1 0.451 0.124 0.124 94.3 1.9
β1,1 0.452 0.102 0.100 94.6 0.010 0.446 0.173 0.166 93.8 2.9 0.447 0.171 0.164 94.2 2.8
β2,0 0.449 0.091 0.092 95.9 0.008 0.449 0.119 0.117 94.8 1.7 0.450 0.102 0.101 94.7 1.3
β2,1 0.440 0.117 0.120 95.7 0.014 0.430 0.191 0.180 92.3 2.7 0.439 0.150 0.146 94.2 1.6
β3,0 0.446 0.081 0.080 95.0 0.006 0.446 0.107 0.108 95.6 1.8 0.444 0.084 0.082 94.7 1.1
β3,1 0.454 0.099 0.099 94.8 0.010 0.451 0.175 0.169 94.2 3.2 0.456 0.114 0.112 94.0 1.3

REL MSE denotes mean squared error relative to the 2-Stage Estimator.