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# Kinetics methods for clinical epidemiology problems

### Alexandru Dan Corlan,
John Ross,

### Proc Natl Acad Sci U S A 112(46):14150-14155, 2015

## ABSTRACT

Calculating the probability of each possible outcome
for a patient at any time in the future is currently possible only
in the simplest cases: short-term prediction in acute diseases of
otherwise healthy persons. This problem is to some extent analogous
to predicting the concentrations of species in a reactor when
knowing initial concentrations and after examining reaction rates at
the individual molecule level. The existing theoretical framework
behind predicting contagion and the immediate outcome of acute
diseases in previously healthy individuals is largely analogous to
deterministic kinetics of chemical systems consisting of one or a
few reactions. We show that current statistical models commonly used
in chronic disease epidemiology correspond to simple stochastic
treatment of single reaction systems. The general problem
corresponds to stochastic kinetics of complex reaction systems. We
attempt to formulate epidemiologic problems related to chronic
diseases in chemical kinetics terms. We review methods that may be
adapted for use in epidemiology. We show that some reactions cannot
fit into the mass-action law paradigm and solutions to these systems
would frequently exhibit an antiportfolio effect. We provide a
complete example application of stochastic kinetics modeling for a
deductive meta-analysis of two papers on atrial fibrillation
incidence, prevalence, and mortality.
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