ORAU Team

Dose Reconstruction Project for NIOSH

Technical Information Bulletin: Individual Dose Adjustment 

Procedure for Y-12 Dose Reconstruction

Document Number:

ORAUT-OTIB-0013

Effective Date: 09/09/2004

Revision No.: 00

Controlled Copy No.: ______

Page 1 of 9

Subject Experts: E. L. Frome and P. G. Groer

Approval: Signature on File Date: 09/03/2004

Judson L. Kenoyer, Task 3 Manager

Concurrence: Signature on File Date: 09/02/2004

Richard E. Toohey, Project Director

Approval: Signature on File Date: 09/09/2004

James W. Neton, Associate Director for Science

Supersedes:

None
Effective Date: 09/09/2004 Revision No.: 00 Document No.: ORAUT-OTIB-0013 Page 2 of 9

RECORD OF ISSUE/REVISIONS

ISSUE 

AUTHORIZATION 

DATE

EFFECTIVE 

DATE

REV. 

NO. DESCRIPTION

Draft 05/26/2004 00-A New technical information bulletin which 

describes an individual dose adjustment 

procedure that can be used as part of the dose 

reconstruction for certain workers at the Oak 

Ridge Y-12 Plant. Initiated by Judson L. Kenoyer.

Draft 08/30/2004 00-B Incorporates internal review and NIOSH 

comments. Initiated by Judson L. Kenoyer.

09/09/2004 09/09/2004 00 First approved issue. Initiated by Judson L. 

Kenoyer.
Effective Date: 09/09/2004 Revision No.: 00 Document No.: ORAUT-OTIB-0013 Page 3 of 9

1.0

This document describes an individual dose adjustment procedure that can be used as part of the 

dose reconstruction for certain workers at the Oak Ridge Y-12 Plant. It provides a derivation of the 

"scaling procedure", tables required for the calculation, and an example. The method can be used for 

workers who were not monitored prior to 1961 who have at least five quarters of monitoring data 

during the period from 1961 through 1965. For a detailed explanation of how to use this procedure 

see Kerr and Smith (2004).

INTRODUCTION

2.0

Kerr (2003), Watkins et al. (2004), and Watkins et al. (1993) provide a detailed description of the film 

badge dosimetry program at the Oak Ridge Y-12 facility. Prior to 1961 only workers with the highest 

potential for external radiation exposure were required to wear personnel dosimeters. A recent review 

of all film badge monitoring data from Y-12 workers used data available at the Center for 

Epidemiological Research (CER) at Oak Ridge Associated Universities (ORAU; Watkins et al. 2004). 

This review determined that the population dose for each quarter can be described by a lognormal 

distribution. The "missed dose" in each quarter of employment for a worker who was not monitored is 

based on the lognormal population distribution. This is consistent with procedures described in 

NIOSH (2002, Sections 1.1.4 and 1.6).

BACKGROUND

The probability density function for the lognormal distribution (Johnson, Kota, and Balakrishnan 1994) 

is

p(d;μ,σ) = exp[-

1

2

(log d – μ)2/σ2] ( 2π σd)

-1 , (1)

where d is film badge dose and μ and σ are lognormal parameters. For a review of the lognormal 

distribution with alternative parameterization and its use in risk analysis see Strom and Stansbury 

(2000). Table 1 at the end of this document contains the lognormal parameters for each quarter from 

1947 through 1965. These values were obtained based on assumptions described in Watkins et al. 

(2004) using statistical methods described in Frome and Watkins (2004). Starting in the fourth 

quarter of 1956 the values of σ in column 5 of Table 1 are slightly larger than the corresponding 

values in column 4 of Table 5 in Watkins et al.(2004). This difference is the result of an unnecessary 

bias adjustment that was applied to Table 1---see Frome and Watkins (2004) for details. The values 

of σ in Table 1 are always larger by about 0.1 percent and therefore claimant favorable. In the 

scaling procedure, these parameters are considered as known values because they are based on

population data and their relative uncertainty will have little material effect on the individual quarterly 

dose distribution required for dose reconstruction.

3.0

If a Y-12 worker was employed for at least five quarters from 1961 to 1965, that individual’s 

monitoring data can be used to "adjust" the dose distributions for unmonitored quarters from 1951 

through 1960. The method is based on the assumption that the individual’s potential for exposure 

during the 1950s is similar to that from 1961 to 1965, and that the individual’s doses differ from the 

population dose by a constant factor. Suppose that dt is the recorded dose during quarter t and μt and 

σt are the known lognormal parameter values for that same quarter from the first quarter of 1961 to 

the fourth quarter of 1965 (see Table 1, columns 4 and 5).

SCALING PROCEDURE BASED ON MAXIMUM LIKELIHOOD METHOD
Effective Date: 09/09/2004 Revision No.: 00 Document No.: ORAUT-OTIB-0013 Page 4 of 9

Then yt = log(dt) follows the normal distribution with mean μt + φ, and standard deviation σt , where φ 

represents the average relative difference (on the log scale) of the individual’s doses from the 

population values. The likelihood function for φ is

L(φ|d,μ,σ) = ∏

t

exp[-

2

1 {logdt – (μt + φ)}2

/σt

2

] ( 2π σtdt)

-1

, (2)

where t = t1,. . ., tn are quarters (see column 1 of Table 2 from 1961 through 1965 during which the 

worker was employed. The maximum likelihood estimate ∧

φ is the value of φ that maximizes equation 

(2) or equivalently the log-likelihood 

L(φ|d,μ,σ) = -

2

1 Σt wt(vt-φ)2 + constant. (3)

In equation (3), wt = 1/σt

2 , and vt = yt-μt . The likelihood equation is 

∂L/∂φ = Σt wt(vt-φ) = 0 ,

and the ML estimate of φ is ∧

φ = Σt wtvt/Σt wt . The variance of φ is [-∂2

L/∂φ2]

-1 = [Σt wt]-1

. If for any 

quarter dt = 0 (indicating a non-detect), then replace yt with o yt , the conditional expectation of y given it 

is less than the log (LOD), where LOD is the limit of detection. To obtain o yt , first calculate zt = 

(log(LOD) - μt) / σt and then o yt = μt - [n(zt)/N(zt)] σt , where n(z) is the standard normal density and 

N(z) is the standard normal cumulative distribution function (Johnson, Kota, and Balakrishnan 1994, 

Section 10.1). Table 2 lists the values of μ, σ, w, o y (based on a LOD of 30 mrem). 

Example

Consider a worker with recorded dose dt for each quarter from 1961 through 1965 as listed in column 

8 of Table 2. The calculated values of yt and vt are in columns 9 and 10 of Table 2. Then 

∧

φ = Σt wtvt/Σt wt = 0.46976 and

var( ∧

φ ) = 1/Σt wt = 0.03661 .

Note that the values in columns 4-7 of Table 2 are the same for each worker, whereas the values in 

columns 8, 9, and 10 will be determined by the individual recorded doses for each quarter of 

employment from 1961 through 1965.

The estimate of the scaling factor φ and its variance described above are based on the maximum 

likelihood principle. Equivalent results can be obtained using a Bayesian approach Groer (2004).

4.0

Let t indicate a quarter for which a dose distribution is required for a worker unmonitored between 

January 1951 and December 1960. Without scaling, the unmonitored dose is lognormal with 

parameters (on the log scale) μt and σt (from Table 1), i.e. yt = log(dt) is normally distributed with mean 

μt and standard deviation σt . The mean and standard deviation of the adjusted log dose are

APPLICATION OF THE SCALING PROCEDURE
Effective Date: 09/09/2004 Revision No.: 00 Document No.: ORAUT-OTIB-0013 Page 5 of 9

* μt = μt + ∧

φ (4)

σt

* = [σt

2 + var( ∧

φ )]

1/2,

i.e., the unmonitored dose in quarter t is lognormal with mean * μt and standard deviation σt

*

. If a 

worker was unmonitored for all four quarters in a given year, the adjusted lognormal parameters are 

calculated for each quarter and the annual dose estimate is obtained by Monte Carlo sampling as 

described by Kerr and Smith (2004).

Example – continued

To estimate the unmonitored dose in the first quarter of 1957 for the worker in the example, use ∧

φ = 

0.46976, var( ∧

φ ) = 0.03661 in equation 4.

μt

* = 4.5501 + 0.46976 = 5.0198

σt

* = [0.74862 + 0.03661]1/2 = 0.7727 ,

where μt = 4.5501 and σt = 0.7486 are obtained from line 39 of Table 1. The unmonitored dose for 

the quarter is lognormal with * μt = 5.0198 and σt

* = 0.7727. The adjusted geometric mean is 

exp( * μt ) = 151.38 and the adjusted geometric standard deviation of exp(σt

*

) = 2.166.

The 1st percentile of this distribution is 25 mrem and the 99th percentile is 914 mrem. These are 

shown as red triangles connected by a vertical straight line in Figure 1 for the first quarter of 1957.

The open red circle is the geometric mean. The solid green circles are the recorded doses that are 

known for this individual (see column 8 of Table 2 for 1961 through 1965). If this individual had not 

been monitored prior to 1961, Monte Carlo sampling from the quarterly lognormal distribution 

(described by the vertical bars in Figure 1) would be used to estimate the annual dose distribution in 

the dose reconstruction procedure.
Effective Date: 09/09/2004 Revision No.: 00 Document No. ORAUT-OTIB-0013 Page 6 of 9

Figure 1

56 58 60 62 64 66

2

5

10

50

200

1000

Year

Dose

Y-12 Individual Dose Adjustment Procedure 

1956 to 1960 1st to 99th Percentile Of Quarterly Dose Distribution 
Effective Date: 09/09/2004 Revision No.: 00 Document No. ORAUT-OTIB-0013 Page 7 of 9

REFERENCES

Frome, E. L. and J. Watkins, (2004), Statistical Analysis of Data with Non-detectable Values, 

ORNL/TM-2004/146. (http://www.csm.ornl.gov/~frome/sand/)

Groer, P. G., 2004, Bayesian Methods for Estimation of Unmonitored Y-12 External Penetrating 

Doses with a Time Dependent Lognormal Model, ORAUT-OTIB-0015-00-A. 

Johnson, N. L, S. Kota, and N. Balakrishnan, 1994, Continuous Univariate Distributions, Vol. 1, 2nd

Edition, J. Wiley and Sons, New York, New York.

NIOSH (National Institute for Occupational Safety and Health), 2002, External Dose Reconstruction 

Implementation Guideline, OCAS-IG-001, Revision 1, Cincinnati, Ohio. 

Kerr, G. D., 2003, Technical Basis Document for the Y-12 National Security Complex – Occupational 

External Dosimetry, ORAUT-TBBS-0014-6, Oak Ridge, Tennessee.

Kerr, G. D., and M. H. Smith, 2004, A Procedure to Account for Incomplete Personal Monitoring Data 

on Penetrating Gamma-Ray Doses to Workers in Radiation Areas at the Oak Ridge Y-12 Plant 

Prior to 1961, ORAUT-PROC-0042.

Strom, D. J., and P. S. Stansbury, 2000, Determining Parameters of Lognormal Distributions from 

Minimal Information, AIHAJ 61:877-880.

Watkins, J. P., J. L. Reagan, D. L. Cagle, E. L. Frome, C. M. West, D. J. Crawford-Brown, and W. G. 

Tankersley, 1993, Data Collection, Validation, and Description for the Oak Ridge Nuclear 

Facilities Mortality Study, ORISE-93/J-42, Oak Ridge Institute for Science and Education, Oak 

Ridge, Tennessee. (http://www.orau.gov/cer/reports.htm)

Watkins, J. P., G. D. Kerr, E. L. Frome, W. G. Tankersley, and C. M. West, (2004), Historical 

Evaluation of the Film Badge Dosimetry Program at the Y-12 Facility in Oak Ridge, 

Tennessee, ORAU Technical Report # 2004-0888. (http://www.orau.gov/cer/reports.htm)
Effective Date: 09/09/2004 Revision No.: 00 Document No. ORAUT-OTIB-0013 Page 8 of 9

Table 1. Lognormal parameters for Y-12 population for penetrating gamma-ray doses 1951 to 1965.

t Yr Qt μ σ GM GSD

1 47 3 5.2684 1.1710 194.109 3.2254

2 47 4 5.2380 1.1710 188.302 3.2251

3 48 1 5.2077 1.1709 182.668 3.2248

4 48 2 5.1773 1.1708 177.203 3.2245

5 48 3 5.1469 1.1707 171.901 3.2243

6 48 4 5.1165 1.1706 166.758 3.2240

7 49 1 5.0862 1.1706 161.769 3.2238

8 49 2 5.0558 1.1705 156.929 3.2235

9 49 3 5.0254 1.1704 152.233 3.2233

10 49 4 4.9950 1.1703 147.679 3.2230

11 50 1 4.9647 1.1703 143.260 3.2228

12 50 2 4.9343 1.1702 138.974 3.2226

13 50 3 4.9039 1.1701 134.816 3.2224

14 50 4 4.8735 1.1701 130.782 3.2222

15 51 1 4.8432 1.1700 126.870 3.2220

16 51 2 4.8128 1.1699 123.074 3.2217

17 51 3 4.7824 1.1699 119.392 3.2216

18 51 4 4.7520 1.1698 115.819 3.2214

19 52 1 4.7217 1.1698 112.354 3.2212

20 52 2 4.6913 1.1697 108.993 3.2210

21 52 3 4.6609 1.1696 105.732 3.2208

22 52 4 4.6305 1.1696 102.568 3.2206

23 53 1 4.6002 1.1695 99.500 3.2205

24 53 2 4.5698 1.1695 96.523 3.2203

25 53 3 4.5394 1.1694 93.635 3.2202

26 53 4 4.5090 1.1694 90.833 3.2200

27 54 1 4.4787 1.1694 88.116 3.2199

28 54 2 4.4483 1.1693 85.479 3.2197

29 54 3 4.4179 1.1693 82.922 3.2196

30 54 4 4.3875 1.1692 80.441 3.2195

31 55 1 4.3571 1.1692 78.034 3.2193

32 55 2 4.3268 1.1691 75.699 3.2192

33 55 3 4.2964 1.1691 73.435 3.2191

34 55 4 4.2660 1.1691 71.237 3.2190

35 56 1 4.2356 1.1690 69.106 3.2189

36 56 2 4.2053 1.1690 67.039 3.2188

37 56 3 4.1749 1.1690 65.033 3.2187

38 56 4 4.4804 1.1860 88.267 3.2740

t Yr Qt μ σ GM GSD

39 57 1 4.5501 0.7486 94.643 2.1140

40 57 2 3.6461 1.1936 38.324 3.2990

41 57 3 3.5629 1.2879 35.267 3.6250

42 57 4 3.0381 1.0039 20.865 2.7290

43 58 1 3.7262 0.9666 41.523 2.6290

44 58 2 4.3847 1.1885 80.218 3.2820

45 58 3 4.5488 1.0217 94.520 2.7780

46 58 4 4.1164 1.0668 61.337 2.9060

47 59 1 4.7269 0.8705 112.948 2.3880

48 59 2 3.6119 1.2459 37.037 3.4760

49 59 3 3.7927 1.0260 44.374 2.7900

50 59 4 4.1740 1.0047 64.972 2.7310

51 60 1 3.5687 1.1151 35.469 3.0500

52 60 2 3.9611 1.0561 52.513 2.8750

53 60 3 4.2164 1.0160 67.792 2.7620

54 60 4 4.4589 0.9381 86.396 2.5550

55 61 1 2.0601 1.2390 7.847 3.4520

56 61 2 3.8154 0.5983 45.395 1.8190

57 61 3 3.0126 0.8527 20.341 2.3460

58 61 4 3.9514 0.5300 52.006 1.6990

59 62 1 2.4602 0.9400 11.707 2.5600

60 62 2 3.9103 0.5839 49.915 1.7930

61 62 3 3.6301 0.7948 37.718 2.2140

62 62 4 3.3465 1.0791 28.402 2.9420

63 63 1 2.4188 1.2170 11.232 3.3770

64 63 2 2.7573 0.8825 15.758 2.4170

65 63 3 1.9958 1.5819 7.358 4.8640

66 63 4 2.4319 0.9034 11.381 2.4680

67 64 1 2.1856 1.3010 8.896 3.6730

68 64 2 2.1811 1.2667 8.856 3.5490

69 64 3 3.0904 1.2069 21.986 3.3430

70 64 4 2.1822 1.3368 8.866 3.8070

71 65 1 2.7352 1.0438 15.413 2.8400

72 65 2 2.4326 1.1581 11.388 3.1840

73 65 3 2.7134 0.9353 15.080 2.5480

74 65 4 3.5052 0.5289 33.288 1.6970
Effective Date: 09/09/2004 Revision No.: 00 Document No. ORAUT-OTIB-0013 Page 9 of 9

Table 2. Calculation of scaling factor with example.*

t yr qt μ σ w y0 d y v

1 61 1 2.060 1.239 0.651 1.740 12 2.485 0.425

2 61 2 3.815 0.598 2.794 3.047 74 4.304 0.489

3 61 3 3.013 0.853 1.375 2.559 62 4.127 1.114

4 61 4 3.951 0.530 3.559 3.127 98 4.585 0.634

5 62 1 2.460 0.940 1.132 2.190 43 3.761 1.301

6 62 2 3.910 0.584 2.933 3.079 88 4.477 0.567

7 62 3 3.630 0.795 1.583 2.843 46 3.829 0.199

8 62 4 3.346 1.079 0.859 2.520 51 3.932 0.585

9 63 1 2.419 1.217 0.675 1.975 32 3.466 1.047

10 63 2 2.757 0.883 1.284 2.406 52 3.951 1.194

11 63 3 1.996 1.582 0.400 1.473 66 4.190 2.194

12 63 4 2.432 0.903 1.225 2.196 0 2.196 -0.236

13 64 1 2.186 1.301 0.591 1.779 0 1.779 -0.407

14 64 2 2.181 1.267 0.623 1.799 0 1.799 -0.382

15 64 3 3.090 1.207 0.687 2.316 47 3.850 0.760

16 64 4 2.182 1.337 0.560 1.753 8 2.079 -0.103

17 65 1 2.735 1.044 0.918 2.275 50 3.912 1.177

18 65 2 2.433 1.158 0.746 2.025 17 2.833 0.401

19 65 3 2.713 0.935 1.143 2.343 25 3.219 0.506

20 65 4 3.505 0.529 3.575 3.015 23 3.135 -0.370

*Note- The last three columns depend on individual workers’ film badge doses.