Analyzing Landmine Incidents via Zero-Inflated Poisson Models

Lawrence H. Moultonwww.larrymoulton.com

Departments of International Health and BiostatisticsJohns 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

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…

Global Landmine Survey: Chad

SAC subcontracted to Handicap International/France Marc Lucet, Team Leader

UN Office for Project Services provided Quality Assurance Monitor

Survey implemented Q4, 2000

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

Chad: Flow of Surveyed CommunitiesAll communities in

137 suspected territorial units; 9,905 entries in

locality dictionary

Suspected loc.: 1,361

(618 by experts; 743 full enum.)

Not suspected: 8,861

False positives among expert-

design. loc.:457

Sampled and visited:

932

False positives in full-enum.

areas:665

True negatives:922

False negatives:

10

True positives:239

249 Total Affected

Communities

Period When Mines / UXO Last Emplaced

Victims by Type and Period

Victims

Communities involved Killed Injured All

Period Recent victims 102 122 217 339

Victims of less recent date 154 703 646 1,349 All victims 180 825 863 1,688

Had no victims 69 - - -

Recent Victims Per CommunityF

ract

ion

Total Recent Victims0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

0

.2

.4

.6

Zero-Inflated Poisson Model (ZIP)First publication of regression model: D Lambert Technometrics 1992Notation 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.

zi i

xi i

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 yi=0,

( ) exp( ) /(1 exp( ))P

exp( )i i

log ln[ ( ) (1 ( ))exp( )]lik P Pi i ii S

[ln(1 ( )) ln( !)]P y

i i i i ii S

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

Results of ZIP Fit to Chad Data

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

Observed-Expected DistributionF

requ

ency

Round(O-E)-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

0

50

100

Raw Residuals (O-E)From Similar ZIP Model

Fitted Splines for Log10PopulationLo

g O

dds

(Z

ero

Infla

tion)

Log10 Current population1 2 3 4

0

2

4

6

8

Log

Rat

e R

atio

for

Vic

tims

Log10 Current population1 2 3 4

0

.5

1

1.5

Inflation Component Poisson Component

ZIP Fit for Thai-Cambodia Border Data Poisson | IRR P>|z| [95% CI]-------------+---------------------------------WATER | 1.43 0.021 1.06 1.93HOUSE | 1.53 0.043 1.01 2.32L10POP | 1.93 0.002 1.27 2.92L10AREAPERP | 1.37 0.001 1.14 1.65LAST2YR | 0.44 <0.001 0.31 0.64L10DISTBORD | 0.52 <0.001 0.39 0.69----+------------------------------------------ Zero-inflation OR-------------+---------------------------------PASTURE | 0.55 0.055 0.30 1.01BACKROADS | 0.75 0.683 0.19 2.97UXO | 0.51 0.054 0.26 1.01L10POP | 0.45 0.067 0.19 1.06L10DISTAFF | 4.03 <0.001 2.33 6.97LAST2YR | 2.35 0.059 0.97 5.70 

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