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. Author manuscript; available in PMC: 2015 Jan 1.
Published in final edited form as: Stat. 2014 Mar 27;3(1):83–94. doi: 10.1002/sta4.46

Table 1.

Simulation: Propensity score parameter estimation. α̂: Estimated parameters using the proposed method. α̂w: Estimated parameters using the CW method. α̂wm: Estimated parameters using the CW method when the hazard model is misspecified. α̂Un: Estimated parameters when unadjusted for the length-biased sampling. α=(−0.1,1,−1).

Method Bias S.D. Bias S.D.
10 % Cens. n = 500 n = 5000
α̂ (0.01,0.04,0.03) (0.21,0.43,0.45) (0.00,0.01,0.01) (0.09,0.18,0.19)
α̂w (0.08,0.02,0.01) (0.17,0.28,0.28) (0.01,0.00,0.01) (0.06,0.10,0.10)
α̂wm
(0.03,0.02,0.49) (0.17,0.29,0.23) (0.08,0.03,0.48) (0.06,0.09,0.08)
α̂Un (0.10,0.50,0.50) (0.11,0.21,0.22) (0.10,0.51,0.50) (0.04,0.07,0.08)

20 % Cens. n = 500 n = 5000
α̂ (0.01,0.05,0.05) (0.22,0.42,0.43) (0.02,0.03,0.03) (0.09,0.18,0.20)
α̂w (0.02,0.01,0.01) (0.17,0.29,0.27) (0.02,0.01,0.01) (0.06,0.10,0.10)
α̂wm
(0.01,0.02,0.47) (0.16,0.29,0.21) (0.02,0.05,0.46) (0.06,0.10,0.08)
α̂Un (0.11,0.49,0.50) (0.10,0.22,0.20) (0.10,0.51,0.50) (0.04,0.07,0.08)

30 % Cens. n = 500 n = 5000
α̂ (0.04,0.08,0.09) (0.22,0.44,0.44) (0.03,0.06,0.07) (0.10,0.19,0.20)
α̂w (0.07,0.00,0.02) (0.17,0.29,0.29) (0.08,0.03,0.02) (0.06,0.10,0.11)
α̂wm
(0.07,0.02,0.45) (0.17,0.29,0.21) (0.03,0.06,0.45) (0.06,0.10,0.08)
α̂Un (0.11,0.49,0.50) (0.10,0.22,0.20) (0.10,0.51,0.50) (0.04,0.07,0.08)