Modeling the effect of distance from a hydro-electric dam on malaria incidence based on frailty & mixed Poisson regression

models

Department of Comparative Physiology and Biometrics

Yehenew Getachew and Luc Duchateau

• Malaria: epidemiology and burden• Data structure and survival analysis• Modeling:

o standard modelso mixed Poisson & frailty modelso different Cox models and confounding

• Concluding remarks and future research

Outline

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Malaria

• Life-threatening • caused by Plasmodium

parasite

• P. falciparum(70%)• P. vivax (30%)• P. ovale • P. malariae

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Malaria status: worldwide, Africa &

Eth• In 2010:

o 3.3 billion people at risko 1.24 million died worldwide

• In Africa:o leading

cause of U5 mortality • 68% live in malaria risk

areas• leading cause of

morbidity & mortality• malaria is seasonal with

unstable transmission

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• Involves a complex interaction• Plasmodium parasites (causative agent) • female Anopheles mosquitoes (vector) • humans (host)

Malaria transmision

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In Ethiopia:o An. arabiensis o An. gambiaeo An. funestus

The vector (mosquito: Anopheles spp.)

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

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• Eth has built several mega dams:o for hydropower generation, irrigation and flood control

Dams and malaria in Ethiopia

Operational:• Gibe I (Gilgel Gibe):

• 184MW• Gibe II:

• 420MW

Under construction:• Gibe III:

• 1870MW• Great renaissance:

• 6000MW

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Pre-dam construction(baseline data)

Dam, mosquito and malaria

Post-dam construction

• No baseline data:o for Gilgel Gibe

• Baseline:o Gibe III

HH distance from GG dam &

malaria incidence

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Ethiopia, Jimma zone & GG dam

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Distance from Village center

HH distance

Time-to-event (malaria)

• 2082 children• 16 villages• 2 years• Weekly basis

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Dataset

Dataset I: Time to event (malaria)

Dataset II: Mosquito count data

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Mixed Poisson

and

frailty models

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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

Aggregating time to malaria data

Year1 – Season1r0-r1

Time-cens-covVillage

1

.

.

.

16

, , …,

,

𝒙𝟏 ,.

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, …,

…

𝒙𝟏6 ,.

…

Year2 – Season3r5-r6

… ,

…

… ,

…

…

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Mixed Poisson regression model

iikikik wη)log(a)log(ξ

)σ(0,~w 2pi N

i.dks3,s3ks2,s2yky0ik xβxβxβxββη

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Frailty model

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1kij )(I)exp()(h k1-kiijk rtruλt

)σ(0,~u 2fi N

ijdks3,s3ks2,s2yky0 xxxx ijk

• Time to event more efficient approach ? use detailed information in data

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Mean versus individual distance

Risk dist Hazard dist

Replace i.ij xx Exactly same

IRR=1.06 HR=0.96

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Equivalence: frailty & mixed Poisson

Getachew et al., SIM 2013

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1k

)(I)exp()( k1-kiijkij rtruλth

i.dks3,s3ks2,s2yky0 xxxx

iikikik wη)log(a)log(ξ

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ika Keeping the SAME VALUEo things can be done differently

• Assumptions: PWC baseline hazard & o equivalence

• What matters: total time at risk per village–period

Equivalence consequences

Child 1

Child 2 Child 2 Child 1

Child 3 Child 4

Weekly follow-up Monthly follow-up

• Question: is that important to have LARGE value?

Less fatigue

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Assessing individual distance effect:

various Cox survival models

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Confounding

Most of the variation in distance is to a large extent explained by the village• village is correlated to distance

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Conditional models

Marginal model

Frailty model

Change in direction

Results

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Extended BW frailty model

• Distance: 2-orthogonal.ix

.ixxd ijij

)exp()(h)(h 0ij ibi.wij wβxβdtt

),0(N)(~ 2iwi σwfw

)seβw 075.0(116.0ˆ

Result: malaria data

)seβb 233.0(072.0ˆ

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Conclusion: study III• Contradictory results:

o 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

o weighted combination of the within & between

• Makes only sense: if the same relationship holdso questionable in our situation

• There are cases: scientific interest focuses on cluster level effects

• In such situation: o covariate splitting, is one option

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• Time varying covariates: