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Table 3 Simulation results for the estimation of attributable risk A(.) under proportional hazards, increasing baseline hazard (γ=4/3) with regression parameter β= ln(2) and probability of exposure q=0.5

From: Comparison of methods for estimating the attributable risk in the context of survival analysis

Estimation method

  

n=1, 000

n=10, 000

 

Time

A(t)

Bias

SEE

SSD

CP

Bias

SEE

SSD

CP

KM

τ/4

0.299

0.000814

0.064311

0.064377

0.947

−0.000024

0.020388

0.020204

0.956

 

τ/2

0.250

0.002020

0.043388

0.043169

0.952

0.000210

0.013761

0.013651

0.944

 

3 τ/4

0.200

0.001174

0.037152

0.037027

0.955

−0.000469

0.011824

0.011798

0.960

 

τ

0.153

0.007382

0.043968

0.054032

0.891

0.000554

0.018140

0.021081

0.939

WKM

τ/4

0.299

0.000805

0.064427

0.064296

0.950

−0.000010

0.020380

0.020196

0.954

 

τ/2

0.250

0.002055

0.043322

0.042973

0.949

0.000272

0.013722

0.013643

0.947

 

3 τ/4

0.200

0.001193

0.036838

0.036463

0.962

−0.000410

0.011739

0.011741

0.958

 

τ

0.153

0.005596

0.040652

0.048586

0.898

0.000055

0.017280

0.019095

0.935

COX

τ/4

0.299

0.001207

0.041863

0.040891

0.960

−0.000209

0.013250

0.013076

0.962

 

τ/2

0.250

0.001321

0.036377

0.035580

0.954

−0.000062

0.011499

0.011341

0.958

 

3 τ/4

0.200

0.001300

0.030350

0.029672

0.956

−0.000121

0.009572

0.009502

0.965

 

τ

0.153

0.002791

0.027165

0.028199

0.945

−0.000309

0.009206

0.010402

0.945

PCH

τ/4

0.299

−0.000084

0.041594

0.040674

0.961

−0.001831

0.013151

0.013022

0.957

 

τ/2

0.250

0.000876

0.036176

0.035464

0.956

−0.000759

0.011424

0.011313

0.958

 

3 τ/4

0.200

0.001462

0.030163

0.029655

0.959

−0.000051

0.009509

0.009485

0.961

 

τ

0.153

0.002572

0.025716

0.024704

0.961

0.000622

0.008058

0.007962

0.945

Simpler

0.333

0.001129

0.044983

0.044481

0.955

−0.000242

0.014226

0.014195

0.957

  1. KM nonparametric approach based on Kaplan-Meier estimation for S(t), WKM nonparametric approach based on weighted Kaplan-Meier estimation for S(t), COX semiparametric approach, PCH parametric approach using a piecewise constant hazards model, Simpler simpler approach based on proportion of exposed subjects, Bias sampling mean of the difference between \(\hat {A}(t)\) and A(t), SEE sampling mean of standard error estimate of A(t), SSD sampling standard deviation of \(\hat {A}(t)\), CP coverage probability of the 95% Wald confidence interval