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Table 3 Simulation results for the comparison of the proposed method with Wu et al. (2018)’s method under right censored data, including the estimated bias (Bias), the sample standard error (SSE) of the estimates, the average of the standard error estimates (SEE), and the 95% empirical coverage probability (CP)

From: A pairwise pseudo-likelihood approach for regression analysis of left-truncated failure time data with various types of censoring

  

Proposed method

    

Wu et al. (2018)’s method

   

n

Par

True

Bias

SSE

SEE

CP

Bias

SSE

SEE

CP

\(A^{*}\) follows the uniform distribution

          

100

\(\beta _1\)

1

0.025

0.244

0.247

95.0

0.026

0.244

0.227

92.8

 

\(\beta _2\)

1

0.027

0.391

0.398

94.9

0.027

0.391

0.368

93.6

300

\(\beta _1\)

1

0.011

0.129

0.133

96.0

0.012

0.129

0.130

95.2

 

\(\beta _2\)

1

0.005

0.246

0.216

94.8

0.005

0.216

0.211

95.1

500

\(\beta _1\)

1

0.005

0.100

0.102

95.2

0.005

0.100

0.100

95.1

 

\(\beta _2\)

1

0.002

0.166

0.165

95.1

0.003

0.166

0.162

94.9

\(A^{*}\) follows the exponential distribution

          

100

\(\beta _1\)

1

0.024

0.248

0.257

95.8

0.024

0.248

0.237

94.3

 

\(\beta _2\)

1

0.015

0.398

0.416

95.7

0.015

0.398

0.383

93.6

300

\(\beta _1\)

1

0.003

0.134

0.138

95.6

0.003

0.134

0.135

95.3

 

\(\beta _2\)

1

0.008

0.218

0.223

95.4

0.008

0.218

0.219

95.2

500

\(\beta _1\)

1

0.010

0.107

0.106

94.7

0.010

0.107

0.105

95.2

 

\(\beta _2\)

1

0.011

0.172

0.171

94.8

0.011

0.172

0.169

94.6