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Table 1 Performance measures of the simulated biomarker coefficient \(\left(\widehat{\alpha }\right)\): Bias (emp SD; CP)

From: Goodness-of-fit two-phase sampling designs for time-to-event outcomes: a simulation study based on New York University Women’s Health Study for breast cancer

Stratification

Event rate

\(\alpha\)

Ratio

Cox:Full cohort

IPW:Two-phase

SMLE:Two-phase

Standard:CC

SMLE:CC

Unstratified

5%

0.2

1:1

0.001 (0.098; 0.954)

0.004 (0.150; 0.936)

-0.002 (0.120; 0.944)

0.030 (0.195; 0.918)

0.005 (0.146; 0.940)

1:2

-0.003 (0.103; 0.940)

-0.005 (0.121; 0.920)

-0.003 (0.111; 0.926)

0.010 (0.150; 0.944)

-0.002 (0.128; 0.952)

0.5

1:1

0.008 (0.106; 0.934)

0.026 (0.163; 0.916)

0.007 (0.131; 0.946)

0.070 (0.209; 0.942)

0.013 (0.152; 0.940)

1:2

0.003 (0.104; 0.928)

0.004 (0.124; 0.950)

0.005 (0.115; 0.948)

0.043 (0.171; 0.928)

0.002 (0.135; 0.948)

10%

0.2

1:1

-0.003 (0.070; 0.946)

-0.009 (0.090; 0.940)

-0.005 (0.081; 0.944)

0.001 (0.123; 0.952)

-0.008 (0.099; 0.948)

1:2

-0.001 (0.075; 0.940)

-0.007 (0.082; 0.934)

-0.001 (0.078; 0.936)

0.009 (0.096; 0.942)

0.003 (0.088; 0.946)

0.5

1:1

0.003 (0.070; 0.940)

-0.007 (0.094; 0.954)

0.001 (0.082; 0.954)

0.042 (0.137; 0.936)

0.008 (0.100; 0.956)

1:2

0.001 (0.074; 0.936)

-0.016 (0.081; 0.926)

0.001 (0.078; 0.940)

0.010 (0.105; 0.934)

0.000 (0.087; 0.950)

Stratified by median AGE

5%

0.2

1:1

0.001 (0.098; 0.954)

0.009 (0.146; 0.940)

0.003 (0.121; 0.944)

0.053 (0.218; 0.888)

0.008 (0.139; 0.946)

1:2

-0.003 (0.103; 0.940)

-0.003 (0.123; 0.930)

-0.001 (0.112; 0.938)

0.024 (0.159; 0.926)

0.003 (0.129; 0.946)

0.5

1:1

0.008 (0.106; 0.934)

0.040 (0.161; 0.936)

0.017 (0.132; 0.942)

0.143 (0.293; 0.832)

0.009 (0.157; 0.924)

1:2

0.003 (0.104; 0.928)

0.006 (0.131; 0.936)

0.009 (0.115; 0.934)

0.069 (0.187; 0.902)

0.010 (0.131; 0.942)

10%

0.2

1:1

-0.003 (0.070; 0.946)

-0.014 (0.088; 0.954)

-0.004 (0.080; 0.964)

0.014 (0.131; 0.934)

0.001 (0.104; 0.952)

1:2

-0.001 (0.075; 0.940)

-0.008 (0.084; 0.930)

-0.001 (0.078; 0.944)

0.011 (0.101; 0.938)

0.005 (0.089; 0.942)

0.5

1:1

0.003 (0.070; 0.940)

-0.004 (0.097; 0.926)

0.005 (0.085; 0.944)

0.043 (0.133; 0.948)

0.003 (0.095; 0.964)

1:2

0.001 (0.074; 0.936)

-0.014 (0.080; 0.948)

0.001 (0.078; 0.948)

0.026 (0.114; 0.916)

0.005 (0.091; 0.934)

  1. Abbreviations: Ratio Case and control ratio, empSD standard deviation of the estimates, CP coverage probability of the 95% CI, Cox Standard Cox PH model, Full cohort full cohort design, IPW IPW based Cox PH model, Two-phase GOF two-phase sampling design, SMLE semiparametric maximum-likelihood method, Standard Prentice method as unstratified approach and Borgan I method as stratified approach, CC standard case-cohort design. Note that we describe each method under each design as method:design using the abbreviations
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BMC Medical Research Methodology

ISSN: 1471-2288

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