Statistically, a regression model
computes a line of best fit and compares its slope to the population variation
to determine if this slope is significant. All statistical analysis
programs test regression models for significance. Practically speaking,
significance is generally desired when such a model is developed because
it would imply that there is a real trend across time or a relationship
between the variables involved. However, for the purpose of determining
when activity is stable, the slope should not deviate significantly from
zero as this would imply that the network is continuing to drift toward
a higher or lower level of activity.
Defining the parameters
Ideally this test would be applied
to the most recent period of activity. Thus, a dynamic or “floating”
window of time should be designated as the “population” of bins from which
the regression line will be calculated. The boundaries of this window
would be defined by x and (x - n) where x is the most recent 60 second
bin of activity and n is the duration (in minutes) of the window (and,
consequently, the population of the model). This duration is the
first of two main parameters that must be considered and optimal values
determined through laboratory experience.
The second parameter is the alpha level,
that is, the level of significance required before an experimenter (or
robot) is satisfied that the activity of a network is stable. Traditionally,
a level of 0.05 would be required for significance. This value represents
the ability of the model to demonstrate a trend across roughly two standard
deviations of a normally distributed series of points. By contrast,
a smaller alpha level, say, 0.01, would demand a greater degree of significance
for identifying a model. Returning to the earlier point, this is
the opposite of the intent for our purposes as we wish to know if any consistent
trend exists. A relatively minor “drift” over a few minutes may,
for example, skew multiple points in a dose-response experiment.
A series of points may be shifted beyond or contrary to the actual effects
of a pharmacological manipulation as the effect of the drug application
"rides" this drift.
Where’s the p?
While the calculation of the regression
model is relatively easy to accomplish, determination of the exact probability
of significance is not. As with all statistical tests, the critical
value upon which comparisons are made between the experimental and theoretically
derived models is dependent upon the number of cases (which yields the
degrees of freedom) and the desired alpha level. Out of ignorance,
I will assume LabView (the program being used to develop software for this
purpose) does not contain such a library of critical values. If both
of these parameters were held static for all experiments, a single critical
value (or series of values representing “red,” “yellow,” and “green” levels
of significance) might be obtained for comparison and this would not be
a problem. However, there are situations which might require adjustments
of n, as is discussed below. A solution for this problem is not apparent
at this time.
A dynamic n
Ideally, the model should be calculated
from a series of at least 20 bins. However, network activity has
been known at times to be fairly erratic independent of obvious outside
influences such as temperature (or prayer and political lobbying).
A calculation based on a short window of time in which activity oscillates
about a mean might indicate that activity is not stable, when, in the long
term, it in fact, is. Conversely, competing trends might obscure
a real trend in a short period. To guard against such cases, a test
for excessively high coefficients of variation (CVs) would be desirable
so that the duration of the window might be expanded. Again, these
parameters (what is a “high” CV? How much longer should the window be made?)
can be determined later.
One of the benefits of implementation
of this code is that it may yield an additional measure of drug effect:
the time to stabilization. As this characteristic presents itself
in the earliest stages of a culture’s exposure to a pharmacological manipulation,
this measure could assist in the very rapid identification of a toxin in
the application of neuronal networks as broad band biosensors. This
could be especially important in the field where personal are susceptible
to the effects of such an agent.
There are additional directions
these concepts might take, and any reader who understands the above discussion
(and maybe a few who don’t) may see further applications of these procedures
or, just as important, more efficient means of effecting these calculations.