Analyzing Landmine Incidents via ZeroInflated Poisson Models - PowerPoint PPT Presentation

Title: Analyzing Landmine Incidents via ZeroInflated Poisson Models


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Analyzing Landmine Incidents via Zero-Inflated
Poisson Models

• Lawrence H. Moulton
• www.larrymoulton.com
• Departments of International Health and
  Biostatistics
• Johns Hopkins Bloomberg School of Public Health
• Aldo A. Benini, Charles E. Conley, Shawn Messick
  Survey Action Center, Global Landmine Survey

APHA Annual Meetings, Atlanta, October 2001
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Introduction Global Landmine Survey

• Survey Task
• To conduct nationwide, community-level
  assessments of minefield locations and impact on
  local citizens in countries with significant
  landmine hazards 
• Survey Organization
• Formed by the Survey Working Group, a
  collaboration among the United Nations Mine
  Action Service, the Geneva International Centre
  for Humanitarian Demining, the Vietnam Veterans
  of America Foundation, and many other NGOs.
• The Survey Action Center implements the GLS
  in countries, sending advance missions,
  organizing funds and personnel, devising data
  collection instruments, providing GIS support

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Global Landmine Survey Chad

• SAC subcontracted to Handicap International/Franc
  e
• Marc Lucet, Team Leader
• UN Office for Project Services provided Quality
  Assurance Monitor
• Survey implemented Q4, 2000

4
Core Data Collected

•  
• Survey team data
• General location data
• Terrain/geographic data
• Accessibility data
• Infrastructure data, including victim
  rehabilitation service data
• Historical conflict data
• Minefield/UXO location data
• Mine/UXO recognition and technical data
• Informant source data
• Social-economic data
• Mine victim/ accident data
• Behavioral data
• Qualitative observations of surveyors to
  provide clarity to quantitative data collected
  in the field

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Chad Flow of Surveyed Communities
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Period When Mines / UXO Last Emplaced
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Victims by Type and Period
Victims



Communities
All


involved

Killed

Injured

Period





Recent victims

102

122

217

339

Victims of less recent date

154

703

646

1,349

All victims

180

8
25

863

1,688

Had no victims

69

-

-

-


8
Recent Victims Per Community
.6
.4
Fraction
.2
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Total Recent Victims
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Zero-Inflated Poisson Model (ZIP)
First publication of regression model D Lambert
Technometrics 1992 Notation here similar to that
used by Stata
Two linear predictors For Poisson regression
component, have For logistic regression
component, have where I denotes the ith
district.
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ZIP Log-Likelihood Function

• The inverse link function for the logit is
• which distinguishes the mixture of the two
  distributions
• (Poisson and point distribution at zero, P is
  prob of latter),
• and the inverse log link for the Poisson
  component is
• With this notation, and with S the obsns with
  count yi0,

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Chad Model Variables

• Dependent Total victims in a community in prior
  2 yrs
• Explanatory
• WATER blockage of drinking water
• HOUSE blockage of housing
• PASTURE blockage of fixed pasture
• BACKROADS blockage of non-admin center roads
• UXO has unexploded ordnance
• LAST2YR mine/UXO emplacement in last 2
  years
• L10POP log10(current population)
• L10AREAPERP log10(contaminated
  area(m2)/person)
• L10DISTAFF log10(distance(km)nearest comm.
  w/victim)
• NORTH dummy for northern region

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Results of ZIP Fit to Chad Data

•  
• Poisson IRR Pgtz 95 CI
• ----------------------------------------------
• WATER 1.35 0.041 1.01 1.80
• HOUSE 1.31 0.085 0.96 1.79
• L10POP 1.36 0.017 1.06 1.74
• L10AREAPERP 1.05 0.009 1.01 1.08
• LAST2YR 0.96 0.002 0.93 0.98
• ----------------------------------------------
•  
• Zero-inflation OR
• ----------------------------------------------
• PASTURE 0.20 0.000 0.079 0.48
• BACKROADS 0.084 0.002 0.017 0.41
• UXO 0.040 0.004 0.0046 0.35
• L10POP 0.23 0.002 0.090 0.60
• L10DISTAFF 2.14 0.031 1.07 4.26
• NORTH 0.24 0.005 0.086 0.65
•  

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Observed-Expected Distribution
100
Frequency
50
0
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
9
Round(O-E)
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Raw Residuals (O-E) From Similar ZIP Model
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Fitted Splines for Log10Population
Inflation Component
Poisson Component
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ZIP Fit for Thai-Cambodia Border Data

•  
• Poisson IRR Pgtz 95 CI
• ----------------------------------------------
• WATER 1.43 0.021 1.06 1.93
• HOUSE 1.53 0.043 1.01 2.32
• L10POP 1.93 0.002 1.27 2.92
• L10AREAPERP 1.37 0.001 1.14 1.65
• LAST2YR 0.44 lt0.001 0.31 0.64
• L10DISTBORD 0.52 lt0.001 0.39 0.69
• ----------------------------------------------
•  
• Zero-inflation OR
• ----------------------------------------------
• PASTURE 0.55 0.055 0.30 1.01
• BACKROADS 0.75 0.683 0.19 2.97
• UXO 0.51 0.054 0.26 1.01
• L10POP 0.45 0.067 0.19 1.06
• L10DISTAFF 4.03 lt0.001 2.33 6.97
• LAST2YR 2.35 0.059 0.97 5.70

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Summary

• Zero-inflated count models can be appropriate for
  injury data
• Flexibility of using a mixture of two populations
  and two covariate vectors can be useful for
  landmine victim data modeling
• At the community level, offsetting person-years
  may not always be the right thing to do
• Common, important physical factors affect
  landmine injury rates