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Table 1 Benchmark results for the age-5 serum sum of serum-PFAS concentrations (ng/mL) in regard to tetanus and diphtheria antibody concentrations at age 7 years in the Faroese individual data [15]. \(-2\log (L)\) is minus two times the log-maximum likelihood function and p is the number of parameters. \(\Delta\)AIC is the difference in AIC [\(-2\log (L)+2p\)] of current model and the model with the minimum AIC (disregarding Hockey stick model as BMDL was not available). Coverage is the coverage probability of the BMDL as estimated in a simulation study

From: Benchmark dose calculations for PFAS exposure based on two data sets on immunotoxic effects

  

BMR=5%

BMR=10%

    

Antibody

DR-model

BMD

BMDL

BMD

BMDL

\(-2 \log (L)\)

p

\(\Delta\)AIC

coverage

Tetanus

Linear

2.577

1.434

5.294

2.946

1717.94

5

0

0.944

 

K-power

2.577

1.448

5.294

2.959

1717.94

6

2.00

0.880

 

Piecewise

1.516

0.673

3.113

1.383

1717.59

6

1.65

0.951

 

Hockey stick

15.067

-

17.762

-

1717.91

6

-

-

Diphtheria

Linear

2.672

1.513

5.488

3.108

1656.10

5

0

0.954

 

K-power

2.672

1.531

5.488

3.123

1656.10

6

2

0.890

 

Piecewise

1.222

0.632

2.511

1.298

1655.02

6

0.92

0.951

 

Hockey stick

2.672

-

5.488

-

1656.10

6

-

-