Biology Reference
In-Depth Information
two-step process. The first step looks for statistically significant increases
within the data time series, while the second step looks for statistically
significant decreases. Specifically, step 1 in Figure 9-17 is comparing a
nadir (minimum) group size of 2, in this case data points 2 and 3 (each of
which contains three replicates), with a peak (maximum) group size
of 2, in this case data points 4 and 5. If this comparison indicates a
statistically significant increase, as assessed by a grouped t-test, then the
first data point in the peak group (in this case, data point 4) is marked as
being a significant increase. This process is repeated with the group
locations increased by one (i.e., points 3 and 4 are compared with points
5 and 6) until the end of the time series is reached. Every location
corresponding to a statistically significant increase is recorded. Step 2 is
identical to step 1, except that the grouped t-test is used to locate
statistically significant decreases. Nadirs are then identified as
significant decreases followed by significant increases, with peaks
identified as the regions between the nadirs. One of the consequences of
this definition of peaks and nadirs is that partial peaks at the
beginning and the end of the hormone concentration time series are not
identified. Neglecting these partial peaks is a design feature of the
algorithm because the characteristics of a partial peak cannot be
evaluated accurately.
The sawtooth pattern at the top of the LH and GH time series in
Figures 9-5 and 9-6 is a diagrammatic depiction of the locations of the
peaks and nadirs identified by the CLUSTER algorithm. The algorithm
located six peaks in the LH time series and nine peaks in the GH
time series. The CLUSTER algorithm provides a good illustration of the
importance of using a correct variance model to evaluate the precision
of the hormone concentrations. For example, the six peaks within the
LH data in Figure 9-5 were based upon an MDC of 1 and a CV of 5%. If,
however, we use MDC
3%, the CLUSTER algorithm
will locate 12 statistically significant peaks in the LH time series. Clearly,
the results obtained depend upon the assumed variance model for
the data.
¼
0.3 and CV
¼
The CLUSTER algorithm provides some, but not all, of the desired
characterizations of the hormone concentration time series. It provides
information about the number, location, and size of the peaks in the data
that meet its statistical criterion of significance. However, no information
about the shape and size of the underlying secretion events and
clearance mechanisms, which combine to create pulses, or any
underlying basal secretion is provided by this method. Methods more
powerful than CLUSTER in this regard are described next.
IV. DECONVOLUTION METHODS
Deconvolution methods are standard mathematical techniques widely
used in science and engineering. A typical application is to remove the
