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Table 1 Estimated parameters (\(\widehat{\theta }\)) and its standard error (SE) for the association between the longitudinal intraocular pressure (IOP) and the risk of developing primary open-angle glaucoma (POAG) based on the OHTS data

From: Comparing statistical methods in assessing the prognostic effect of biomarker variability on time-to-event clinical outcomes

Parameters

Joint Model

RC

Naive

LMAa

tdCoxa

\(\widehat{\theta }\)

SE

\(\widehat{\theta }\)

SE

\(\widehat{\theta }\)

SE

\(\widehat{\theta }\)

SE

\(\widehat{\theta }\)

SE

Longitudinal model:

 Fixed effects

  Intercept (\({\beta }_{0})\)

24.55*

0.108

24.57*

0.109

24.60

 

24.65

 

24.65

 

  Slope (\({\beta }_{1})\)

-0.169*

0.021

-0.179*

0.021

-0.037

 

-0.180

 

-0.180

 

  Age (decades)\({(\beta }_{2})\)

0.244*

0.106

0.235*

0.112

–

 

–

 

–

 

  CCT \({(\beta }_{3})\)

0.045

0.108

0.031

0.103

–

 

–

 

–

 

  VCD \({(\beta }_{4})\)

-0.063

0.110

-0.071

0.110

–

 

–

 

–

 

 Random effects

  SD of Intercept (\({\sigma }_{I})\)

2.514*

0.088

2.518*

0.088

3.098

 

3.031

 

3.031

 

  SD of slope (\({\sigma }_{S})\)

0.412*

0.021

0.410*

0.021

1.393

 

1.664

 

1.664

 

  SD of variation (\({\sigma }_{V})\)

0.668*

0.027

0.668*

0.027

0.905

 

1.012

 

1.012

 

  Mean of variation (\({\mu }_{V})\)

1.641*

0.031

1.639*

0.030

2.185

 

1.090

 

1.090

 

  Correlation (\({\rho }_{12})\)

0.131*

0.060

0.113*

0.059

–

 

–

 

–

 

  Correlation (\({\rho }_{13})\)

0.183*

0.051

0.181*

0.050

–

 

–

 

–

 

  Correlation (\({\rho }_{23})\)

0.235*

0.059

0.228*

0.060

–

 

–

 

–

 

Survival model:

 Baseline factor

   Age (decades)\({(\alpha }_{1})\)

0.216

0.125

0.182

0.110

0.082

0.107

0.114

0.109

0.102

0.107

   CCT \({(\alpha }_{2})\)

-0.639*

0.129

-0.644*

0.113

-0.672*

0.110

-0.643*

0.129

-0.662*

0.112

   VCD \({(\alpha }_{3})\)

0.543*

0.142

0.526*

0.116

0.549*

0.111

0.425*

0.112

0.517*

0.112

 Effects of follow-up IOP

  Intercept (\({\gamma }_{1})\)

0.226*

0.056

0.275*

0.047

0.212*

0.034

0.161*

0.038

0.203*

0.034

  Slope (\({\gamma }_{2})\)

1.190*

0.514

0.852*

0.348

0.038

0.054

0.017

0.048

0.026

0.051

  Variation (\({\gamma }_{3})\)

0.121

0.228

0.103

0.183

-0.052

0.094

0.108

0.084

0.071

0.084

  1. *P < 0.05; RC Regression calibration; Naïve: simple OLS; LMA Landmark analysis, td-Cox: time-dependent Cox model
  2. aBased on the subject-specific intercept, slope, and logarithm transformed variance of residuals estimated at the 3-year landmark point
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