TABLE 6.
Classification of Uncertain Parameters in the Dosimetry System
| Time period | Parameters being estimated |
Uncertain component | Type of uncertainty |
Description of uncertainty |
Uncertainty distribution parameters |
|---|---|---|---|---|---|
| Badge dose estimation | |||||
| Pre-1940 | Population badge dose GM/GSD estimates. | Realization-specific random bias factor. | Shared† assignment error*. | Beta (2,2) scaled to range from 0.5–1.5. | GM: mean = 72; σ = 16; GSD: mean = 2.85. |
| 1940–1949 | Population badge dose GM/GSD estimates. | Realization specific random weights for literature reports. | Shared assignment error. | Random sample of weights chosen using a Dirichlet distribution. | GM: mean = 18; σ = 4.3; GSD: mean = 4.3; σ = 0.10. |
| Realization-specific random bias factor. | Shared assignment error. | Beta (2,2) scaled to range from 1 to 5. | |||
| 1950–1955 | Population badge dose GM/GSD estimates. | Realization specific random weights for literature reports. | Shared assignment error. | Random sample of weights chosen using a Dirichlet distribution. | GM: mean = 6.1; σ = 0.41; GSD: mean = 2.3; σ = 0.07. |
| Realization-specific random bias factor. | Shared assignment error. | Beta (2,2) scaled to range from 0.5–1.5. | |||
| 1956–1997 | Population badge dose GM/GSD estimates. | Realization-specific weight for interpolation between GM limits. | Shared assignment error. | Uniform (0, 1). | Interpolation weight: mean = 0.5; σ = 0.29. |
| Realization-specific weight for random bias factor (dependent on 1950–1955 bias factor, interpolation weight and year). | Shared assignment error. | Linear interpolation of bias factor between 1950–1955 value in 1955 and 1 for the 1983–1997 period. | Annual value determined by year, random bias factor and random interpolation weight. | ||
| All | Individual annual badge dose GM/GSD estimates. | Individual exposure-score-category-based adjustment of population badge dose GM and GSD. | Unshared† assignment error. | GM scaled by individual, period specific exposure score scaling factor, GSD scaled to preserve 99th percentile standard population distribution. | If has exposure score (ES), GM adjustment mean = 0.96; σ = 0.51; GSD adjustment mean = 0.93; σ = 0.06; if no ES, then GM and GSD adjustment factors are both 1. |
| All | Film badge dose generation (given individualized badge dose GM and GSD) with no film badge reading. | Random dose from individualized lognormal population distribution. | Unshared assignment error. | Multivariate lognormal (GMiry, GSDiry) and autoregressive correlation structure. | ** |
| Adjustment for between-year dose correlations. | Unshared assignment error. | ||||
| All | Film badge dose generation (given individualized badge dose GM and GSD) with film badge reading above MDL. | Regression calibration adjustment using individualized population badge dose GM/GSD estimates assuming 20% measurement error. | Unshared classical measurement error. | Calibration assumes multiplicative lognormal measurement error and an individualized lognormal population dose distribution with the GM and GSD individualized for person and year within realization. | Measurement error with GM = 1, GSD = 1.2; population GM/GSD by year within realization. |
| Random badge dose with calibration-adjusted badge dose as GM and a GSD representing 20% measurement error. | Unshared assignment error. | Lognormal measurement error. | Measurement error: GM = 1; GSD = 1.2 with individualized annual population GMiry; and GSDiry. | ||
| All | Film badge dose generation (given individualized badge dose GM and GSD) with film badge reading below MDL. | Random assignment as inside or outside apron reading | Unshared assignment error. | Location is treated as binomial with year-dependent probabilities determined from questionnaire data. | ** |
| Inside apron (generate dose from individualized unconditional population distribution) | |||||
| Outside apron (generate dose from individualized population distribution conditional on dose being less than the MDL). | |||||
| Organ dose estimation | |||||
| Pre-1940 | Apron usage probability. | Assumption that apron was never worn. | Shared, assignment error. | Assume never wore apron. | None. |
| 1940–1979 | Apron usage probability. | Parameters of the probability distribution for the year of transition from use of “literature-based” apron usage to “questionnaire-based” usage. | Shared, assignment error. | Realization-specific beta distribution for year of transition from literature- to questionnaire-based usage probability distribution with parameters chosen as independent uniform (8, 16) variables. | Mean transition year 1959, standard deviation 4.8 years. |
| Individual literature-based to questionnaire-based apron usage PDF transition year. | Unshared assignment error. | Sampled from beta density defined above. | |||
| Individual apron-usage probability (from individual work-history and period specific apron usage PDFs). | Unshared assignment error. | Sampled from literature- or questionnaire-based empirical work-history-dependent apron-usage densities. | ** | ||
| 1980–1997 | Apron usage probability. | Individual apron usage probability (from questionnaire-based individual work-history and period specific apron usage PDFs). | Unshared assignment error. | Sampled from questionnaire-based empirical work-history-dependent apron-usage densities. | ** |
| All | Apron thickness (0.25 or 0.5 mm Pb equivalent). | Period-specific probability of 0.5mm Pb equivalent apron. | Shared assignment error. | 0.5 mm Pb apron probability = 0.5 before 1970 and = 0.9 after 1969. | Before 1970: mean = 0.375 mm; σ = 0.125; 1970–1997: mean = 0.475 mm; σ = 0.076 mm. |
| Individual annual apron thickness. | Unshared assignment error. | Binomial using period-specific probabilities with transitions allowed only once every j years where j is the period-specific average job length. | ** | ||
| All | Hp(10) to air kerma ratio (i.e., Hp(10)/Ka). | Period-specific ratio GM for realization. | Shared assignment error. | Select individual kV (70, 80 or 90) with equal probability. Assign, period- and kV-dependent GM. | 1916–1949: mean = 0.83; σ = 0.13; 1950–1954: mean = 1.14; σ = 0.17; 1955–1968: mean = 1.28; σ = 0.18; 1968+ mean = 1.34; σ = 0.19. |
| Individual ratio. | Individual assignment error. | Lognormal with selected GM and GSD=1.15 with range restricted to 0.135 to 7.39. | |||
| All | Tissue dose to air kerma ratio (i.e., DT/Ka), without apron shielding and with shielding by 0.5 or 0.25 mm thick Pb aprons. | Period-specific ratio GMs for realization. | Shared assignment error. | Assign organ-, period- and kV-dependent GM. | ** |
| Individual ratios. | Unshared assignment error. | Lognormal with selected GM and GSD = 1.15 with range restricted to 0.75–1.32. | |||
| All | BMI-adjusted marrow dose: tissue dose to air kerma ratio (i.e., DT/Ka). | Period-specific, body mass index (BMI)-group slope and intercept for GM. | Shared assignment error. | Use period- and kV-dependent functions of BMI to compute GM. | ** |
| Individual ratio. | Unshared assignment error. | Lognormal with selected GM and GSD = 1.15 with range restricted to 0.75–1.32. | |||
| All | Organ dose realization. | Individual organ doses computed as apron-usage probability-weighted average of organ dose with and without apron usage. | Unshared assignment error. | Apron-usage probability-weighted average of organ dose with and without apron usage. | ** |
†
“Shared errors” refer to uncertain values for which the same values are used for all cohort member doses in a specific realization of cohort member doses. Unshared errors refer to uncertain values that vary independently from person-to-person within a realization of cohort doses.
*
“Assignment error” refers to errors that arise when a quantity of interest is assigned a representative value, the expected value of which is believed to be equal to the true value of the quantity. This is a form of Berkson error.
**
Complex function of year and individual parameters that is not amenable to a useful, simple summary description.