# Calibrating Self-Reported Measures of Maternal Smoking in Pregnancy via Bioassays Using a Monte Carlo Approach

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## Abstract

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## 1. Introduction

## 2. Methods

_{w_i}

_{,}where (i = 1, ... ,45), from a normal distribution with mean 8.78 hours and standard deviation 1.67 hours. These data were taken from a study of nicotine and cotinine metabolism in pregnant women [20]. The trimester effect is assumed to modify each woman’s half-life parameter by a different amount in each trimester, but those amounts are assumed to be the same for all women. Due to lack of strong theory about shape of metabolic trends over pregnancy, we assume that these deviations are also normally distributed with a mean of zero, and the standard deviation equal to the standard deviation of the women effects. We denote the trimester effect by h

_{t_j}where j = 1, 2, 3, and then the cotinine half-life for a woman i in trimester j is obtained by adding the two effects: h

_{w_ij}= h

_{w_i}+ h

_{t_j}. We repeat this procedure 200 times, yielding 200 woman-trimester specific cotinine half-lives.

_{w_i}by forming a product of two other normal variables: the blood-urine conversion factor generated from a Normal distribution with a mean of 8 and standard deviation of 0.5 (N(8,0.5)), and the serum-cotinine-per-cigarette from a Normal distribution with mean 12.5 and standard deviation of 2 (N(12.5,2)). These Normal distributions were chosen again based on expert advice, and they reflect the experimental ranges of the ratio of cotinine in urine to cotinine in blood, of and the cotinine per cigarette in blood, respectively. We assume again that trimester effects are normally distributed with mean zero and standard deviation equal to the standard deviation of woman-specific effects. The equality of standard deviation is somewhat arbitrary, but reflecting the belief that deviations across time are on the same scale as deviations from woman to woman. Again, we generate the cotinine per cigarette amount for a woman i in trimester j by adding her individual and trimester effect, like we did for half-lives.

## 3. Results: Classification and Calibration of Self-Report

#### 3.1. Sensitivity Analysis

## 4. Discussion

## Acknowledgments

## Appendix: Calculations of Uncertainty in Cotinine-Nicotine Cigarette Relationship

which is equivalent to:Nicotine intake per cigarette = [Cotinine concentration] x [Cotinine clearance] / [f]

where:Blood cotinine concentration per cigarette = (Nicotine per cigarette) / (Cotinine clearance),

- Nicotine per cigarette is distributed normally with mean 1.2 mg/cig and range of 0.5 to 2.
- Cotinine clearance per kg of body weight has mean of 1.46 ranging from 0.9 to 2.
- f is a scalar with mean 0.78 and ranging from 0.69 to 0.87.

## References

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**Table 1.**Classification of women based on the individual MC corrections. For each category, the first column (“n”) is the number of women in that classification group. The second column (“mean”) is the mean of the differences between the weighted self-report and the number of cigarettes from cotinine. The third column (“sd”) is the standard deviation of these differences.

Scen. | Trim. | Category | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

over reporting | accurate reporting | under reporting | extreme under reporting | ||||||||||

freq | mean | sd | n | mean | sd | n | mean | sd | n | mean | sd | ||

1 | 1 | - | - | - | 13 | −1.39 | 3.24 | 12 | −7.92 | 5.31 | 13 | −8.81 | 6.18 |

1 | 2 | 2 | 2.55 | 1.98 | 18 | −1.06 | 2.22 | 13 | −6.62 | 3.37 | 12 | −8.42 | 4.34 |

1 | 3 | - | - | - | 15 | −0.99 | 1.67 | 11 | −5.85 | 3.16 | 15 | −8.27 | 5.81 |

2 | 1 | - | - | - | 9 | −2.28 | 1.76 | 14 | −7.51 | 5.23 | 15 | −10.15 | 6.34 |

2 | 2 | - | - | - | 14 | −1.84 | 2.71 | 17 | −6.80 | 3.70 | 14 | −9.52 | 4.83 |

2 | 3 | - | - | - | 11 | −2.13 | 1.79 | 13 | −6.47 | 3.77 | 17 | −8.69 | 5.96 |

3 | 1 | - | - | - | 10 | −1.90 | 1.78 | 16 | −6.48 | 4.71 | 12 | −11.24 | 6.44 |

3 | 2 | 1 | 3.26 | - | 17 | −1.95 | 2.15 | 15 | −7.59 | 3.55 | 12 | −8.88 | 4.76 |

3 | 3 | - | - | - | 13 | −1.21 | 1.30 | 13 | −7.13 | 3.80 | 15 | −8.04 | 5.82 |

**Table 2.**Classification of women based on the individual MC corrections, under scenario 3. For each trimester, the first column (“Mean self-report”) shows the self-reported trimester daily average number of cigarettes. The second column (“Cot”) shows the cotinine level from the urine test in the given trimester. The third column (“Class”) shows the classification of the woman: O for over-reporter, A for accurate reporter, U for underreporter, and E for extreme under-reporter. The fourth column (“Corrected self-rep”) shows the corrected average trimester self-report. No adjustment could be calculated for women with missing cotinine measurements.

ID | Trimester 1 | Trimester 2 | Trimester 3 | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Mean self-rep | Cot (ng/mL) | Class | Corrected self-rep | Mean self-rep | Cot (ng/mL) | Class | Corrected self-rep | Mean self-rep | Cot (ng/mL) | Class | Corrected self-rep | |

1 | 10 | 509 | A | 13.29 | 8.67 | 543 | A | 11.38 | 10 | 1280 | E | 20.77 |

2 | 9.67 | 254 | A | 11.19 | 8 | 175 | A | 9.20 | 4 | 170 | A | 5.04 |

4 | 2 | 547 | E | 6.25 | 1 | 342 | E | 4.50 | 3 | 199 | U | 5.01 |

8 | 18.67 | 1130 | U | 26.97 | 20 | 1240 | U | 30.51 | 19 | 506 | A | 20.58 |

10 | 9.33 | 366 | A | 12.34 | 4 | 507 | U | 7.43 | 7 | 1230 | E | 19.01 |

11 | 13 | 1270 | U | 22.69 | 10 | 1840 | E | 26.76 | 12 | 2010 | E | 29.24 |

12 | 20 | 1670 | U | 31.61 | 20 | 1340 | U | 29.74 | 20 | |||

13 | 0.09 | 61.5 | E | 0.54 | 0 | 0 | A | 0.00 | 0.5 | 57.9 | E | 1.19 |

19 | 13.33 | 1680 | E | 26.61 | 11.67 | 655 | A | 15.76 | 10 | 1020 | U | 16.99 |

20 | 13.67 | 1840 | E | 28.11 | 15 | 1570 | U | 27.73 | 14 | 776 | U | 19.90 |

22 | 8.67 | 769 | U | 13.78 | 13 | 784 | U | 18.21 | 7.5 | 550 | A | 7.79 |

26 | 10 | 1110 | U | 18.93 | 13.33 | 1260 | U | 23.65 | 15.5 | 997 | U | 21.36 |

31 | 0 | 33 | U | 0.38 | 0 | 10.7 | A | 0.11 | 0 | 61.6 | U | 0.69 |

35 | 6 | 1480 | E | 17.54 | 5 | 793 | E | 12.77 | 4.5 | 1130 | E | 13.28 |

38 | 0 | 596 | E | 6.05 | 0 | 632 | E | 6.31 | 0 | 319 | E | 3.23 |

41 | 20 | 266 | A | 18.75 | 23.33 | 704 | A | 26.63 | 20 | 490 | A | 22.44 |

47 | 10 | 1280 | E | 19.22 | 10 | 1100 | U | 17.15 | 10 | 991 | U | 16.42 |

48 | 9 | 1020 | E | 17.89 | 12.33 | 64.4 | O | 8.79 | 9 | 619 | U | 13.56 |

50 | 5 | 561 | U | 9.05 | 5 | 1480 | E | 18.42 | 8.5 | 714 | U | 13.72 |

53 | 13 | 587 | A | 15.94 | 16.67 | 692 | A | 21.08 | 19 | 1740 | U | 36.15 |

55 | 0.67 | 34.5 | U | 1.10 | 0.67 | 30.3 | A | 0.69 | 1.5 | 69 | A | 1.96 |

60 | 10 | 10 | 335 | A | 10.50 | 15 | 596 | A | 16.74 | |||

67 | 16.67 | 570 | A | 18.18 | 26.33 | 570 | A | 29.98 | 12.5 | 1020 | U | 21.15 |

68 | 8.67 | 2.67 | 565 | E | 6.76 | 0 | 1490 | E | 20.42 | |||

70 | 0 | 6.67 | 789 | U | 12.23 | 12.5 | 1020 | U | 21.04 | |||

74 | 8 | 322 | A | 10.46 | 8 | 618 | U | 12.97 | 8 | 420 | A | 7.63 |

75 | 10 | 10 | 870 | U | 16.88 | 10 | 1200 | E | 19.06 | |||

81 | 13.33 | 362 | A | 15.49 | 13 | 534 | A | 16.35 | 15 | 552 | A | 17.80 |

82 | 20 | 1430 | U | 30.81 | 12.33 | 388 | A | 14.32 | 8 | 388 | A | 10.03 |

84 | 10 | 5 | 31.8 | A | 5.38 | 0.5 | 129 | E | 1.42 | |||

87 | 12 | 865 | U | 18.52 | 10 | 871 | U | 17.94 | 5 | 1010 | E | 16.74 |

88 | 3 | 582 | U | 5.88 | 10 | 671 | U | 14.44 | 10 | 981 | U | 17.72 |

93 | 4 | 4 | 1180 | E | 14.28 | 4 | ||||||

95 | 20 | 10 | 398 | A | 12.76 | 4 | 379 | E | 7.75 | |||

97 | 7.33 | 506 | U | 11.45 | 10 | 314 | A | 11.22 | 12.5 | 382 | A | 13.01 |

99 | 7.33 | 863 | U | 14.03 | 1.33 | 0 | A | 1.33 | 0 | 0 | A | 0.00 |

100 | 33.33 | 1760 | U | 48.64 | 11 | 829 | U | 17.99 | 0 | |||

102 | 7.33 | 1770 | E | 23.86 | 9.33 | 1420 | E | 25.27 | 16 | |||

105 | 4 | 490 | E | 8.45 | 2.83 | 138 | U | 3.95 | 2 | 294 | E | 4.37 |

106 | 10 | 315 | A | 11.28 | 10 | 728 | U | 14.56 | 10 | 910 | U | 16.78 |

108 | 3.67 | 345 | U | 6.31 | 4.33 | 723 | E | 10.49 | 6 | 342 | A | 9.16 |

109 | 7 | 473 | U | 11.66 | 0.33 | 776 | E | 7.52 | 0 | 289 | E | 2.47 |

114 | 0 | 11.3 | A | 0.12 | 0 | 0 | A | 0.00 | 0 | 0 | A | 0.00 |

115 | 0 | 826 | E | 5.74 | 0 | 331 | E | 4.20 | 0 | 367 | E | 3.02 |

116 | 8 | 1970 | E | 22.07 | 1.83 | 860 | E | 8.90 | 10 | 1100 | E | 19.71 |

**Table 3.**Average numbers of adjusted cigarettes in each category over trimesters using group-correction method.

Method | Trimester | Category | |||
---|---|---|---|---|---|

over reporter | accurate reporter | under reporter | extreme under reporter | ||

MC | 1 | - | 1.70 | 6.38 | 9.07 |

MC | 2 | −3.54 | 1.75 | 6.77 | 8.56 |

MC | 3 | - | 1.21 | 6.65 | 7.75 |

Det | 1 | 1.36 | 5.69 | 8.32 | |

Det | 2 | −3.67 | 1.49 | 6.07 | 7.84 |

Det | 3 | 0.73 | 6.06 | 7.09 |

**Table 4.**The ratio is the women’s cotinine levels divided by their weighted number of self-reported cigarettes. This ratio shows how much of urinary cotinine a cigarette produces according to women’s self-reports. This table shows the means and the standard deviation for each classification in each trimester.

Category | Trimester 1 | Trimester 2 | Trimester 3 | |||
---|---|---|---|---|---|---|

Mean ratio | SD ratio | Mean ratio | SD ratio | Mean ratio | SD ratio | |

Over reporter | - | - | 16.24 | - | - | - |

Accurate reporter | 309.79 | 251.84 | 278.01 | 153.03 | 207.21 | 152.77 |

Under reporter | 1005.53 | 2486.65 | 577.44 | 579.49 | 895.17 | 1002.75 |

Extreme under reporter | 7829.90 | 21275.18 | 4740.71 | 10678.09 | 2169.90 | 3019.95 |

Total | 2883.77 | 11869.41 | 1434.85 | 5272.85 | 1085.01 | 1941.18 |

**Table 5.**The average numbers of adjusted cigarettes in each category over trimesters, under different values of cotinine half-life.

Trimester | Category | ||||
---|---|---|---|---|---|

Half-life mean | over reporter | accurate reporter | under reporter | extreme under reporter | |

1 | 5 hours | - | 1.65 | 6.16 | 9.14 |

2 | 5 hours | - | 1.41 | 6.81 | 8.60 |

3 | 5 hours | - | 1.10 | 6.88 | 7.92 |

1 | 20 hours | - | 1.76 | 6.87 | 8.75 |

2 | 20 hours | −3.47 | 1.84 | 6.46 | 8.88 |

3 | 20 hours | - | 1.41 | 5.79 | 8.42 |

**Table 6.**The number of women classified into each group in each trimester, using different values of urinary cotinine a cigarette produces. Rows 1–3 use 100 ng/mL, rows 4–6 use 150 ng/mL, and rows 7–9 use 300 ng/mL.

Cotinine/Cigarette (ng/mL) | Trimester | Over reporters | Accurate reporters | Under reporters | Extreme under reporters |
---|---|---|---|---|---|

100 | 1 | 0 | 10 | 16 | 12 |

100 | 2 | 1 | 17 | 15 | 12 |

100 | 3 | 0 | 13 | 13 | 15 |

150 | 1 | 0 | 21 | 10 | 7 |

150 | 2 | 1 | 25 | 8 | 11 |

150 | 3 | 2 | 15 | 15 | 9 |

300 | 1 | 1 | 30 | 5 | 2 |

300 | 2 | 1 | 35 | 5 | 4 |

300 | 3 | 2 | 30 | 5 | 4 |

© 2009 by the authors; licensee Molecular Diversity Preservation International, Basel, Switzerland. This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Dukic, V.M.; Niessner, M.; Pickett, K.E.; Benowitz, N.L.; Wakschlag, L.S.
Calibrating Self-Reported Measures of Maternal Smoking in Pregnancy via Bioassays Using a Monte Carlo Approach. *Int. J. Environ. Res. Public Health* **2009**, *6*, 1744-1759.
https://doi.org/10.3390/ijerph6061744

**AMA Style**

Dukic VM, Niessner M, Pickett KE, Benowitz NL, Wakschlag LS.
Calibrating Self-Reported Measures of Maternal Smoking in Pregnancy via Bioassays Using a Monte Carlo Approach. *International Journal of Environmental Research and Public Health*. 2009; 6(6):1744-1759.
https://doi.org/10.3390/ijerph6061744

**Chicago/Turabian Style**

Dukic, Vanja M., Marina Niessner, Kate E. Pickett, Neal L. Benowitz, and Lauren S. Wakschlag.
2009. "Calibrating Self-Reported Measures of Maternal Smoking in Pregnancy via Bioassays Using a Monte Carlo Approach" *International Journal of Environmental Research and Public Health* 6, no. 6: 1744-1759.
https://doi.org/10.3390/ijerph6061744