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Research
Seasonal Forecast of St. Louis
Encephalitis Virus Transmission, Florida
Jeffrey Shaman,*
Jonathan F. Day,† Marc Stieglitz,* Stephen Zebiak,‡ and Mark Cane*
*Columbia University, New York, New York, USA; †University of Florida,
Gainesville, Florida, USA; and ‡International Research Institute for Climate
Prediction, Palisades, New York, USA
Appendix C (Online Only)
Empirical Methods
Whole model goodness-of-fit was measured by log-likelihood ratio and
the pseudo r-squared (uncertainty) coefficient. The significance of individual
parameter estimates was evaluated by Wald’s chi-square test. Confidence
intervals were based on Wald tests of the parameter estimates, following
the methods of Hosmer and Lemeshow (A11).
For transmission incidence and epidemic transmission, we examined the
residuals of our logistic regression model fits, specifically the individual
components of the chi-squared goodness of fit, following the methods of
Pregibon (A12). Time series lag autocorrelations
among these residuals were then compared with time series lag autocorrelations
of the respective transmission category. A reduced autocorrelation among
the residuals provides evidence that the explanatory variables of the
regression model (WTD) are also accounting for the autocorrelation evident
in the SLEV transmission data. Because we have no time series records
for individual chickens, this analysis was not performed for the transmission
number category.
The logistic regression of SLEV transmission incidence yields an empirical
relationship between modeled WTD and the probability that any transmission
of SLEV will occur. Logistic regression of SLEV transmission number on
modeled WTD derives an empirical relationship expressing the probability
that each individual chicken will become infected with SLEV. Lastly,
logistic regression of SLEV epidemic transmission on modeled WTD derives
the probability that epidemic levels of transmission will occur.
A number of factors other than changes in local land surface wetness
can affect rates of sentinel chicken seroconversion. For instance, even
with a severe, well-timed drought, immunity in avian populations can reduce
rates of amplification. Such immunity often develops in the year following
an epidemic (A13). This factor, avian susceptibility,
is an additional variable in the SLEV transmission cycle, which can complicate
prediction of SLEV transmission with modeled WTD. Consequently, while
drought followed by wetting may be necessary for SLEV amplification and
subsequent transmission, it is not, in and of itself, sufficient. A further
complication results from the mobility of both the avian hosts and vectors,
e.g., infected birds and mosquitoes may arrive in one location having
undergone amplification in another. As a result, it is possible for transmission
to occur in a location where amplification has not occurred.
These additional factors, host immunity and host and vector mobility,
are noise in an SLEV prediction system that (at present) only considers
variations in local modeled WTD. In spite of these effects, we previously
were able to identify the mechanism of drought-induced amplification using
transmission incidence for the 1986–1991 time period (A14).
Here we extend the analysis to transmission number and epidemic transmission
for the same 1986–1991 time span to determine if the same mechanism governs
all three transmission categories.
For the purposes of accurate forecast, however, it is to the advantage
of the forecaster to develop an empirical relationship based upon a more
inclusive, longer period of record, during which the influence of additional
factors is present. We therefore also applied the same logistic regression
analyses to a longer, 1978–1997 record of sentinel chicken seroconversion
in Indian River County. By using this longer record, we no longer focus
upon the 1990 epidemic and the mechanism of amplification, but
instead look for a more general statistical relationship that describes
local, SLEV transmission based on local, modeled hydrologic conditions.
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