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Table 8 Root Mean Squared Error (MSE) and Bias for the estimation of the marginal survival probability S(1000) for the three groups defined by the number of nodes received

From: Effect of the number of removed lymph nodes on prostate cancer recurrence and survival: evidence from an observational study

Generation

Estimation

   

Unadjusted

Weighted

Doubly Robust

PM

SM

PM

SM

n

Nodes

S(1000)

\(\sqrt {\text {MSE}}\)

Bias

\(\sqrt {\text {MSE}}\)

Bias

\(\sqrt {\text {MSE}}\)

Bias

2

2

3

2

1000

1-10

0.4108

0.0948

-0.0329

0.1144

0.0423

0.0929

0.0095

     

11-20

0.4108

0.0293

-0.0070

0.0287

-0.0027

0.0265

0.0005

     

>20

0.4108

0.1091

0.0728

0.1038

-0.0715

0.0895

0.0159

2

2

3

2

5000

1-10

0.4067

0.0498

-0.0312

0.0668

0.0483

0.0398

0.0029

     

11-20

0.4067

0.0141

-0.0068

0.0126

-0.0023

0.0116

-0.0001

     

>20

0.4067

0.0778

0.0697

0.0813

-0.0747

0.0377

0.0011

2

2

3

2

10000

1-10

0.4069

0.0394

-0.0294

0.0569

0.0471

0.0283

0.0000

     

11-20

0.4069

0.0112

-0.0064

0.0094

-0.0021

0.0085

0.0002

     

>20

0.4069

0.0735

0.0692

0.0809

-0.0776

0.0275

0.0006

[5pt] 2

3

3

3

1000

1-10

0.4108

0.0948

-0.0329

0.1144

0.0423

0.0929

0.0095

     

11-20

0.2971

0.0283

-0.0044

0.0282

-0.0010

0.0269

0.0014

     

>20

0.5514

0.1056

0.0727

0.1250

-0.0866

0.0882

0.0173

2

3

3

3

5000

1-10

0.4067

0.0507

-0.0325

0.0657

0.0468

0.0397

0.0020

     

11-20

0.2941

0.0131

-0.0044

0.0125

-0.0008

0.0121

0.0003

     

>20

0.5461

0.0769

0.0690

0.1004

-0.0923

0.0373

0.0022

2

3

3

3

10000

1-10

0.4069

0.0391

-0.0289

0.0575

0.0478

0.0279

0.0001

     

11-20

0.2936

0.0099

-0.0045

0.0090

-0.0010

0.0086

0.0001

     

>20

0.5473

0.0708

0.0666

0.1008

-0.0969

0.0270

0.0013

[5pt] 2

3

2

4

1000

1-10

0.4108

0.0948

-0.0329

0.1067

-0.0060

0.0920

0.0186

     

11-20

0.2971

0.0283

-0.0044

0.0284

0.0001

0.0270

0.0082

     

>20

0.5514

0.1056

0.0727

0.0978

0.0009

0.1013

-0.0114

2

3

2

4

5000

1-10

0.4067

0.0498

-0.0312

0.0463

0.0003

0.0413

0.0056

     

11-20

0.2941

0.0131

-0.0046

0.0125

-0.0000

0.0134

0.0069

     

3

0.5461

0.0764

0.0687

0.0443

0.0002

0.0470

-0.0029

2

3

2

4

10000

1-10

0.4069

0.0391

-0.0289

0.0320

-0.0012

0.0290

0.0019

     

11-20

0.2936

0.0099

-0.0045

0.0090

0.0000

0.0105

0.0065

     

>20

0.5473

0.0708

0.0666

0.0317

-0.0001

0.0335

-0.0024

  1. Either the propensity score model or the survival model (but not both) used in the estimation process is different from the corresponding model used for data generation. Results are based on 3000 simulated samples. PM stands for Propensity Score Model, and SM stands for Survival Model. Please refer to the text for the description of the models