Analyzing Landmine Incidents via Zero-Inflated Poisson Models Lawrence

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

Introduction: Global Landmine 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 Ø SAC subcontracted to Handicap International/France Marc Lucet, Team Leader Ø UN Office for Project Services provided Quality Assurance Monitor Ø Survey implemented Q 4, 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 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 Community. 6 Fraction . 4 . 2 0 0 1 2 3 4 5 6 7 8 9 10 Total Recent Victims 11 12 13 14 15

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.

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,

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 LAST 2 YR mine/UXO emplacement in last 2 years L 10 POP log 10(current population) L 10 AREAPERP log 10(contaminated area(m 2)/person) L 10 DISTAFF log 10(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. 80 HOUSE | 1. 31 0. 085 0. 96 1. 79 L 10 POP | 1. 36 0. 017 1. 06 1. 74 L 10 AREAPERP | 1. 05 0. 009 1. 01 1. 08 LAST 2 YR | 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. 0046 0. 35 L 10 POP | 0. 23 0. 002 0. 090 0. 60 L 10 DISTAFF | 2. 14 0. 031 1. 07 4. 26 NORTH | 0. 24 0. 005 0. 086 0. 65

Observed-Expected Distribution Frequency 100 50 0 -4 -3 -2 -1 0 1 2 3 Round(O-E) 4 5 6 7 8 9

Raw Residuals (O-E) From Similar ZIP Model

Fitted Splines for Log 10 Population Inflation Component Poisson Component 1. 5 Log Rate Ratio for Victims Log Odds (Zero Inflation) 8 6 4 2 1 . 5 0 0 1 2 3 Log 10 Current population 4

ZIP Fit for Thai-Cambodia Border Data Poisson | IRR P>|z| [95% CI] -------+----------------WATER | 1. 43 0. 021 1. 06 1. 93 HOUSE | 1. 53 0. 043 1. 01 2. 32 L 10 POP | 1. 93 0. 002 1. 27 2. 92 L 10 AREAPERP | 1. 37 0. 001 1. 14 1. 65 LAST 2 YR | 0. 44 <0. 001 0. 31 0. 64 L 10 DISTBORD | 0. 52 <0. 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 L 10 POP | 0. 45 0. 067 0. 19 1. 06 L 10 DISTAFF | 4. 03 <0. 001 2. 33 6. 97 LAST 2 YR | 2. 35 0. 059 0. 97 5. 70

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