Selecting the “Best” Food Fortification Plan
∗
∗
∗∗
Dave Osthus , Alicia Carriquiry and Todd Campbell
∗
Department of Statistics, Iowa State University
∗∗
Center for Agricultural and Rural Development, Iowa State University
ICDAM 8, May 14 - 17, 2012
Food Fortification Plan Goal:
• Reduce the proportion of the population
with inadequate/excessive nutrient consumption, at a reasonable cost
Our Objective:
• Propose a method to select the optimal amount of nutrient to add to a set
of promising vehicles so that a target
prevalence of inadequacy/excess in the
population can be met, at minimal cost
(i.e. select the “best” plan)
Food Fortification Plan Considerations
Considerations for selecting a food fortification plan:
1. Select a goal for nutrient inadequacy/excess in the target population
(e.g. inadequacies and excesses not to
exceed 5%, respectively)
2. Select candidate food vehicles for food
fortification
3. Determine food fortification limits for
each food vehicle
4. Select the amount of fortificant to add to
each food vehicle
The fourth step defines a fortification plan
Approaches to Plan Selection
Current Approach:
Manually select candidate food fortification
plan. Check to see if the plan effectively
achieves the goal. Drawbacks of this approach
include:
1. Guess and check
2. Time consuming
3. Cost of plan not considered
Our Approach:
For a given goal, automatically select the food
fortification plan, amongst all possible plans,
that achieves the goal for minimal cost. Steps
to execute our approach:
1. Select candidate food fortification plans
2. Estimate prevalence of nutrient inadequacy/excess under fortification, via the
methodology proposed by Nusser et. al.,
1996
3. Amongst candidate plans, employ a
genetic search algorithm to propose new
and better candidate plans
Repeat steps 2 and 3 until convergence.
Acknowledgments
Thanks to the NIH for supporting this work, to
the IFPRI for the use of these data and to Dr.
Omar Dary of the Academy of Education Development for his valuable insight throughout
this process.
• Data provided by International Food Policy Research Institute (IFPRI)
density
• 437 children between 6 and 24 months from
Uganda
Estimated Usual Intake Distribution for Vitamin A
Baseline
0.005
0.004
0.003
0.002
0.001
0.000
Bad
0
200
Good
400
600
800
Vitamin A Consumption (µg RAE/day)
• 24-hr recall
Estimated Usual Intake Distribution for Retinol
Baseline
• Vitamin A (µg RAE) and retinol (µg)
• Estimated prevalence of vitamin A inadequacy (αP oI ); 93%
• Estimated prevalence of retinol excess
(αP oE ); 0%
density
Typical Food Fortification Plan:
• One or more nutrients are added to food
vehicles in order to increase the supply of
the nutrient in the population
Data Collection and Description
0.008
0.006
0.004
0.002
0.000
Good
0
200
Bad
400
600
800
Retinol Consumption (µg/day)
Assumption: Retinol consumption was 60% of the total vitamin A consumption
Objective Function
Objective Function
f (γ1 , γ2 , . . . , γK ) =
K
X
(ck ∗ γk ) + λ[|αP oI − βP oI | + |αP oE − βP oE |]
k=1
Notation
• γk : Additional amount of nutrient added to one unit of food vehicle k, k ∈ {1, 2, . . . , K} and
γk ∈ [0, fortification limit for food vehicle k]
• ck : Cost to add one unit of nutrient to one unit of food vehicle k, ck ≥ 0
• αP oI : Estimated proportion of individuals in a population with usual daily nutrient consumption below the estimated average requirement (EAR), a function of γk
• αP oE : Estimated proportion of individuals in a population with usual daily nutrient consumption above the tolerable upper limit (UL), a function of γk
• βP oI : Goal for αP oI
• βP oE : Goal for αP oE
• λ: A large number (e.g. 1, 000, 000). A penalty for selecting a plan that does not meet the
prevalence of inadequacy/excess goals
Note: Minimization of the objective function f (γ1 , γ2 , . . . , γK ) is analytically intractable, thus a genetic search algorithm is employed
Prevalence of Adequacy vs. Cost Graph
Prevalence of Nutrient Adequacy vs. Cost
Prevalence of Excess
Prevalence of Nutrient Adequacy
Introduction
Prevalence of Inadequacy
1.0
0.8
Nutrient
1 − PoI
0.6
1 − PoE
Confidence_Bands
0.4
Actual Data
95% Confidence Bands
0.2
20
25
30
35
20
25
30
35
Cost ($/Metric Ton)
We claim the above graph will be a useful tool in selecting the “best” fortification plan. That is, for
a given cost, the above graph tells you the best possible prevalence of adequacy for retinol (left)
or the best possible prevalence of adequacy for vitamin A (right). The dashed lines represent 95%
confidence limits based on 500 bootstrap samples.
For Further Information
Please contact dosthus@iastate.edu.
More information
http://www.public.iastate.edu/ dosthus/research.html.
can
be
obtained
at