Curve Fitting (Weighting of Data)

DOE-STD-1121-98

The goal of a regression may be the best assessment of intake, dose, model parameters, or something

else. Computation of weighted averages of intake from ratios3 differs in terms of weighting from direct

regression of a retention function or an excretion function. Regression to predict intake differs from

regression to predict dose; the best assessment of intake may not be the same intake that gives the best

assessment of dose.

Because regressions differ when goals differ, weighting for the MLE of dose may differ from

weighting for other choices of estimators, such as the MLE of intake or the best model for predicting later

bioassay data. Furthermore, regression differs when it is done to excretion data rather than retention data.

Excretion data (e.g., urine or fecal data) represent the first derivative of a retention function, while

retention data (e.g., a lung count) represent the retention function itself.

Data taken from later times represent radioactive material that has been in the body a long time and

that would have emitted more energy than did the activity already eliminated from the body. Therefore,

the dose per unit activity is an increasing function of the time the activity has been in the body. The

relative contribution of a data point to the assessment of dose (in contrast to its influence on quantifying

the intake or defining the excretion function) may need to be considered. The MLE of dose is related to,

but generally not directly proportional to, the following product: [activity excreted per unit time at time t]

[t]. The MLE of the intake is related to the t=0 intercept of an intake retention function. Different

weighting factors may be needed for the two different MLEs. Thus, the amount of dose represented by a

data point long after intake may be relatively greater than the amount of dose represented by data points

occurring soon after intake. This kind of weighting is currently done by experienced analysts by simply

ignoring or throwing out early data (i.e., these data are given a weight of zero).

The selection of the method for dose assessment affects consideration of information available to the

internal dose assessor. Two methods can be identified:

Assessing Intake. The first method is to use bioassay data to assess the intake by a given route,

multiply the intake by 5 rems, and divide it by the stochastic Annual Limit on Intake (SALI) for that

route and chemical form. Essentially equivalent approaches are to use the "committed dose

equivalent per unit intake" factors from Federal Guidance Report 11 (Eckerman et al. 1988) or the

ICRP Publication 30 "weighted committed dose equivalent to target organs or tissues per intake of

unit activity" factors. The intake assessment approach is essentially computing a weighted average

intake from ratios of bioassay data to values of a fixed-parameter biokinetic model such as is done in

CINDY (Kennedy and Strenge 1992) and in NUREG-4884 (Lessard et al. 1987).

Assessing Dose from First Principles. A second approach is to start from basic principles,

employing bioassay data to infer the number of transitions occurring in organs or tissues of interest,

employing absorbed fractions for energy emitted, using quality factors, and, finally summing

committed dose equivalent values over the body. Bioassay data can be used to assess parameters of

a variety of intake retention functions, including excretion functions, that may be used to infer the

number of radioactive transitions that have or will occur.

Both methods share the foundation of a biokinetic model with at least one adjustable parameter.

In this context, "ratios" refers to bioassay measurements Xi observed at times ti divided by intake

retention functions IRF[ti] for the appropriate bioassay compartment.