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Table 1 Results for the Gompertz distribution

From: Limitations of the incidence density ratio as approximation of the hazard ratio

BLR

True HR

CP

MPE

MSE

SE

IDR

HR

IDR

HR

IDR

HR

IDR

HR

0.01

0.4

0.976

0.978

−22.678

−9.860

0.595

0.580

0.026

0.027

0.7

0.964

0.978

−45.271

−5.351

0.612

0.634

0.023

0.024

0.9

0.983

0.989

− 128.131

1.149

0.466

0.461

0.021

0.022

1

0.977

0.976

NA

–

0.458

0.455

0.020

0.021

0.02

0.4

0.956

0.970

−7.247

7.156

0.369

0.404

0.018

0.019

0.7

0.952

0.956

−34.036

1.679

0.280

0.285

0.015

0.016

0.9

0.943

0.953

− 118.042

4.062

0.240

0.243

0.014

0.015

1

0.956

0.973

NA

NA

0.209

0.214

0.014

0.014

0.05

0.4

0.930

0.948

−11.000

3.343

0.145

0.149

0.011

0.012

0.7

0.928

0.964

−35.534

1.250

0.098

0.091

0.009

0.010

0.9

0.936

0.966

− 133.290

−13.655

0.095

0.083

0.009

0.009

1

0.929

0.946

NA

NA

0.087

0.077

0.009

0.009

0.075

0.4

0.931

0.970

−12.835

2.092

0.086

0.082

0.009

0.009

0.7

0.921

0.958

− 37.182

−1.180

0.070

0.059

0.008

0.008

0.9

0.914

0.954

− 125.979

−6.983

0.069

0.055

0.007

0.007

1

0.916

0.945

–

–

0.065

0.053

0.007

0.007

0.1

0.4

0.914

0.943

−11.975

2.503

0.076

0.072

0.008

0.008

0.7

0.907

0.941

−33.896

2.140

0.061

0.052

0.007

0.007

0.9

0.927

0.968

−102.743

13.059

0.047

0.038

0.006

0.006

1

0.902

0.959

NA

NA

0.053

0.038

0.006

0.006

0.15

0.4

0.885

0.942

−14.697

0.333

0.058

0.046

0.006

0.006

0.7

0.875

0.943

−35.599

0.407

0.045

0.033

0.005

0.006

0.9

0.888

0.953

− 115.852

0.054

0.039

0.027

0.005

0.005

1

0.884

0.958

NA

NA

0.037

0.024

0.005

0.005

0.2

0.4

0.851

0.949

−15.946

−1.037

0.049

0.031

0.005

0.006

0.7

0.852

0.945

−36.576

−1.049

0.037

0.023

0.005

0.005

0.9

0.869

0.955

− 111.602

0.545

0.031

0.019

0.004

0.004

1

0.862

0.951

NA

NA

0.031

0.019

0.004

0.004

0.25

0.4

0.835

0.957

−15.713

−0.142

0.043

0.025

0.005

0.005

0.7

0.830

0.951

−36.719

−0.629

0.033

0.019

0.004

0.004

0.9

0.854

0.950

−115.785

−5.196

0.028

0.015

0.004

0.004

1

0.872

0.956

NA

NA

0.024

0.015

0.004

0.004

0.3

0.4

0.829

0.950

−16.209

0.014

0.038

0.019

0.004

0.004

0.7

0.818

0.956

−36.302

− 0.295

0.029

0.014

0.004

0.004

0.9

0.862

0.946

− 103.272

6.879

0.023

0.013

0.004

0.004

1

0.857

0.948

NA

NA

0.021

0.013

0.003

0.004

  1. Gompertz distribution with shape parameter α = 1, sample size N = 1000, and a relative average follow-up duration of 90% in the control group
  2. If the true HR is 1 the MPE cannot be calculated
  3. BLR baseline risk, CP coverage probability, HR hazard ratio, IDR incidence density ratio, MPE mean percent error, MSE mean square error, SE standard error
  4. Numbers in boldface indicate a CP below 90%