Table 3 Threshold effect analysis of serum carotenoids and OA based on dataset A

OA ~ Total carotenoid

Model 1 Fitting model by standard linear regression

0.891(0.776–1.022)0.097

Model 2 Fitting model by two-piecewise linear regression

 Inflection point

4.313

 < 4.313 Effect 1

1.011(0.811–1.26)0.922

 > 4.313 Effect 2

0.722(0.502–1.038)0.077

Effect2-Effect1

0.714(0.431–1.184)0.186

P for likelihood ratio test

0.1851

OA ~ Trans Lycopene

 Model 1 Fitting model by standard linear regression

0.928(0.844–1.021)0.12

Model 2 Fitting model by two-piecewise linear regression

 Inflection point

2.97

 < 2.97 Effect 1

1.145(0.958–1.37)0.133

 > 2.97 Effect 2

0.596(0.411–0.864)0.007

 Effect2-Effect1

0.52(0.313–0.866)0.013

P for likelihood ratio test

0.0128

OA ~ β-cryptoxanthin

 Model 1 Fitting model by standard linear regression

0.898(0.806–1)0.051

Model 2 Fitting model by two-piecewise linear regression

 Inflection point

3.8

 < 3.8 Effect 1

0.908(0.813–1.014)0.085

 > 3.8 Effect 2

0.131(0.024–0.721)0.021

 Effect2-Effect1

0.145(0.026–0.805)0.028

P for likelihood ratio test

0.0095

OA ~ lutein/zeaxanthin

Model 1 Fitting model by standard linear regression

0.874(0.764–1)0.051

Model 2 Fitting model by two-piecewise linear regression

 Inflection point

3.153

 < 3.153 Effect 1

0.826(0.704–0.971)0.021

 > 3.153 Effect 2

1.074(0.681–1.694)0.752

 Effect2-Effect1

1.3(0.765–2.21)0.324

P for likelihood ratio test

0.3281

OA ~ α Carotene

 Model 1 Fitting model by standard linear regression

1.004(0.902–1.118)0.944

Model 2 Fitting model by two-piecewise linear regression

 Inflection point

0.525

 < 0.525 Effect 1

1.408(0.954–2.076)0.083

 > 0.525 Effect 2

0.95(0.835–1.08)0.421

 Effect2-Effect1

0.675(0.434–1.05)0.079

P for likelihood ratio test

0.0786

OA ~ β Carotene

Model 1 Fitting model by standard linear regression

0.991(0.892–1.101)0.859

Model 2 Fitting model by two-piecewise linear regression

 Inflection point

2.027

 < 2.027 Effect 1

1.322(0.97–1.802)0.076

 > 2.027 Effect 2

0.924(0.806–1.058)0.243

 Effect2-Effect1

0.699(0.48–1.016)0.06

P for likelihood ratio test

0.0582