Here is a summary of the answers I received concerning my question about interpolation techniques for malaria vector data.

Many thanks once more for the helpful suggestions.

HP

Hugo Pilkington

Epidemiologist

____________________________________________________________

EuroHIV - European Centre for the Epidemiological Monitoring of AIDS

Institut de Veille Sanitaire (InVS)

12, rue du Val d'Osne

94415 Saint-Maurice cedex

France

h.pilkington@...

Tel: +33 (0)141 79 68 68 http://www.ceses.org

Fax: +33 (0)141 79 68 02 http://www.invs.sante.fr

_____________________________________________________________________

I've little background about how to study malaria distribution using

geostatsitics. But I'd like to mention you that, there is a program (called

SaTScan) that can be used for studying cluster analysis of disease spread

like malaria. It provides you locations of clusters and their significance.

It is free for download from this site

http://dcp.nci.nih.gov/bb/SaTScan.html

I hope this will help you in your study.

Thank you

Isam Salih

Linkoping University, SWEDEN.

_______________________________________________________________

You should better compute the correlations on the 21 informed

houses than perform an interpolation, especially for only

21 samples that are generally not sufficient for an accurate

spatial analysis and the interpolated field will not be very obective.

The best thing you can do is make sure

that the 21 exposure rates are equally certain (if they are not,

i.e. if some houses were sampled during one year only instead of two,

then you should account for this in the following step giving

different weights to your data),

then compute a simple omni-directional variogram (for 21 values,

the variographic cloud will be enough) and hope

a structure will come out. If any sample has an exceptionnally

high or low rate value, then you should discard it from the

dataset and redraw the variogram to catch the hidden structures.

If the exposure rate has rather local variations

and, as you wrote in your message, the 21 houses are

well spread all over the village, then probably this

variogram will look completely flat (pure nugget effect).

In that case you can rely on classical statistics and

compute the correlations between malaria and exposure rates

on the 21 samples.

If a structured variogram appears then you can compute cross-

covariances between the exposure rate and the other covariates

and use them for co-kriging to see if it brings some improvements

compared to ordinary monovariate kriging.

Interpolating should always take place after data analysis, I guess.

I would be interested in the results of this study

please send me a copy of the published works,

Yours sincerely

Laurent Bertino

__________________________________________________________

I too work on modeling mosquito counts. I am the lead statistician at the

Center for Disease Control who supports all of our malaria projects. I have

used kriging as a fast, rough method to interpolate mosquito counts to all

houses in our region of study - Asembo Bay(90 villages) near Kisumu, Kenya.

There are definitely problems with this approach and I don't plan to publish

using regular kriging.

Kriging really isn't the way to go because the number of mosquitoes is count

data with excess zeros and over-dispersion (many high counts). Some houses

just seem to be mosquito houses; Others have none. One way to consider

modeling this is to use a mixture model where you have a binomial model

which determines whether or not there are mosquitoes in the house and an

over-dispersed Poisson to estimate the number of mosquitoes in the mosquito

houses. Of course you have to work in the spatial correlation matrix. As far

as I know, no one has implemented this procedure now. A colleague and I are

planning to work on this as soon as I can complete the analysis of our

long-awaited bed net study. Hopefully we will start on this by next fall.

Also you could consider (as we are) some type of Bayesian analysis. Tom

Smith, head of the Biometrics Unit of the Swiss Tropical Institute, works on

malaria issues on the Kenyan coast. This is the units website:

http://www.sti.unibas.ch/biomet.htm

I don't think they have solved the exact problem that the two of us seem to

be working on, but they are working on very similar issues. Actually I am

planning to use some of the software they have developed to calibrate the

results of our bed net traps. We used three collection methods in a sample

of our household, but only bed net traps in the majority. You may want to

contact Tom Smith directly as I'm not sure that he monitors the AI-GEOSTATS

list.

Could you please forward any solutions you receive to me? I would be

extremely happy to have someone else solve this problem. If someone else

doesn't have a solution, I will be happy to share what we come up with. It

will probably be too late for your current project, but may help with future

projects.

Margarette

Margarette Smith Kolczak, Ph.D.

__________________________________________________________________

Madelaine Thomson, Peter Diggle and collaborators have been publishing

results on a study of Malaria in Gambia using geostatistical models

Concerning modelling strategies there are two basic approaches discussed

in the following papers:

1) using linear mixed models + GEE (generalised estimating equations) to

account for the spatial variation.

Basically, residuals from a GLM (generalised linear model) are used to

find a variogram model which is them used to correct std. errors for the

covariates coefficients.

Thomson, M.C., Connor, S.J., D'Alessandro, U., Rowlingson, B.S., Diggle,

P.J., Cresswell, M. and Greenwood, B.M. (2000). A spatial model of malaria

risk: satellite data used to predict the impact of bednets in The

Gambia. American Journal of Tropical Medicine and Hygiene. To appear.

2) Using a generalised spatial linear mixed model with inference via MCMC

(Markov Chain Monte Carlo).

The basic paper is:

Diggle, P.J., Moyeed, R.A. and Tawn, J.A. (1998). Model-based

geostatistics (with Discussion). Applied Statistics, 47, 299-350.

Cheers

P.J.

_________________________________________________________________

Dear Hugo,

I'd use the kernel estimation technique. It is very sound and reliable, and

easier to perform than bayesian modelling techniques. I've used it in

producing an oncological mortality atlas in my region, but I think you can

easily adopt it also in case of infective pathologies.

Moreover, you can find a freeware called "Crimestat", very nice and

performing the kernel estimates.

You can find a description at

http://directionsmag.com/pressreleases.asp?PressID=2196

where you can redirect to

http://www.ojp.usdoj.gov/cmrc/tools/welcome.html

to download it.

I'd be interested also in other replies you had.

Let me know.

My best regards

Dr. Alberto Zucchi

MD, Epidemiologist

Resp. Epidemiology Unit

Local Health Authority of Bergamo Province

Italy

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