Q&A: What to do when thereís not enough data?
A: Yes... and yes.
This is a fairly common roadblock for individuals and organizations involved in
decision-making and policy with respect to infectious diseases: they sorely need the
predictive power and scenario-analysis capabilities of a mathematical model, but the
current state of research on the epidemiology for the particular disease or population
under consideration doesnít quite fill in all the blanks in terms of model parameter
values and ranges.
Depending on whatís missing, these unknown values can severely hinder both the
development of a quality predictive model, and the utility of its results. Unfortunately,
it is highly improbable - even impossible - that all details can be accurately
quantified for every single disease under consideration. This means every disease model
will have at least some "unknowns". So how can we get around this?
A very useful approach to these kinds of issues is the implementation of
uncertainty and sensitivity analyses. This means exploring a range of values for the
input parameters under consideration, either individually or in combination, and
evaluating the resulting variation in model outcomes. The product of this effort can be
qualitative - for instance, slight perturbations of the birth rate yield dramatic
changes in measles incidence over time, implying that measles transmission is highly
dependent upon susceptible population sizes - or quantitative - for example, a 10%
decrease in mortality rate yields a 200% increase in total cases over a given simulation
period for some hypothetical disease system.
This type of procedure can be implemented with surprisingly patchy data on
disease and population values, but must be accompanied by significant caveats and
discussion of model and parameter uncertainties. However the real value of uncertainty
and sensitivity analyses - and, I believe, the true power of mathematical modeling as a
whole - is that the knowledge gained from these efforts can guide additional research
and data gathering!
These analyses illuminate where the greatest degree of uncertainty exists for a
given disease or population, and where the greatest benefit can be gained from further
primary and secondary data collection efforts. The new data gathered can then be applied
to existing or enhanced models, which can again expose areas of uncertainty... and the
modeling / data gathering interaction can continue iteratively to lead to a highly
accurate and useful suite of transmission models, along with a detailed map of the
process that leads there. In the process, research efforts can focus on areas of
greatest potential return, maximizing research budgets and minimizing waste.
Finally, the extremely valuable lessons learned from the iterative progression
can subsequently be applied to other disease systems, streamlining the effort for
future models and decision-making processes, and shortening the path from problem-
identification to policy-application.
So even when it seems like there just isnít enough knowledge-base to construct a
model, the model itself can contribute dramatically to building that knowledge-base in
the most efficient and effective manner possible. Let our mathematical modeling experts
at MathEcology help you get there from here!