Biology Reference
In-Depth Information
Clearly, what is needed is an objective criterion to evaluate the statistical
significance of a presumptive secretion event. Gold's method does not
provide for such a criterion per se and does not even provide an obvious
method to propagate the uncertainties of the data into an uncertainty of
the secretion rates obtained with the deconvolution. This is typical of
many of the standard deconvolution methods, some of which require
equally spaced data points and do not allow for variable experimental
uncertainties. Many of these methods simply ignore the existence of
experimental measurement errors within the data. Gold's deconvolution
method is also typical, in that it requires assumed values for half-lives
and produces the same number of data points of a secretion time series
as existed in the original concentration time series. These limitations
are partially resolved by the newer methods outlined in the next section.
More details about Gold's method can be found in Jansson (1984).
C. Multiparameter Deconvolution Methods
In order to account for variable measurement errors, missing values, and
to perform accurate secretion event identification, iterative weighted
least-squares fitting of the convolution integral from Eq. (9-12) can be
used for hormone concentration time series. The first step is to define
a mathematical model for the shape of the secretion function S(t).
Once this model is defined, the parameters of the model can be
determined by fitting the model to the hormone concentration time
series, as described in Chapter 8. The weighted nonlinear least-squares
fitting addresses the variable measurement errors and the possibility of
missing values inherent to a hormone concentration time series. The
estimated model parameter values provide the locations and sizes of the
secretion events, the basal secretion, and the elimination properties.
The goodness-of-fit methods that can be used with weighted nonlinear
least-squares fitting provide ways to test the adequacy of the assumed
secretion model. Furthermore, the weighted nonlinear least-squares
techniques also include methods to estimate the precision of the model
parameters, which can be used to test the significance of individual
secretion events. Such methods are usually referred to as multiparameter
deconvolution methods.
The original multiparameter deconvolution method DECONV (Veldhuis
et al. [1987]) operated under the assumption that the secretion events
can be described as the sum of Gaussian curves occurring at different
times, PP
k
, and having different magnitudes, H
k
, but all having the same
width, Secretion SD, as is shown in Eq. (9-18).
2
X
PP
k
Secretion SD
t
1
2
H
k
e
S
ð
t
Þ¼
S
0
þ
:
(9-18)
k
The positive constant S
0
in Eq. (9-18) is the basal secretion. One way to
approximate the locations of the secretion events is to use statistical
