Table 1 Performance of TD-LR under the proportional and non-proportional hazards situations with various sample sizes, censoring percentage, time points, and marker values

Proportional Hazard (PH)

x=-1

x=0

x=1

N

Censoring

2 yr

8 yr

2 yr

8 yr

2 yr

8 yr

100

10-15%

Bias

-0.0034

-0.0218

-0.0118

-0.1755

-0.0410

-6.747

MSE

0.0053

0.0060

0.0103

1.757

1.031

5.6×10⁷

60-80%

Bias

-0.0061

-0.0074

-0.0085

-0.0098

-0.0434

-0.0444

MSE

0.0164

0.0141

0.0132

0.0102

0.0448

0.1669

500

10-15%

Bias

-0.0023

-0.0035

-0.0029

-0.0226

-0.0126

2.729

MSE

0.0010

0.0010

0.0016

0.1587

0.1275

3634

60-80%

Bias

0.0066

0.005

0.0028

0.0010

-0.0084

-0.0177

MSE

0.0033

0.0028

0.0026

0.0019

0.0082

0.0315

1000

10-15%

Bias

0.0013

-0.0021

-0.0006

-0.0248

-0.0169

-2.286

MSE

0.0005

0.0005

0.0009

0.0760

0.0654

1042

60-80%

Bias

0.0030

0.0030

0.0013

0.0013

-0.0071

-0.0116

MSE

0.0015

0.0013

0.0012

0.0009

0.0041

0.0156

Non-Proportional Hazard (PH), γ=0.2

x=-1

x=0

x=1

N

Censoring

2 yr

8 yr

2 yr

8 yr

2 yr

8 yr

100

10-15%

Bias

0.0257

0.1984

-0.0749

-5.774

-2.542

−2.01×10¹³

MSE

0.0036

0.0430

0.0198

33.84

11.16

4.02×10²⁶

60-80%

Bias

0.0324

0.0949

-0.0020

0.1766

-27.64

−2.95×10⁶⁴

MSE

0.0018

0.0103

0.0103

0.0509

766.8

8.72×10¹²⁸

500

10-15%

Bias

0.0275

0.2080

-0.0669

-5.744

-2.87

−2.01×10¹³

MSE

0.0013

0.0439

0.0068

33.06

8.664

4.02×10²⁶

60-80%

Bias

0.0324

0.0984

0.0046

0.2033

-27.98

−2.95×10⁶⁴

MSE

0.0012

0.0099

0.0021

0.045

783.2

8.72×10¹²⁸

1000

10-15%

Bias

0.0263

0.2082

-0.069

-5.742

-2.89

−2.01×10¹³

MSE

0.0010

0.0437

0.0060

33.01

8.597

4.02×10²⁶

60-80%

Bias

0.0328

0.0997

0.0076

0.2128

-27.99

−2.95×10⁶⁴

MSE

0.0012

0.0101

0.0014

0.0474

783.8

8.72×10¹²⁸