1. Department of Comparative Physiology and Biometrics
Modeling the effect of distance from a hydro-electric dam on malaria incidence based on frailty & mixed Poisson regression models
Yehenew Getachew and
Luc Duchateau
Department of Comparative Physiology and Biometrics

2. Outline Malaria: epidemiology and burden
Data structure and survival analysis
Modeling:
standard models
mixed Poisson & frailty models
different Cox models and confounding
Concluding remarks and future research

3. Malaria Life-threatening caused by Plasmodium parasite
P. falciparum (70%)
P. vivax (30%)
P. ovale
P. malariae

4. Malaria status: worldwide, Africa & Eth
In 2010:
3.3 billion people at risk
1.24 million died worldwide
In Africa:
leading cause of U5 mortality
68% live in malaria risk areas
leading cause of morbidity & mortality
malaria is seasonal with unstable transmission

5. Malaria transmision Involves a complex interaction
Plasmodium parasites (causative agent)
female Anopheles mosquitoes (vector)
humans (host)

6. The vector (mosquito: Anopheles spp.)
In Ethiopia:
An. arabiensis
An. gambiae
An. funestus
Breeding behaviour
Non or slow flowing water bodies unaffected by waves
lakes, dams, irrigation water, hoof print, etc
Construction of dams:
resulted in creation of suitable breeding habitats
favorable microclimate

7. Dams and malaria in Ethiopia
Eth has built several mega dams:
for hydropower generation, irrigation and flood control
Operational:
Gibe I (Gilgel Gibe):
184MW
Gibe II:
420MW
Under construction:
Gibe III:
1870MW
Great renaissance:
6000MW

8. Dam, mosquito and malaria
Pre-dam construction
(baseline data)
Post-dam construction
HH distance from GG dam
&
malaria incidence
No baseline data:
for Gilgel Gibe
Baseline:
Gibe III

9. Ethiopia, Jimma zone & GG dam

10. Time-to-event (malaria)
2082 children
16 villages
2 years
Weekly basis
HH distance
Distance from
Village center
Time-to-event (malaria)

11. Dataset Dataset I: Time to event (malaria)
Dataset II: Mosquito count data

12. Mixed Poisson
and
frailty models

13. Mixed Poisson & frailty models
Time to event  more efficient approach ?
 use the most detailed information
The standard  mixed Poisson models
 counts
Aggregation:
Time: period
Space: village

14. Aggregating time to malaria data
Village
Time-cens-cov
Year1 – Season1
r0-r1
Year2 – Season3
r5-r6 …
𝒅 𝟏,𝟔 , 𝒂 𝟏,𝟔
𝒅 𝟏𝟔,𝟔 , 𝒂 𝟏𝟔,𝟔
𝒚 𝟏,𝟏 , 𝜹 𝟏𝟏 , 𝒙 𝟏,𝟏 …
𝒚 𝟏,𝒏𝟏 , 𝜹 𝟏𝒏𝟏 , 𝒙 𝟏,𝒏𝟏
𝒅 𝟏,𝟏 , 𝒂 𝟏,𝟏
𝒙 𝟏,. 1 . 16 … …
𝒚 𝟏𝟔,𝟏 , 𝜹 𝟏6,𝟏 , 𝒙 𝟏6,𝟏 …
𝒚 𝟏6,𝒏𝟏6 , 𝜹 𝟏6,𝒏𝟏6 , 𝒙 𝟏6,𝒏𝟏6
𝒅 𝟏𝟔,𝟏 , 𝒂 𝟏𝟔,𝟏
𝒙 𝟏6,.

15. Mixed Poisson regression model

16. Frailty model Time to event  more efficient approach ?
 use detailed information in data

17. Mean versus individual distance
HR=0.96
IRR=1.06
Risk dist
Hazard dist
Exactly same
Replace

18. Equivalence: frailty & mixed Poisson
Getachew et al., SIM 2013

19. Equivalence consequences
Assumptions: PWC baseline hazard & 𝑥 𝑖𝑗 ≈ 𝑥 𝑖.
equivalence
What matters: total time at risk per village–period
Keeping the SAME VALUE
things can be done differently
Weekly follow-up
Monthly follow-up
Child 2
Child 1
Child 3
Child 4
Child 1
Child 2
Less fatigue
Question: is that important to have LARGE 𝑎 𝑖𝑘 value?

20. Assessing individual distance effect: various Cox survival models

21. Confounding
Most of the variation in distance is to a large extent explained by the village
village is correlated to distance

22. Results Marginal model Conditional models Frailty model
Change in direction
Conditional models
Frailty
model

23. Extended BW frailty model
Distance: 2-orthogonal
Result: malaria data

24. Conclusion: study III Contradictory results:
various Cox models that cope with clustering.. CONFOUNDING
Marginal model  overall distance effect is studied
Fixed effects & stratified model within distance effect
Frailty model  combines these two approaches
weighted combination of the within & between
Makes only sense: if the same relationship holds
questionable in our situation
There are cases: scientific interest focuses on cluster level effects
In such situation:
covariate splitting, is one option

25. Time varying covariates: