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. Author manuscript; available in PMC: 2014 Feb 18.
Published in final edited form as: Biometrics. 2012 Sep 24;68(4):1028–1036. doi: 10.1111/j.1541-0420.2012.01781.x

Table 1.

Simulations to assess sensitivity of estimate of NIE to violations in Assumption 3: n=60

χ = 1
ε = 50 ε = 75 ε = 100
NIE s.d. NIE s.d. NIE s.d.
β2 = 0 Our Approach 0.024 (0.058) 0.030 (0.054) 0.029 (0.058)
Truth 0.024 (0.058) 0.030 (0.054) 0.029 (0.058)
β2 = 1.28 Our Approach 0.0051 (0.058) 0.0065 (0.055) 0.0079 (0.060)
Truth 0.0021 (0.058) 0.0036 (0.055) 0.0040 (0.058)
β2 = 2.56 Our Approach −0.025 (0.051) −0.017 (0.055) −0.016 (0.047)
Truth −0.0034 (0.048) 0.0073 (0.051) 0.0067 (0.045)
β2 = 5.12 Our Approach −0.058 (0.044) −0.072 (0.048) −0.062 (0.049)
Truth 0.0045 (0.037) 0.0012 (0.038) 0.00075 (0.038)
χ = 1.15
ε = 50 ε = 75 ε = 100
NIE s.d. NIE s.d. NIE s.d.
β2 = 0 Our Approach 0.021 (0.053) 0.029 (0.052) 0.028 (0.061)
Truth 0.021 (0.053) 0.029 (0.052) 0.028 (0.061)
β2 = 1.28 Our Approach −0.0046 (0.056) 0.0026 (0.058) 0.0057 (0.049)
Truth −0.0075 (0.056) 0.00001 (0.056) 0.0032 (0.047)
β2 = 2.56 Our Approach −0.015 (0.062) −0.015 (0.055) −0.016 (0.053)
Truth 0.0042 (0.057) 0.0038 (0.055) 0.0033 (0.050)
β2 = 5.12 Our Approach −0.060 (0.047) −0.048 (0.051) −0.075 (0.060)
Truth −0.0007 (0.031) 0.0072 (0.039) −0.010 (0.044)
χ = 1.3
ε = 50 ε = 75 ε = 100
NIE s.d. NIE s.d. NIE s.d.
β2 = 0 Our Approach 0.020 (0.055) 0.030 (0.060) 0.017 (0.054)
Truth 0.020 (0.055) 0.030 (0.060) 0.017 (0.054)
β2 = 1.28 Our Approach 0.00052 (0.055) −0.0015 (0.053) −0.0055 (0.058)
Truth −0.0014 (0.056) −0.0049 (0.053) −0.0076 (0.058)
β2 = 2.56 Our Approach −0.012 (0.053) −0.011 (0.054) −0.015 (0.062)
Truth 0.0044 (0.052) 0.0056 (0.051) 0.0022 (0.058)
β2 = 5.12 Our Approach −0.040 (0.052) −0.054 (0.051) −0.051 (0.052)
Truth 0.014 (0.037) 0.0021 (0.040) 0.0066 (0.042)
χ = 2
ε = 50 ε = 75 ε = 100
NIE s.d. NIE s.d. NIE s.d.
β2 = 0 Our Approach 0.015 (0.052) 0.010 (0.062) 0.021 (0.055)
Truth 0.015 (0.052) 0.010 (0.062) 0.021 (0.055)
β2 = 1.28 Our Approach −0.0053 (0.052) 0.010 (0.054) 0.012 (0.059)
Truth −0.0068 (0.053) 0.010 (0.052) 0.010 (0.057)
β2 = 2.56 Our Approach 0.016 (0.057) 0.00037 (0.058) 0.00064 (0.061)
Truth 0.023 (0.052) 0.0098 (0.053) 0.012 (0.057)
β2 = 5.12 Our Approach −0.0049 (0.064) −0.018 (0.055) −0.020 (0.055)
Truth 0.030 (0.048) 0.022 (0.040) 0.020 (0.043)