Areas and slopes
Abstract
It is frequently necessary to estimate
areas, slopes, arc lengths, averages, lag times or asymptotes
in circumstances where the data are too noisy to fit a
deterministic equation or where a mathematical model cannot
be derived and an empirical equation or numerical procedure
has to be used. Use program AVERAGE to estimate areas, averages and
fractions above and below thresholds by the trapeziodal method
or use COMPARE with splines under tension if this is preferred.
program INRATE estimates initial and final rates, lag times and
areas using empirical equations, while program QNFIT uses a
deterministic model.
Details
If a process can be described by a mathematical equation then
this can be fitted to a data set and the best fit model can
then be used to estimate areas and derivatives, etc. Program
QNFIT in the SIMFIT package can be used for this purpose.
Frequently the exact model may be unknown or too complicated
to be used in this way or the data may be too noisy. In such
cicumstances the noisy data may be used without correction,
as in the trapezoidal method for estimating area under curves
or perhaps joining up the early points to define initial rates,
but in many instances data smoothing and use of an empirical
model may be preferred.
Data smoothing
This process is the use of empirical equations to fit noisy
data sets in order to use all the data to estimate parameters
that characterise the underlying process. Choosing the correct
smoothing technique is not always easy and requires care.
Program AVERAGE (Trapezoidal method)
This accepts curve fit files and joins the points (or means of
if replicates are supplied) by straight lines. These are used
as a robust method to calculate AUC, time above threshold or
average concentrations in pharmacokinetic studies.
Program INRATE (Polynomials, exponentials and power laws)
This can fit lines, quadratics, exponentials, Hill equations
or lag time equations. It is used for enzyme catalysed initial
rates, emptying of vesicles, diffusion into cells, etc. It is
very important to use the correct type of model with INRATE.
Programs CALCURVE, COMPARE and SPLINE (splines)
These use cubic splines to fit arbitrary curves. They are most
useful with complicated wavy curves where it is required to
estimate derivatives, areas and arc lengths. Care is needed to
check plots to ensure that best fit splines are not too wavy.
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