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Table 3 Benchmark results for the sum of serum-PFAS concentrations (ng/mL) in regard to tetanus, diphtheria and HiB antibody concentrations in the decile data of the German study [11]. \(-2\log (L)\) 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

4.213

2.326

8.654

4.778

-18.90

2

2.54

0.949

 

K-power

31.10

13.51

36.16

19.82

-23.18

3

0.26

0.918

 

Piecewise

36.90

3.810

38.63

7.825

-23.44

3

0

0.954

 

Hockey stick

38.08

-

39.34

-

-25.92

3

-

-

Diphtheria

Linear

3.575

1.864

7.343

3.829

-13.14

2

6.51

0.941

 

K-power

31.29

18.64

35.78

24.22

-20.17

3

1.48

0.895

 

Piecewise

40.96

8.309

42.14

17.07

-21.65

3

0

0.951

 

Hockey stick

37.58

-

38.56

-

-22.27

3

-

-

HiB

Linear

2.107

1.148

4.327

2.357

-4.44

2

0

0.955

 

K-power

2.107

1.236

4.327

2.533

-4.44

3

2.00

0.818

 

Piecewise

2.075

0.724

4.261

1.487

-4.44

3

2.00

0.940

 

Hockey stick

13.52

-

15.66

-

-4.55

3

-

-