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Chemical Mixtures and Combined Chemical and Nonchemical Stressors pp 291–306Cite as

Comparing Predicted Additivity Models to Observed Mixture Data

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Abstract

Dose-response relationships are generally assumed to be nonlinear. Standard multiple regression models may approximate the relationship in a narrow dose range but may not adequately approximate the relationship over a wider dose range – which may have a sigmoidal shape. Further, when the number of components in a mixture is large, the required experimental design to test for interactions becomes infeasible using factorial designs. In contrast, tests for departure from additivity may be based on comparing additivity-predicted models to those of mixtures data along fixed-ratio rays of the components. As such, tests for departure from additivity in mixtures should accommodate both nonlinear relationships and efficient experimental designs. In this chapter, we illustrate the strategy using three different basic assumptions about the underlying response surface from single chemical data.

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Author information

Authors and Affiliations

  1. Icahn School of Medicine at Mount Sinai, New York, NY, USA

    Chris Gennings

Authors
  1. Chris Gennings
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Corresponding author

Correspondence to Chris Gennings .

Editor information

Editors and Affiliations

  1. National Toxicology Program, National Institute of Environmental, Health Sciences, Research Triangle Park, North Carolina, USA

    Cynthia V. Rider

  2. National Health and Environmental Effects Research Laboratory, Office of Research and Development, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina, USA

    Jane Ellen Simmons

Appendices

Appendix

Extracted data from Fig. 3 in Gennings et al. (2004)

Chemical

CONC

FoldIND

Chemical

CONC

FoldIND

Chemical

CONC

FoldIND

MXC

0

0.9

b-HCH

0

0.6

BPA

0

0.6

MXC

0

1

b-HCH

0

1.1

BPA

0

1

MXC

0

1.2

b-HCH

0

1.4

BPA

0

1.4

MXC

1

0.8

b-HCH

1

0.8

BPA

0.008

1.4

MXC

1

1

b-HCH

1

0.9

BPA

0.008

1

MXC

2

0.9

b-HCH

1

1

BPA

0.008

0.08

MXC

2

1.6

b-HCH

2

1

BPA

0.01

3.2

MXC

2

1.6

b-HCH

2

1.3

BPA

0.01

2.4

MXC

4

2

b-HCH

2

2.3

BPA

0.01

2.2

MXC

4

3

b-HCH

4

1.8

BPA

0.02

3

MXC

4

4.2

b-HCH

4

3

BPA

0.02

1.4

MXC

8

3

b-HCH

4

4.2

BPA

0.02

1.4

MXC

8

3.2

b-HCH

8

2.4

BPA

0.04

1.8

MXC

8

3.5

b-HCH

8

3.4

BPA

0.04

1.2

MXC

10

3.8

b-HCH

8

4.2

BPA

0.04

1

MXC

10

6.6

b-HCH

10

2.4

BPA

0.08

1.1

MXC

10

6.8

b-HCH

10

3

BPA

0.08

1.1

DPN

0

0.6

b-HCH

10

4.3

BPA

0.08

1

DPN

0

1

OCT

0

0.6

BPA

0.1

2.5

DPN

0

1.4

OCT

0

1

BPA

0.1

1.5

DPN

0.01

0.6

OCT

0

1.4

BPA

0.1

1.5

DPN

0.01

1

OCT

0.01

0.8

BPA

0.5

2

DPN

0.01

1

OCT

0.01

0.9

BPA

0.5

2.1

DPN

0.02

1

OCT

0.01

1.2

BPA

0.5

3.2

DPN

0.02

1.4

OCT

0.02

1

BPA

1

4.4

DPN

0.02

1.4

OCT

0.02

1.2

BPA

1

8

DPN

0.04

2.6

OCT

0.02

1.8

BPA

1

10

DPN

0.04

4

OCT

0.04

0.9

MIX

0

0.06

DPN

0.04

4.4

OCT

0.04

1

MIX

0

0.09

DPN

0.08

4

OCT

0.04

3.6

MIX

0

0.09

DPN

0.08

4.4

OCT

0.08

1

MIX

0

1

DPN

0.08

4.4

OCT

0.08

1.2

MIX

0

1.1

DPN

0.1

5.5

OCT

0.08

1.2

MIX

0

1.4

DPN

0.1

6

OCT

0.1

1.6

MIX

0.2

0.8

DPN

0.1

11.5

OCT

0.1

2.4

MIX

0.2

0.8

DDT

0

0.8

OCT

0.1

2.8

MIX

0.2

1

DDT

0

1

OCT

0.2

3.4

MIX

1

1

DDT

0

1.2

OCT

0.2

3.4

MIX

1

1.1

DDT

1

5

OCT

0.2

4.8

MIX

1

1.5

DDT

1

6.8

OCT

0.4

4

MIX

2

1

DDT

1

9

OCT

0.4

4.2

MIX

2

1.4

DDT

2

4.8

OCT

0.4

6.8

MIX

2

1.8

DDT

2

7

OCT

0.8

3.8

MIX

3

2

DDT

2

7

OCT

0.8

6

MIX

3

2.4

DDT

4

4.5

OCT

0.8

6.2

MIX

3

2.8

DDT

4

6.5

OCT

1

5.5

MIX

4

3.2

DDT

4

6.9

OCT

1

6

MIX

4

4.8

DDT

8

11

OCT

1

7

MIX

4

6

DDT

8

11.2

   

MIX

8

5.8

DDT

8

11.2

   

MIX

8

6.2

DDT

10

8.2

   

MIX

8

9.5

DDT

10

9

      

DDT

10

15.5

      

SAS Code for Example Data

figure a
figure b
figure c

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Gennings, C. (2018). Comparing Predicted Additivity Models to Observed Mixture Data. In: Rider, C., Simmons, J. (eds) Chemical Mixtures and Combined Chemical and Nonchemical Stressors. Springer, Cham. https://doi.org/10.1007/978-3-319-56234-6_11

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