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AI-GEOSTATS: Re: Spatial-temporal clustering by chance

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  • Basil_LOH@ENV.gov.sg
    Hi everyone, A million THANKS to everyone who replied. I m always touched by the prompt helpfulness and the high quality answers of these listserves. Here are
    Message 1 of 1 , Oct 30, 2001
      Hi everyone,

      A million THANKS to everyone who replied. I'm always touched by the prompt
      helpfulness and the high quality answers of these listserves.

      Here are the answers I got.

      I'd probably explore those free softwares, starting with SatSCAN.

      Thanks very much again, guys!

      ----- Forwarded by Basil LOH/ENV/SINGOV on 30-10-2001 17:01 -----

      "P. Philippe"
      <philippp@SYMPA To: METHODS@...
      TICO.CA> cc:
      Sent by: Subject: Re: Spatial-temporal clustering by
      METHODS chance

      Please respond
      to METHODS

      21/10/01 09:30, « Basil_LOH@... » wrote/a écrit :

      > Hi everyone,
      > In Singapore, we define a dengue cluster (referring to an outbreak when
      dengue fever is spreading contagiously from one person to the next) as at
      least 2 cases (points) within 200 m of each other and within 3 weeks of
      incidence of each other. With about 2,000 cases so far this year, I have
      about about 80 clusters according to this definition.
      > However, I suspect that the occurence of some clusters (especially the
      > with just 2 or 3 cases) may be by chance, instead of an actual disease
      > transmission happening. How can I test this? Possibly, a Monte Carlo
      > simulation of some kind will help. Is there any software out there that
      > help to do this? SATScan has got some promising functions, unfortunately
      > deals with areal or polygon data and not point data (I think).
      > Will sum answers.
      > Thanks for your attention. Cheers.
      > Basil

      I would suggest the use of Knox' test that is based on distances. You need
      no control group to undertake Knox' test. Space-time interaction is tested
      with the Poisson distribution of pairs of cases near in space and time.

      The Atlanta CDC distributes the CLUSTER software at no cost. You will find
      CLUSTER softare at: http://www.atsdr.cdc.gov/HS/cluster.html

      Best of luck.

      NOUVEAU: Premier cours complet d'épidémiologie "en ligne"

      IEA'2002 Montreal Meeting: http://www.iea2002.com/
      U of Montreal HAS THOUGHT --- Nobel A. Szent-Gyorgyi
      Quebec ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
      Canada email:philippp@...
      ~~~~~~~~~~~~~~~~~~~~~~~~Listowner EPIDEMIO-L (Listproc@...)

      ----- Forwarded by Basil LOH/ENV/SINGOV on 22-10-2001 22:23 -----

      Roger Bivand
      <Roger.Bivand To: Basil LOH/ENV/SINGOV@SINGOV
      @...> cc: ai-geostats@...
      Subject: Re: AI-GEOSTATS: Spatial-temporal
      22-10-2001 clustering by chance
      respond to

      One possibility are the stkhat family of functions in Splancs, including
      stmctest - a Monte-Carlo test of space-time clustering, see: Diggle, P.,
      Chetwynd, A., Haggkvist, R. and Morris, S. 1995 Second-order analysis of
      space-time clustering. Statistical Methods in Medical Research, 4, 124-136.

      Software to run this in R (www.r-project.org) is contributed as a package
      to be found on the same site (maintained by me), in S-PLUS at the original
      site: http://www.maths.lancs.ac.uk/~rowlings/Splancs/. The article is not
      very easy to get at, a further short description can be found in: Bailey,
      T. C. and Gatrell, A. C. 1995, Interactive spatial data analysis. Longman,
      Harlow, pp. 122-125.

      A student from Thailand (Wutjanun Muttitanon <nungeog@...>) also
      drew my attention to an article I think using stkhat: Exploratory
      space-time analysis of reported dengue cases during an outbreak in
      Florida,Puerto Rico,1991-1992 Author : Amy C.Morrison and et al. Journal :
      American Tropical Hygine ,Vol 58(3) pp287-298.

      If you follow up this route using the splancs package for R, I'd be very
      grateful for feedback to help improve its documentation and functionality.


      Roger Bivand
      Economic Geography Section, Department of Economics, Norwegian School of
      Economics and Business Administration, Breiviksveien 40, N-5045 Bergen,
      Norway. voice: +47 55 95 93 55; fax +47 55 95 93 93
      e-mail: Roger.Bivand@...
      and: Department of Geography and Regional Development, University of
      Gdansk, al. Mar. J. Pilsudskiego 46, PL-81 378 Gdynia, Poland.

      ----- Forwarded by Basil LOH/ENV/SINGOV on 22-10-2001 22:23 -----

      "Dr. Ned
      Levine" To: Basil LOH/ENV/SINGOV@SINGOV
      <ned@NedLevin cc:
      e.com> Subject: Re: Probability of clustering of
      points by chance


      Thanks for writing. You're right that the Nnh routine does not
      incorporate. We're adding some space-time techniques to the next version
      of CrimeStat, but they are not quite ready yet. For example, the Knox
      index allows you to test a 2 x 2 table of space and time (close in space v.
      not close in space; close in time v. not close in time); you can define
      'closeness' in any way you want. A second technique is the Mantel index
      which is a correlation between closeness in space and closeness in time. As
      soon as these techniques are finished, I'll send you the beta version if
      you will test them for me with your data. I'd like to get a sense of well
      they perform. It sounds like your data would fit both of these techniques.

      Also, we're adding a Correlated Walk Analysis routine which allows
      one to diagnose and then predict the sequencing of actions (i.e., the time
      order in which they occur and its interaction with space). This routine is
      almost finished; we fixing a few bugs in it now. Essentially, you run a
      correlogram of time interval, distance, and direction which looks at
      patterning of the sequential events (a lag of 1 event; a lag of 2 events; a
      lag of 3 events, and so forth up to a lag of 7 events). That is, you are
      trying to see whether there are any repeating patterns by time, distance or
      direction. Then, you can specify a model for time, distance and direction
      and the routine will predict the next event. Again, I'll send you the
      latest version when it's finished (possibly this week).

      I would like you to also test the risk-adjusted Nnh routine (called
      Rnnh). This one is not time specific, but looks for clusters of points
      relative to an underlying population (e.g., dengue incidents per capita).
      Unlike SatScan, it uses point data; zonal data can be treated as
      pseudo-points (i.e., the centroids with weights). That routine is

      Anyway, I'll keep in touch with you.



      At 12:22 AM 10/22/2001 +0800, you wrote:

      Hi Ned,

      Sorry to take so long to get back to you! I was on leave for a while,

      Ned Levine, PhD
      Ned Levine & Associates
      Houston, TX
      ----- Forwarded by Basil LOH/ENV/SINGOV on 22-10-2001 22:23 -----

      "Duane F.
      Marble" To: Basil LOH/ENV/SINGOV@SINGOV
      <marble.1@osu cc: waphgis@...,
      .edu> METHODS@..., ai-geostats@...,
      22-10-2001 GIS-STATES-OTHER@...,
      06:15 health-gis@..., geomed99@...
      Subject: Re: AI-GEOSTATS: Spatial-temporal
      clustering by chance

      And why 200 meters?? Why not 195 or 205 or ??? I keep seeing research
      proposals that use an arbitrary distance (e.g., 200 meters or one-half
      without any discussion of where the figure came from.

      Dr. Duane F. Marble
      Professor Emeritus of Geography Telephone: 614-292-4419
      Center for Mapping Fax: 614-292-8062
      The Ohio State University
      1216 Kinnear Email: marble.1@...
      Columbus, Ohio 43212

      "From now on, space by itself and time by itself
      are doomed to fade away into mere shadows, and
      only a kind of union of the two will preserve
      an independent reality."
      - Minkowski, 1908

      ----- Forwarded by Basil LOH/ENV/SINGOV on 22-10-2001 22:23 -----

      Lewin-Koh To: Basil LOH/ENV/SINGOV@SINGOV
      <kohnicho@comp.n cc:
      us.edu.sg> Subject: Re: AI-GEOSTATS: Spatial-temporal
      clustering by chance
      22-10-2001 13:47

      I think Roger's advice of using Diggle et. al.' s approach for space time
      clustering is quite a sound one. The procedure is implemented in R's
      splancs package (as Roger pointed out). If there is a problem getting the
      data into R. I am working on a package that I haven't released yet for
      importing and manipulating geographic data in R, that I could let you
      use. By the way R is a GNU version of Splus and is free on the internet,
      there should be no license problems using it at the ministry of the
      environment. Also, Diggle's
      approach would help to address Duane Marble's comment of why 200m, becuse
      it will give you an estimate of the scale of clustering.


      N Nicholas Lewin-Koh
      / \ Dept of Statistics
      N----C C==O Program in Ecology and Evolutionary Biology
      || || | Iowa State University
      || || | Ames, IA 50011
      CH C N--CH3 http://www.public.iastate.edu/~nlewin
      \ / \ / nlewin@...
      N C
      | || Currently
      CH3 O Graphics Lab
      School of Computing
      National University of Singapore
      The Real Part of Coffee kohnicho@...

      ----- Forwarded by Basil LOH/ENV/SINGOV on 22-10-2001 22:23 -----

      Doherr Marcus
      <marcus.doherr@itn To: Basil LOH/ENV/SINGOV@SINGOV
      .unibe.ch> cc:
      Subject: RE: Spatial-temporal clustering by
      22-10-2001 20:05 chance

      SaTScan used point data (x/y coordinates of either the exact location - or
      the centroid of the area/polgon - of the cases and controls, or case status
      of the area or polygon (as identified by x/y of the centroid) and
      count data for each area or polygon so you should be able to use it.

      Cheers Marcus

      -----Original Message-----
      From: Basil_LOH@... [mailto:Basil_LOH@...]
      Sent: Sunday, October 21, 2001 6:31 PM

      ----- Forwarded by Basil LOH/ENV/SINGOV on 22-10-2001 22:23 -----

      Lance Waller
      <lwaller@....e To: waphgis@...
      du> cc:
      Sent by: Subject: Re: Spatial-temporal clustering by
      WAPHGIS-owner@... chance

      22-10-2001 21:37
      Please respond to


      Given that you have definitions of a critical distance in space
      (200m) and a critical distance in time (3 weeks), you could
      apply the Knox test (sort of the "classic" for this situation).

      Diggle et al. (1995) provide a more flexible version using K-functions
      (requiring more involved computation). A few notes on the Knox test:

      - In the discussion of the Knox paper, M.S. Bartlett offers an
      insightful comment regarding testing for space-time clusters:
      "Of course, even when one has demonstrated the existence of
      an interaction (read 'cluster'), say by some such method as
      he (Knox) suggests, one has, as I remarked at the meeting, to
      be on one's guard against spurious effects, such as the detection
      of one case leading to greater efforts, perhaps by a particular
      doctor, to find further cases in the same locality."

      - The Knox test has an implicit assumption of a constant
      population at risk, a feature explored and discussed in detail
      (along with other space-time tests) by Kulldorff and Hjalmars

      Hope this helps,


      Knox, E.G. (1964) The detection of space-time interactions.
      (with discussion). Applied Statistics, 13, 25-30.

      Barlett, M.S. (1964) Discussion of Knox. Applied Statistics,
      13, 30.

      Kulldorff, M., and Hjalmars, U. (1999) The Knox method and other
      tests for space-time interactions. Biometrics 55, 544-552.

      Diggle, P.J., Chetwynd, A.G, Haggkvist, R., and Morris, S.E. (1995)
      Second-order analysis of space-time clustering. Statistical Methods
      in Medical Research 4, 124-136.

      Basil_LOH@... wrote:

      ----- Forwarded by Basil LOH/ENV/SINGOV on 22-10-2001 22:23 -----

      "Telmo Nunes"
      <tnunes@fmv.u To: Basil LOH/ENV/SINGOV@SINGOV
      tl.pt> cc:
      Subject: Re: Spatial-temporal clustering by
      22-10-2001 chance

      Hi Basil

      You can test clustering using point data with Spatial-Time scan
      statistic (SatScan), using the bernouli model you can run
      case-control data (using the location of cases and controls).
      Another way of doing it is to reference your data to some
      administrative area centroid and using its population as denominator.
      The great advantage to Spatial Scan statistic, its that satscan is
      very easy to use, you only have to set the datafiles in space
      delimited text files (using Excel or access) choose the parameters and run
      the model. It will probably find much larger (in space and time) clusters
      (I guess..) than using your scheme, but will give the significance of this
      ones. You can also use co-variables (in your study (Living near or far from
      still waters...).

      Hope that this can help you, I´m not a spatial statiscian but just a
      veterinaian with interest in epidemiology and I've use spatial scan
      to BSE data with "good" results. For surveillance purposes there are
      other test that you can use...

      If you will go for the satscan aproach I'm availlable to help if you
      have some problem setting up the data.


      Telmo Pina Nunes
      UISSE - Unidade de Investigação e Serviços em Epidemiologia Económica
      Faculdade de Medicina Veterinária
      Universidade Técnica de Lisboa

      ----- Forwarded by Basil LOH/ENV/SINGOV on 22-10-2001 22:23 -----

      "James R.
      Blodgett" To: Basil LOH/ENV/SINGOV@SINGOV
      <jrb07@... cc:
      ate.ny.us> Subject: Spatial-temporal clustering by
      22-10-2001 21:55

      It should not be hard to estimate the expected number of chance clusters
      given the assumption of a uniform distribution of population over space.
      This could be done theoretically or by Monte Carlo. The problem is that
      the population is clustered, for example in apartment buildings. It is
      highly likely that several cases will appear by chance in a large building.
      Monte Carlo would be a good choice to model this, but you will need a good
      model of the clustering of the underlying population. This could be
      obtained by geocoding addresses of a representative sample.

      James Blodgett, MA, MBA, MS; NYS Dept. of Health, 1603 Corning Tower,

      ----- Forwarded by Basil LOH/ENV/SINGOV on 22-10-2001 22:23 -----

      Charles M." To: Basil LOH/ENV/SINGOV@SINGOV
      <cmc2@... cc:
      > Subject: RE: Spatial-temporal clustering by


      Please send me your full name and position, office, etc. I will post this
      the November edition.


      Charles M. Croner, Ph.D., Editor
      Public Health GIS News and Information
      Geographer and Survey Statistician
      NCHS/Centers for Disease Control and Prevention
      6525 Belcrest Rd., RM 915
      Hyattsville, MD 20782
      v: 301.458.4168
      f: 301.458.4031

      -----Original Message-----
      From: Basil_LOH@... [mailto:Basil_LOH@...]
      Sent: Sunday, October 21, 2001 12:31 PM
      To: waphgis@...; METHODS@...;
      ai-geostats@...; fnpbb@...;
      GIS-STATES-OTHER@...; health-gis@...;
      Subject: Spatial-temporal clustering by chance
      ----- Forwarded by Basil LOH/ENV/SINGOV on 23-10-2001 15:07 -----

      Philibert To: Basil LOH/ENV/SINGOV@SINGOV,
      <mphilibert@s waphgis@...,
      fu.ca> METHODS@..., ai-geostats@...,
      23-10-2001 GIS-STATES-OTHER@...,
      00:00 health-gis@..., geomed99@...
      Subject: Re: Spatial-temporal clustering by


      Re: software to perform cluster analyses, I would recommand you have a look

      at BoundarySeer (http://www.terraseer.com/clusterseer.html) from TerraSerr
      Inc., a company associated to BioMedWare
      (http://www.biomedware.com). Although I have not used it myself, it was
      presented to me in a workshop and I beleive it could eventually perform the

      analyses you need as it contains randomization procedures. Their web site
      contains probably enough information for you to have a good idea of its
      potential (see Method Descriptions).

      Hope this helps,



      Mathieu Philibert
      Graduate student
      Department of Geography
      Simon Fraser University
      British Columbia, Canada



      ----- Forwarded by Basil LOH/ENV/SINGOV on 23-10-2001 15:07 -----

      "William C.
      Hoffman" To: Basil LOH/ENV/SINGOV@SINGOV
      <whoffman@phr cc:
      l.org> Subject: RE: Spatial-temporal clustering by

      Hi Basil,

      Read the help documentation for SaTScan carefully. You can analyze point as
      well as polygon data. Also, have you compared the CrimeStat Hot Spot
      analysis to the Hot Spot Analysis that you performed using your routines?

      Also, how are you determining the cluster? By time and what is your spatial
      component? Occupational or home or other address or are you using all
      addresses? By determining the dengue type and performing a PCR you may be
      able to investigate the "chance" issue.

      By the way after reading your Hotspot document I do have a question for
      Does it work? Do you gain useful information from the analysis that you can
      use? If it works then it is very good. Please do compare with CrimeStat.
      Have you used the EpiAnalyst? Your feedback would be most appreciated.

      It sounds as if you have your hands full!



      -----Original Message-----
      From: owner-health-gis@... [mailto:owner-health-gis@...]On Behalf Of
      Sent: Sunday, October 21, 2001 9:31 AM
      To: waphgis@...; METHODS@...; ai-geostats@...;
      fnpbb@...; GIS-STATES-OTHER@...;
      health-gis@...; geomed99@...
      Subject: Spatial-temporal clustering by chance

      ----- Forwarded by Basil LOH/ENV/SINGOV on 23-10-2001 15:07 -----

      matthew stone
      <mstone@... To: Basil LOH/ENV/SINGOV@SINGOV
      h.tmc.edu> cc:
      Subject: Re: Spatial-temporal clustering by
      23-10-2001 chance


      You can use the SatScan program with point data as I asked Dr. Kuldorrf
      this very question. I used in conjunction with TB data where I was looking
      at specific print types versus all other cases, much like a case-control
      setup. If you think you can organize your data this way, such as the cases
      you are interested in versus all others, then follow the description below.


      1. Create a personal ID for each person.

      2. In the coordinates file, list the ID and coordinates for each
      person on
      a separate row. (If two persons have exactly the same
      coordinates, they
      need to be assigned a common ID, and have one line only.)

      3. Create the case file as before, but with one line for each
      person, and
      the personal ID instead of the census area ID.

      4. Create a control file for the controls in the same way as the
      case file.

      5. No population file is needed.

      Run SaTScan with the Bernoulli option.


      Matthew Stone
      GIS Research Assistant II
      University of Texas- School of Public Health
      Center for Health Policy--RAS Suite E929
      1200 Herman Pressler
      Houston, TX 77030
      E-mail: mstone@... OR mstone02@...
      Work 713-500-9395
      Fax 713-500-9493

      ----- Forwarded by Basil LOH/ENV/SINGOV on 23-10-2001 15:07 -----

      oh.govt.nz To: Basil LOH/ENV/SINGOV@SINGOV
      23-10-2001 Subject: Re: Spatial-temporal clustering by
      16:32 chance


      I wouldn't (at first thought) worry too much about the statistical nature
      of the clusters.

      Focus on what you really want to know...do you really need to know whether
      some cases fit the definition of sophisticated (but arbitrary!) statistical
      model? What is it that you really want to know? I bet what you are really
      interested in is determining where to focus your resources, right?

      Be wary of the term 'chance', remembering that absolutely nothing happens
      by chance! 'Chance' or probability are simply statistical models of our
      (and sometimes our knowledge). What happens if those one or two cases
      reflect the relatively recent establishment of Ae. or the recent
      transmission of
      infection to a previously 'isolated' group of Ae. in Mrs Jones' backyard?
      Maybe by ignoring those 'isolated' cases of dengue you are missing the
      opportunity to 'nip a new cluster in the bud'.

      Instead of following the clustering route as your only criteria for
      prioritising where you will spend your staff resources, why not include
      much more
      simple criteria, e.g. distance between nodes, which makes it more efficient
      for staff to get to multiple nodes quickly, size of nodes, which may be
      indicative of the size and extent of the infected Ae. population. Note that
      coastal and other areas with increased wind speed at morning and night
      will disperse Ae. more effectively that inner parts of Sing that are more
      sheltered from wind.

      Good luck Basil,

      Dr Chris Skelly
      Senior Advisor (Health GeoInformatics)
      Public Health Intelligence
      Public Health Directorate
      Ministry of Health
      DDI: 496 2215
      Mobile: 021 211 6370
      Fax: 496 2340


      ----- Forwarded by Basil LOH/ENV/SINGOV on 23-10-2001 15:07 -----

      Charlotte Morgan
      <charlotte.morgan@flinde To: Basil LOH/ENV/SINGOV@SINGOV
      rs.edu.au> cc:
      Subject: Re: Spatial-temporal clustering by
      23-10-2001 06:49 chance

      Dear Basil

      I am using Satscan with 'point' data. In my research I have aggregated
      cases and population at risk to census centroids, But you can use case
      locations if you also have control location

      I have written to Martin Kulldorf (SaTscan) with specific queries and he
      has offered valuable advise on appropriate analyses.


      Charlotte Morgan
      Lecturer in GIS
      School of Geography, Population & Env. Management
      Flinders University

      GPO Box 2100
      Adelaide 2001

      Phone 82012374
      Fax 82013521

      ----- Forwarded by Basil LOH/ENV/SINGOV on 23-10-2001 15:07 -----

      Geoffrey Jacquez
      <jacquez@biomedware. To: waphgis@...
      com> cc:
      Sent by: Subject: Re: Spatial-temporal clustering by
      WAPHGIS-owner@... chance

      22-10-2001 22:52
      Please respond to

      A few years ago I proposed a k-NN test for space-time clustering (Jacquez
      1996) that has several advantages over both the Mantel and Knox test, and
      that I believe would serve your needs. Mantel's (1967) test is a
      regression of the waiting time between case-pairs on the spatial distances
      separating those case-pairs. The Knox test is the count of the number of
      case-pairs that are "near" in both space and time, where "near" is defined
      by the investigator. The k-NN test is the count of the number of pairs of
      cases that are nearest neighbors in both space and time. The test can be
      evaluated for any value of k, such as first nearest neighbors, second
      nearest neighbors and so on, and the significance at each level of k is
      evaluated. So if you believe clustering at a certain level of k is (such
      as 2 or 3 cases) is occurring by chance, you can test this hypothesis
      directly by inspecting the probability value associated with k=2 and k=3.
      This test directly quantifies the scale of space-time clustering in terms
      of nearest neighbors.

      The test is available in the Stat! package, and will soon be added to the
      ClusterSeer software.

      1996. Jacquez, G. M. "A k-nearest neighbor test for space-time
      interaction." Statistics
      in Medicine, 15:1934-1949.


      ----- Forwarded by Basil LOH/ENV/SINGOV on 30-10-2001 17:01 -----

      "Eric Fevre"
      <Eric.Fevre@e To: Basil LOH/ENV/SINGOV@SINGOV
      d.ac.uk> cc:
      Subject: RE: Spatial-temporal clustering by
      23-10-2001 chance


      > SATScan has got some promising functions,
      > unfortunately it deals with areal or polygon data and not point data (I

      Not so! SatScan deals best with point data sets, and will run a
      randomization procedure in order to calculate likelihood ratios. What you
      would have to do is drop any prior assumtions of clustering that you
      have (ie forget the 200 metres issue for now), and run the analysis with
      your entire dataset and see. Satscan will give you the most likely
      as well as secondary clusters. You can also run the analysis with a
      temporal component, which would take care of the three weeks between cases.

      Good luck.
      Eric Fevre

      Centre for Tropical Veterinary Medicine
      University of Edinburgh
      Easter Bush, Roslin
      Midlothian EH25 9RG, UK

      Email: Eric.Fevre@...
      tel: +44 131 650 8850
      fax: +44 131 445 5099
      Web: http://web.onetel.net.uk/~eric_fevre/

      ----- Forwarded by Basil LOH/ENV/SINGOV on 30-10-2001 17:01 -----

      "Jo McKenzie"
      <J.S.McKenzie@mas To: Basil LOH/ENV/SINGOV@SINGOV
      sey.ac.nz> cc:
      Subject: cluster analysis
      24-10-2001 17:21
      Please respond to

      Dear Basil
      I have just re-subscribed to the health-gis mailing list after being away
      for a few weeks and saw a reply to your message about spatial clustering of
      Dengue fever.

      I would say that SATScan would be very useful as it deals well with point
      data, and copes with underlying populations at risk that are spatially
      heterogeneous. It generates a whole range of circles around each point,
      starting with a single point and getting larger to include an increasing
      number of points, then compares the observed incidence with the expected.
      So it will produce clusters of varying sizes rather than just testing for
      the presence of significant clustering at a fixed distance. It also tests
      the statistical significance of the clusters by running monte carlo
      simulations. So, I would say that is definitely the preferred software for
      your situation. I haven't used BoundarySeer -referred to Mathieu Philibert.

      I have had some experience with running SATScan so let me know of you'd
      any further help or references, etc.

      Regards Jo McKenzie

      Joanna McKenzie
      EpiCentre, Wool Building, Massey University
      Palmerston North, New Zealand
      Ph (06)3563554

      ----- Forwarded by Basil LOH/ENV/SINGOV on 30-10-2001 17:01 -----

      .cu To: Basil LOH/ENV/SINGOV@SINGOV
      26-10-2001 Subject: cluster software

      <color><param>0100,0100,0100</param>I suggest that you should contact with
      Gladys Casas in the
      Universidad Central de Villa Clara in Cuba, because I have seen the
      software she has developed for detecting time/spatial
      clusters,EPIDET, which is quite useful for this purpose, I personally
      have used it several times. Gladys email is


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