Computations of the Eight Basic Measures in Diagnostic Testing | Chapter 06 | Advances in Mathematics and Computer Science Vol. 2
Diagnostic testing concerning
categorical or dichotomized variables is ubiquitous in many fields including,
in particular, the field of clinical or epidemiological testing. Typically,
results are aggregated in two-by-two contingency-table format, from which a
surprisingly huge number of indicators or measures are obtained. In this
chapter, we study the eight most prominent such measures, using their medical
context. Each of these measures is given as a conditional probability as well
as a quotient of certain natural frequencies. Despite its fundamental theoretical
importance, the conditional probability interpretation does not seem to be appealing
to medical students and practitioners. This paper attempts a partial remedy of
this situation by visually representing conditional probability formulas first
in terms of two-variable Karnaugh maps and later in terms of simplified acyclic
(Mason) Signal Flow Graph (SFGs), resembling those used in digital
communications or DNA replication. These graphs can be used, among other
things, as parallels to trinomial graphs that function as a generative model
for the ternary problems of conditional probabilities, which were earlier
envisioned by Pedro Huerta and coworkers. The arithmetic or algebraic reading
or solving of a typical conditional-probability problem is facilitated and guided
by embedding the problem on the SFG that parallels a trinomial graph. Potential
extensions of this work include utilization of more powerful features of SFGs, interrelations
with Bayesian Networks, and reformulation via Boolean-based probability
methods.
Author(s) Details
Ali Muhammad Ali Rushdi
Department of Electrical and Computer Engineering, King
Abdulaziz University, P.O.Box 80204, Jeddah, 21589, Kingdom of Saudi Arabia.
Fayez Ahmad Talmees
Department of Electrical and Computer Engineering, King
Abdulaziz University, P.O.Box 80204, Jeddah, 21589, Kingdom of Saudi Arabia.
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