• Overview:

  Funded by NCI, Gamma is software for statistical inference from spatial data such as that used in Geographic Information Systems. It uses location models and spatial Monte Carlo methods to fully specify the spatial sampling space. This provides three capabilities:

  1. it greatly increases our ability to make correct statistical inferences;
  2. it accounts for positional uncertainty in spatial data; and
  3. it allows confidentiality (e.g. place of residence) to be preserved without compromising health analysis (e.g. cluster investigations).

  Gamma software is currently under development at BioMedware, although it will soon be released commercially. It has been used heavily by students in the past: for example,

  • Pia McDonald used Gamma to create a statistic based on distance point-line when she studied malaria and the impact on distance from housing to streams and rivers;
  • Maria da Conceicao-Saraiva used Gamma to study periodontal disease: does periodontal disease occur symmetrically in the mouth, or does it show a predisposition to occur on one side (perhaps related to handed-ness)?
  One of the advantages of Gamma is the flexibility it permits in creating the proper combination of geometry (proximity, in Gamma's terms - the relationship between spatial coordinates), and distance in the variables of interest (distance).

• Objectives:

  You (and a partner, if possible!) will work through exercises demonstrating several different proximity and distance metrics. In the final exercise you will use Gamma to analyze a putative clustering of breast cancer cases by calculating your own custom spatial statistic (Gamma product) and comparing it to an appropriate empirical distribution.

• Instructions:
  

  1. Find a partner!

  2. If you do not own a copy of Gamma, then you will need to download the demo version:

     UMich Students: save gamma.zip and extract Gamma to c:\temp

     Download the Gamma software and extract it using WinZip (if necessary, download WinZip):

     • save gamma.zip to your computer
     • double click on the file gamma.zip
     • click the Extract button
     • choose the C:\temp directory (for example),
     • create a new folder - e.g. gamma - and hit the extract button.

  3. Run Gamma.

     UMich students: The demo version is a time-expiring executable; that is, it is good for a limited time only (sound like a commercial?). You can use this copy of Gamma to do your project analysis, or download another copy at any time. The password required to run this beta version is epid624.

  4. Review section 3.6 and complete Exercises 3-1, 3-2, 3-5, and 3-6 using Gamma.

  5. Review section 4.9 and complete Exercises 4-1.

  6. Concerned citizens from a local subdivision contact you regarding a possible cluster of breast cancer in their community. They provide you with the data set breastca.pnt. This data set contains x, y coordinates of homes and a case control id. Cases are coded as 1 and controls are coded as 0. Using the Gamma software, analyze these data to determine whether breast cancer cases are spatially clustered relative to the controls.

     You will need to (finally!) compute your gamma statistic by generating some Monte Carlo runs (so far, you've breezed past the Monte Carlo screen). Proceed as you did for the previous examples:

     1. Start a new session
     2. Set the coordinate type
     3. Choose the data file
     4. Choose distance metric
     5. Choose proximity metric
     6. Skip a couple of screens (Exchangeability and Location);
     7. Set the Monte Carlo runs at 1000
     8. When you reach the output window, do two things from the menus:
        • View -> View Output Session Window, and
        • Plot -> Distribution

     Interpret your results. Did you make good choices of Proximity and Distance metrics? Can you do better? What does the p-value mean?

  7. Finally, don't forget to evaluate this lab. Geoff Jacquez will be especially interested in your comments concerning Gamma, as BioMedware produces and maintains Gamma. Your comments may help him to improve Gamma.

UMich Students: A note for your projects: Gamma does not yet read in ArcView shape files, so you'll need to convert them to Atlas bna files first. If you need help with this, let your instructors know.

1. Jacquez (In prep). Spatial Randomization and Statistical Inference. Chapter 1: Spatial data and statistical inference (complete).
2. Cliff, A. D. and J. Ord. Spatial Processes: Models and Applications. Pion Limited, London. 1981. Chapter 4, pp. 86-99.

1. Jacquez (In prep). Spatial Randomization and Statistical Inference. Chapter 2: Spatial statistics as gamma products, section 2.2., 2.3b.
2. Mollison, D. and K. Kuulasmaa. 1985. Spatial Epidemic Models: Theory and Simulations. In: Population Dynamics of Rabies in Wildlife. Ed. P. J. Bacon. Academic Press.

• Gamma data sets.

• Andy's summary of his presentation.
• More on distributions:
  • the poisson
  • a probabilist's perspective on the negative binomial
  • the binomial
• Geoff Jacquez's Rabies simulation.
• For those who speak French, here's something that may interest you:
  "This software analyses the frequencies of hosts (including vectors) versus their parasite load. It is based on the Negative Binomial Distribution. When the frequency of zero-parasites is composite (false and true negatives), as frequently occurs in natural situations, the zero-Truncated Binomial Distribution is also used. In both cases the maximum likelihood method is used. A program allows to compare the aggregation of several observed distributions. Simulation of a mixture of NB processes is also implemented.
  This software was successfully applied to falciparum oocystes (1) and gametocytes (in press) counts in vectors."
• A little on Poisson modelling.
• A general statistics course on-line. On a similar vein, try Statistics at Square One