Biomedical Engineering Reference
In-Depth Information
14.4 EQUAL PROBABILITY STATES
We cannot measure cell age, but we can get close. Imagine we constructed another
axis where each bin or state is defined by cell age boundaries. These boundaries are
chosen such that the number of events is equal in each state. Associated with each of
these states are the parameter averages evaluated over the same boundaries. Another
way of stating this situation is that we can rebin the cell age axis such that each bin or
state has an equal probability of being associated with a measured event [9].
14.4.1 Probability State Axis and Percentages
From a practical point of view, this probabilistically determined axis is just as
effective in showing coordinated expression of numerous parameters as cell age. In
fact, it has a few advantages over cell age. Since the number of events is uniform along
this axis, any segment of the axis is proportional to the measured population
s
cumulative fraction. For example, if we divide this axis into five equal segments, the
first segment defines the first 20% of events, the second, the next 20%, and so on until
the last 20% of events in the progression.
14.4.2 The Fusion of Intensity Patterns and Percentages
In the early 1980s, cytometerists began to realize that there was a lot more to cyto-
metric analysis than reporting percentages. Reporting CD4
þ
percentages was
valuable, but understanding the disregulation associated with lymphomas and
leukemias required an appreciation of changes in intensity patterns rather than just
percentages. There has always been an uneasy balance between these two ways of
quantifying data, but with this new probability state axis, percentages and intensity
patterns are merged together into one coherent picture of the status of a specimen.
14.4.3 Synthesizing Data Sets
Another advantage of the probability state axis is that it allows us to easily
synthesize complex data sets from the model. The way this is done is quite easy
to understand. A computer algorithm picks one of the states at random. Once it has
selected the state it can then look up the parameter values associated with that state.
It can then add some uncertainty to these values by using Gaussian distributed
random numbers. These synthesized values can be put into a listmode file and stored
on disk. These data sets are valuable because the underlying “truth” associated with
their creation is known.
14.4.4 Calculating the Probability State Axis
The major advantage of the probability state axis, however, is that we can calculate it
from the observed data. This notion at first appears to be untenable, since we initially
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