Page 135 Cite

Suggested Citation:"Appendix B Benchmark Concentration Calculations for Selected Chloroformates." National Academies of Sciences, Engineering, and Medicine. 2016. Acute Exposure Guideline Levels for Selected Airborne Chemicals: Volume 20. Washington, DC: The National Academies Press. doi: 10.17226/23634.

×

Appendix B

Benchmark Concentration Calculations for Selected Chloroformates

Benchmark Concentration Calculation for Methyl Chloroformate

The form of the probability function is:

P[response] = Background + (1-Background)*

CumNorm(Intercept+Slope*Log[Dose]),
where CumNorm(.) is the cumulative normal distribution function

Dependent variable = Mean

Independent variable = Dose

Slope parameter is not restricted

Total number of observations = 4

Total number of records with missing values = 0

Maximum number of iterations = 250

Relative Function Convergence has been set to: 1e-008

Parameter Convergence has been set to: 1e-008

User has chosen the log transformed model

Default Initial (and Specified) Parameter Values

Background = 0

Intercept = -20.4973

Slope = 5.16963

Asymptotic Correlation Matrix of Parameter Estimates

	Intercept
Intercept	1

***The model parameter(s) background has been estimated at a boundary point, or has been specified by the user, and do not appear in the correlation matrix.

Page 136 Cite

Suggested Citation:"Appendix B Benchmark Concentration Calculations for Selected Chloroformates." National Academies of Sciences, Engineering, and Medicine. 2016. Acute Exposure Guideline Levels for Selected Airborne Chemicals: Volume 20. Washington, DC: The National Academies Press. doi: 10.17226/23634.

×

Parameter Estimates

Variable	Estimate	Standard Error
Background	0	NA
Intercept	71.9357	0.449759
Slope	18	NA

NA: indicates that this parameter has hit a bound implied by some inequality constraint and thus has no standard error.

Analysis of Deviance Table

Model	Log (likelihood)	Deviance Test	DF	P-value
Full model	5.00402	–	–	–
Fitted model	5.00722	0.00639048	3	0.9999
Reduced model	27.5256	45.0431	3	<0.0001

AIC: 12.0144.

Goodness of Fit Scaled

Dose	Estimated Probability	Expected	Observed	Size	Residual
35.0000	0.0000	0.000	0	10	1.008e-007
45.0000	0.0003	0.003	0	10	0.0564
57.0000	0.7993	7.993	8	10	0.005272
73.0000	1.0000	10.000	10	10	0.0007765

Chi-square = 0.00; DF = 3; P-value = 1.0000.

Benchmark Dose Computation

Specified effect = 0.05

Risk Type = Extra risk

Confidence level = 0.95

BMD = 49.6524

BMDL = 42.4113

**FIGURE B-1** Prohibit model with 0.95 confidence level.

Page 137 Cite

Suggested Citation:"Appendix B Benchmark Concentration Calculations for Selected Chloroformates." National Academies of Sciences, Engineering, and Medicine. 2016. Acute Exposure Guideline Levels for Selected Airborne Chemicals: Volume 20. Washington, DC: The National Academies Press. doi: 10.17226/23634.

×

Benchmark Concentration Calculation for Allyl Chloroformate

The form of the probability function is:

P[response] = Background + (1-Background)

*CumNorm(Intercept+Slope*Log(Dose)),

where CumNorm(.) is the cumulative normal distribution function

Dependent variable = Mean

Independent variable = Dose

Slope parameter is not restricted

Total number of observations = 6

Total number of records with missing values = 0

Maximum number of iterations = 250

Relative Function Convergence has been set to: 1e-008

Parameter Convergence has been set to: 1e-008

User has chosen the log transformed model

Default Initial (and Specified) Parameter Values

Background = 0

Intercept = -7.2918

Slope = 1.72308

Asymptotic Correlation Matrix of Parameter Estimates

	Intercept	Slope
Intercept	1	-1
Slope	-1	1

***The model parameter(s) background has been estimated at a boundary point, or has been specified by the user, and do not appear in the correlation matrix.

Parameter Estimates

Variable	Estimate	Standard Error
Background	0	NA
Intercept	-10.3866	2.68182
Slope	2.48392	0.621724

NA: indicates that this parameter has hit a bound implied by some inequality constraint and thus has no standard error.

Analysis of Deviance Table

Model	Log (likelihood)	Deviance Test	DF	P-value
Full model	16.0896	–	–	–
Fitted model	17.3239	2.46858	4	0.6503
Reduced model	36.6519	41.1245	5	<0.0001

AIC: 38.6478.

Page 138 Cite

Suggested Citation:"Appendix B Benchmark Concentration Calculations for Selected Chloroformates." National Academies of Sciences, Engineering, and Medicine. 2016. Acute Exposure Guideline Levels for Selected Airborne Chemicals: Volume 20. Washington, DC: The National Academies Press. doi: 10.17226/23634.

×

Goodness of Fit Scaled

Dose	Estimated Probability	Expected	Observed	Size	Residual
33.7000	0.0495	0.495	0	10	0.7219
65.0000	0.4929	4.929	6	10	0.6774
77.7000	0.6648	6.648	7	10	0.236
134.5000	0.9632	9.632	9	10	1.06
175.7000	0.9929	9.929	10	10	0.2674
233.3000	0.9992	9.992	10	10	0.08938

Chi-square = 2.24; DF = 4; P-value = 0.6919.

Benchmark Dose Computation

Specified effect = 0.05

Risk Type = Extra risk

Confidence level = 0.95

BMD = 33.7621

BMDL = 21.098

**FIGURE B-2** Prohibit model with 0.95 confidence level.

Benchmark Concentration Calculation for Phenyl Chloroformate

The form of the probability function is:

P[response] = Background + (1-Background)

*CumNorm(Intercept+Slope*Log(Dose)),

where CumNorm(.) is the cumulative normal distribution function

Page 139 Cite

Suggested Citation:"Appendix B Benchmark Concentration Calculations for Selected Chloroformates." National Academies of Sciences, Engineering, and Medicine. 2016. Acute Exposure Guideline Levels for Selected Airborne Chemicals: Volume 20. Washington, DC: The National Academies Press. doi: 10.17226/23634.

×

Dependent variable = Mean

Independent variable = Dose

Slope parameter is not restricted

Total number of observations = 8

Total number of records with missing values = 0

Maximum number of iterations = 250

Relative Function Convergence has been set to: 1e-008

Parameter Convergence has been set to: 1e-008

User has chosen the log transformed model

Default Initial (and Specified) Parameter Values

Background = 0

Intercept = -2.32244

Slope = 0.759796

Asymptotic Correlation Matrix of Parameter Estimates

	Intercept	Slope
Intercept	1	0.98
Slope	–	1

***The model parameter(s) background has been estimated at a boundary point, or has been specified by the user, and do not appear in the correlation matrix.

Parameter Estimates

Variable	Estimate	Standard Error
Background	0	NA
Intercept	4.60327	1.20324
Slope	1.35407	0.307109

NA: indicates that this parameter has hit a bound implied by some inequality constraint and thus has no standard error.

Analysis of Deviance Table

Model	Log (likelihood)	Deviance Test	DF	P-value
Full model	17.6143	–	–	–
Fitted model	18.0291	0.829451	6	0.9913
Reduced model	47.9918	60.755	7	<0.0001

AIC: 40.0581.

Page 140 Cite

Suggested Citation:"Appendix B Benchmark Concentration Calculations for Selected Chloroformates." National Academies of Sciences, Engineering, and Medicine. 2016. Acute Exposure Guideline Levels for Selected Airborne Chemicals: Volume 20. Washington, DC: The National Academies Press. doi: 10.17226/23634.

×

Goodness of Fit Scaled

Dose	Estimated Probability	Expected	Observed	Size	Residual
1.7600	0.0001	0.001	0	10	0.02491
15.6000	0.1885	1.885	2	10	0.09264
44.5000	0.7040	7.040	7	10	0.02802
74.9000	0.8927	8.927	9	10	0.07446
97.0000	0.9442	9.442	9	10	0.6092
156.0000	0.9873	9.873	10	10	0.359
159.3000	0.9882	9.882	10	10	0.3459
311.0000	0.9992	9.992	10	10	0.08752

Chi-square = 0.64; DF = 6; P-value = 0.9956.

Benchmark Dose Computation

Specified effect = 0.05

Risk Type = Extra risk

Confidence level = 0.95

BMD = 8.88924

BMDL = 3.57025

**FIGURE B-3** Prohibit model with 0.95 confidence level.

Benchmark Concentration Calculation for 2-Ethylhexyl Chloroformate

The form of the probability function is:

P[response] = Background + (1-Background)

*CumNorm(Intercept+Slope*Log(Dose)),

where CumNorm(.) is the cumulative normal distribution function

Page 141 Cite

Suggested Citation:"Appendix B Benchmark Concentration Calculations for Selected Chloroformates." National Academies of Sciences, Engineering, and Medicine. 2016. Acute Exposure Guideline Levels for Selected Airborne Chemicals: Volume 20. Washington, DC: The National Academies Press. doi: 10.17226/23634.

×

Dependent variable = Mean

Independent variable = Dose

Slope parameter is not restricted

Total number of observations = 4

Total number of records with missing values = 0

Maximum number of iterations = 250

Relative Function Convergence has been set to: 1e-008

Parameter Convergence has been set to: 1e-008

User has chosen the log transformed model

Default Initial (and Specified) Parameter Values

Background = 0

Intercept = -15.0226

Slope = 4.37693

Asymptotic Correlation Matrix of Parameter Estimates

	Intercept	Slope
Intercept	1	-1
Slope	-1	1

***The model parameter(s) background has been estimated at a boundary point, or has been specified by the user, and do not appear in the correlation matrix.

NA: This parameter’s variance has been estimated at zero.

Parameter Estimates

Variable	Estimate	Standard Error
Background	0	NA
Intercept	18.7737	5.12639
Slope	5.52218	1.51755

NA: indicates that this parameter has hit a bound implied by some inequality constraint and thus has no standard error.

Analysis of Deviance Table

Model	Log (likelihood)	Deviance Test	DF	P-value
Full model	12.8388	–	–	–
Fitted model	14.2231	2.76871	2	0.2505
Reduced model	27.6759	29.6742	3	<0.0001

AIC: 32.4462.

Goodness of Fit Scaled

Dose	Estimated Probability	Expected	Observed	Size	Residual
22.8000	0.0659	0.659	0	10	0.8398
26.6000	0.2559	2.559	4	10	1.044
34.3000	0.7728	7.728	7	10	-0.5491
46.9000	0.9934	9.934	10	10	0.2587

Chi-square = 2.16; DF = 2; P-value = 0.3390.

Page 142 Cite

Suggested Citation:"Appendix B Benchmark Concentration Calculations for Selected Chloroformates." National Academies of Sciences, Engineering, and Medicine. 2016. Acute Exposure Guideline Levels for Selected Airborne Chemicals: Volume 20. Washington, DC: The National Academies Press. doi: 10.17226/23634.

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