Another issue to consider in weighting regressions is the selection of what parameters are to be
Intake. An estimate of intake is usually part of a regression analysis, but intake may already be
known when radionuclides are administered medically or under experimental conditions.
Time Course of Intake. The regression may include time of intake or time course of intake (for
multiple or chronic intakes) for optimization when these times are unknown. For single exponential
intake retention functions, time of intake cannot be determined from bioassay data, but for other
functional forms, it may be determinable if data are of adequate number and quality.
Mixture of Chemical Forms. The regression may choose an optimum linear combination of
inhalation classes or chemical forms.
Particle Size Distribution. The regression may choose an optimum particle size distribution that best
fits the data.
Rate Constants. Other parameters, such as rate constants used in the biokinetic models, may be
optimized for individuals by the regression.
Optimal use of the information available dictates that once a method has been selected, at least four
categories of information should be considered. Two relate to the measurement value itself; two relate to
maximizing the use of other information that may be available. The discussion below applies to a general
nonlinear regression of a function with more than one adjustable parameter.
There are two components of variance for a measurement result itself:
Measurement-process variance (e.g., net Poisson uncertainty or net fluorimeter uncertainty) depends
on the amount of analyte present. In general, the relative standard deviation (coefficient of
variation) becomes larger as the net activity or amount becomes smaller. Inverse variance weighting
(i.e., computing the weighted sum of squares of deviations from the regression by multiplying each
) is appropriate for this component of variance.
Biological variability is likely to be a fixed (times-or-divided-by) value independent of the amount
of analyte, that is, it is likely to be expressed as a constant geometric standard deviation. Uniform
weighting on a logarithmic scale is appropriate for this component of variance.
There are at least two considerations for regression weighting that are unrelated to the variance
considerations named above.
Unintended "number weighting" (weighting caused by the number of samples) may occur due to a
nonuniform number of data points per unit time. Bioassay data often tend to be non-uniformly
distributed over time, with many points immediately following an acute intake and fewer later on.
An arbitrary weighting adjustment may be needed to avoid having the regression dominated by the
sheer numbers of sample measurements at one time or another.
Other objective or subjective weighting may be needed, such as the degree of confidence in a
measurement's representativeness or calibration. For example, a result from a contractor-operated
mobile whole-body counter may not be considered as reliable as a result measured under more
controlled conditions with more sensitive detectors. Other examples that may require subjective