1. Google Meningitis Modeling
Tom Hopson
October , 2010

2. A role for weather forecasts
Meningitis epidemics are observed to occur in the dust season and end with the onset of the rains
Can we predict the onset of the rains with enough spatial resolution ad enough lead time so that decision makers can prioritize allocation of vaccines to those districts likely to remain dry.
We need a better understanding of all factors involved in disease transmission. Basic research elucidating the environmental and social determinants of disease is needed even if we have a conjugate vaccine as availability will be limited. 2 2

4. More on relevant weather variables …
Consensus?: irritation of the pharynx that allows the bacteria (which may already be there) to enter the body. Dryness?
Diffusion equation (number density):
=> Diffusion ~ number density, or perhaps more accurately, ~ TnA
In terms of what we can forecast (measure), look at ideal gas law: or
Look at terms ~ e and terms ~ (e / TK) (air at body temperature)
=> e ~ esat(T) RH

5. Possible simple model (MRSA) –
Susceptible-Colonized-Infected reservoirs
(over?-) simplifications:
assume can develop a meningitis model that applies for all
assume homogenous mixing over whole district
same model applied to all available districts
St, Ct, It represent numbers of people in each district
β coefficients depend on many factors
Thanks to Vanja Dukic

6. Possible simple model (cont) -
only observations are It (actually positive change in It ), and Population P
=> model last equation only
=> treat St and Ct as roughly fixed ratios of total population across all countries
(proportionally-small variation in S and C)
(a)
(b)
(c)
(d)
Simplifying to:
(a)
(b)
(c)
for closure, treat It ( (d) terms) as sum of previous 2 weeks of cases
(after 2 weeks, no longer infected)
=> It = It-1 + It-2
weekly time increment, so model everything as weekly averages (met variables)

7. Possible simple model (cont) -
Or in terms of cases per 100,000 …

9. 2 other Possible simple models …{ }
=> Per Population dependence
=> Population per Area dependence
n A + m B → C + D or

10. Grouping all possible model terms together …
Or in terms of real-time measurables (i.e. no I terms) …

11. Logistic Regression for probability of occurrence (“any case” or “epidemic 15/105 )

12. Weather Variable fit … RH VP AIRT VP/T TOTWIND NEWIND current const 1
lag1 const
lag2 const
current P
lag1 P
lag2 P
current P/A
lag1 P/A
lag2 P/A
current Pr/r
lag1 Pr/r
lag2 Pr/r
current Pr/r/Ar
lag1 Pr/r/Ar
lag2 Pr/r/Ar

13. Overall Weather Variable fit …
current const 1
lag1 const
lag2 const
current P
lag1 P
lag2 P
current P/A
lag1 P/A
lag2 P/A
current Pr/r
lag1 Pr/r
lag2 Pr/r
current Pr/r/Ar
lag1 Pr/r/Ar
lag2 Pr/r/Ar
Next steps …
1) use cross-validation
2) compare with equation utilizing incidence reports

14. … followed by Quantile Regression (QR) for severity (cases) … E.g.
Our application
Fitting T quantiles using QR conditioned on:
Ranked forecast ens
ensemble mean
ensemble median
4) ensemble stdev
5) Persistence
Quantiles defined by obs (predictand)? Yes. Number of quantiles depends on number of ensemble members available.
L1 measure => minimizing absolute error of each quantile (done by weighting data -- see paper I sent to you)
Red line is the mean
Solid blue is the median
Each gray line are the .05, .1, .25, .75, .9, .95 quantile regression lines, respectively.
Our application: weighted ensemble mean derived by weighting each ensemble-model based on its error variance; “specific ensemble forecasteed quantile” means if, say, we’re regressing for the .25 quantile, we use the .25 ensemble forecast quantile as a regressor variable

15. Using ‘Quantile Regression’ to better calibrate ensembles
Without Quantile Regression: Observations outside range of ensembles
With Quantile Regression: Ensembles bracket observations
From Tom Hopson

16. THORPEX-TIGGE “Grand Ensemble Experiment”
UKMO
CMC
CMA
ECMWF
MeteoFrance
NCAR
NCEP
JMA
NCDC
KMA
IDD/LDM
HTTP
FTP
Archive Centre
CPTEC
Current Data Provider
BoM
Unidata IDD/LDM
Internet Data Distribution / Local Data Manager
Commodity internet application to send and receive data

17. Archive Status and Monitoring, Variability between providers

18. Forecasting: Thorpex-Tigge “grand ensemble” -

19. Forecast “calibration” or “post-processing”
“bias”
obs
Forecast
PDF
Probability
Probability
Forecast
PDF
obs
“spread” or “dispersion”
calibration
Flow rate [m3/s]
Flow rate [m3/s]
Post-processing has corrected:
the “on average” bias
as well as under-representation of the 2nd moment of the empirical forecast PDF (i.e. corrected its “dispersion” or “spread”)
Our approach:
under-utilized “quantile regression” approach
probability distribution function “means what it says”
daily variation in the ensemble dispersion directly relate to changes in forecast skill => informative ensemble skill-spread relationship

20. Calibration Procedure
obs
Forecast
PDF
For each quantile:
Perform a “climatological” fit to the data
Starting with full regressor set, iteratively select best subset using “step-wise cross-validation”
Fitting done using QR
Selection done by:
Minimizing QR cost function
Satisfying the binomial distribution
2nd pass: segregate forecasts into differing ranges of ensemble dispersion, and refit models => ensure ensemble has skill-spread information
Probability 
Temperature [K]
T [K]
in both min and maxT forecasts underforecasting by about 1.5C (i.e. f - o = -1.5)
AR(1) means I’m only using today’s observed error to forecast tomorrow’s error, and then
Removing this from the forecast
16% of ensembles gained by the AR(1) as was determined using “generalized cross-validation”
observed
Forecasts
Time
Regressors for each quantile: 1) ranked forecast ensemble member 2) ens mean 4) ens stdev 5) persistence

21. Questions about weather/health relationship
How does the disease work?
Consensus?: irritation of the pharynx that allows the bacteria (which may already be there) to enter the body
Consistent with dust, cooking smoke, and pneumococcal as risk factors.
Problem of communal eating across belt – exchange of saliva