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Table 2 Mean of the predictive ability estimates (Est), mean of the standard error estimates SE ∧ and standard error of the estimates (SE).

From: Multiple imputation for estimating hazard ratios and predictive abilities in case-cohort surveys

  

β 1 = β 2 = β 3 =0

 

β 1 = β 3 = log(2), β 2 = log(1.5)

β1 = β2 = β3 = log(2)

 

Est

SE ∧

SE

% H 0 rejected

Est

SE ∧

SE

% H 0 rejected

Est

SE ∧

SE

% H 0 rejected

Full Cohort

            

C 1

0.518

0.033

0.012

 

0.727

0.032

0.015

 

0.733

0.029

0.014

 

C 2

0.524

0.033

0.013

 

0.747

0.031

0.015

 

0.733

0.029

0.014

 

Δ

0.006

0.010

0.009

3.7

0.020

0.007

0.007

91.6

0.049

0.010

0.010

100

NRI

0.007

0.017

0.019

4.8

0.071

0.030

0.033

52.5

0.167

0.034

0.035

99.9

IDI

2e-4

2e-4

3e-4

6.0

0.014

0.003

0.005

99.9

0.048

0.006

0.009

99.9

MI1000

            

C 1

0.518

0.033

0.012

 

0.724

0.032

0.016

 

0.733

0.029

0.014

 

C 2

0.526

0.033

0.013

 

0.745

0.031

0.016

 

0.783

0.027

0.014

 

Δ

0.008

0.012

0.010

3.4

0.021

0.008

0.008

90.6

0.049

0.010

0.011

100

NRI

0.009

0.019

0.017

1.5

0.076

0.033

0.033

64.8

0.172

0.037

0.036

100

IDI

3e-4

3e-4

4e-4

3.5

0.014

0.004

0.005

99.0

0.045

0.008

0.010

100

MI300

            

C 1

0.518

0.033

0.012

 

0.724

0.032

0.016

 

0.733

0.029

0.014

 

C 2

0.528

0.033

0.012

 

0.745

0.031

0.017

 

0.783

0.027

0.015

 

Δ

0.010

0.014

0.011

3.0

0.021

0.008

0.009

84.6

0.050

0.011

0.012

100

NRI

0.013

0.023

0.018

1.3

0.076

0.035

0.035

57.0

0.172

0.039

0.039

99.7

IDI

4e-4

4e-4

5e-4

1.8

0.014

0.005

0.006

87.5

0.046

0.010

0.012

100

CC1000

            

C 1

0.528

0.032

0.013

 

0.667

0.033

0.015

 

0.670

0.031

0.014

 

C 2

0.534

0.033

0.015

 

0.709

0.032

0.022

 

0.737

0.029

0.014

 

Δ

0.006

0.010

0.010

4.7

0.043

0.011

0.017

100

0.067

0.012

0.012

100

NRI

0.017

0.031

0.033

6.7

0.147

0.039

0.043

96.7

0.261

0.041

0.043

100

IDI

0.002

0.001

0.003

15.2

0.058

0.009

0.014

100

0.114

0.011

0.017

100

CC300

            

C 1

0.523

0.034

0.013

 

0.620

0.037

0.016

 

0.620

0.034

0.015

 

C 2

0.529

0.034

0.015

 

0.647

0.036

0.016

 

0.668

0.032

0.015

 

Δ

0.006

0.010

0.009

3.6

0.027

0.011

0.011

83.3

0.048

0.013

0.013

99.8

NRI

0.019

0.039

0.043

6.2

0.154

0.043

0.050

94.4

0.257

0.046

0.051

99.9

IDI

0.002

0.001

0.003

13.9

0.040

0.008

0.014

99.8

0.078

0.010

0.017

100

  1. Results from 1000 simulations
  2. C 1 Harrell's C index of the proportional hazard model without the phase-2 variable
  3. C 2 Harrell's C index of the proportional hazard model with the phase-2 variable
  4. Δ, Harrell's predictive value of the phase-2 variable, H 0: Δ = 0
  5. NRI, Net reclassification index by adding the phase-2 variable, H 0: NRI = 0 IDI, Integrated discrimination index by adding the phase-2 variable, H0: IDI = 0
  6. Cohort, full cohort estimates; MI300, MI1000: multiple imputation estimates with subcohort sizes set, respectively, at 300 and 1,000; CC300, CC1000, case-cohort estimates with subcohort sizes set, respectively, at 300 and 1,000