Seydou Doumbia, MD, PhD, Professor of Epidemiology, Department of Public Health

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Seydou Doumbia, MD, PhD, Professor of
Epidemiology, Department of Public Health
Deputy Director of NIAID/NIH Research Program at
Malaria Research Training Center, Faculty of
Medicine, University of Bamako, Mali
Putting non-parametric methods in the service of
public health
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INTRODUCTION

• Importance of forecasting
• Life has to be lived forward but can only be
  understand backward
• Basic and ultimate purposes of forecasting is to
  predict in the near term what will happen in
  order to avoid substantial cost or loss
• The cost of poor prediction may be the loss of
  soldiers in war, jobs in economy, profit in
  business
• With informed opinions on future probabilities
  the planner can mobilize and deploy necessary
  resources and reduce the substantial cost of
  miscalculation

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Introduction (CONTINUED)
Predicting infectious diseases can maximize
intervention impact and minimize cost
? The cost-benefit for an epidemiological
intervention may be measured a posteriori or
estimated a priori. Optimum predictions may
improve outcomes.
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• There are myriad predictive approaches in the
  statistical and mathematical epidemiology,
  ranging in complexity and generalizability.

• Most approaches are parametric and hence, often
  difficult to optimize, disease specific,
  sensitive to outliers, and setting dependent.

• A toolbox encapsulating general-purpose
  approaches, applicable to different diseases and
  settings, is needed.

• Thus, lets discuss a few unorthodox predictive
  approaches that may become part of such toolbox.

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Predicting infectious diseases

• ?Endemic, meso-endemic, or epidemic
• ?Multi- or uni-variate requirements
• ?Temporally or spatially-temporally extended

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Example 1 Non-parametric approach

• ?Exponential smoothing methods
• Econometric tradition (eg inventory control)
• Capture non-linearity for endemic and
  meso-endemic time-series (climates, geography,
  demography)
• Learn from experience (adapt to time-series
  perturbations)
• Usually univariate yet covariates may be
  introduced

• ?District of Niono, Mali
• Meso-endemic time-series Diarrhea, Acute
  Respiratory Infection, Malaria,
• Endemic time-series Schistosomiasis time-series
• Sub-optimum for epidemic time-series

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Irrigation system and stagnant water reservoirs
in the district of Niono, Mali.
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Observed diarrhea consultation rate time-series
are depicted as black lines while red and blue
traces correspond to contemporaneous 2- and
3-month horizon forecasts, respectively their
95 prediction interval bounds are symbolized by
dots of the same colors. Forecasts and prediction
interval bounds are calculated with a
bootstrap-coupled seasonal multiplicative
Holt-Winters method. Panel A 011 months Panel
B 14 years Panel C 515 years and, Panel D
gt15 years. Medina DC et al. (2007) Forecasting
Non-Stationary Diarrhea, Acute Respiratory
Infection, and Malaria Time-Series in Niono,
Mali. PLoS ONE 2(11) e1181.
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Observed ARI consultation rate time-series are
depicted as black lines while red and blue traces
correspond to contemporaneous 2- and 3-month
horizon forecasts, respectively their 95
prediction interval bounds are symbolized by dots
of the same colors. Forecasts and prediction
interval bounds are calculated with a
bootstrap-coupled seasonal multiplicative
Holt-Winters method. Panel A 011 months Panel
B 14 years Panel C 515 years and, Panel D
gt15 years. Medina DC et al. (2007) Forecasting
Non-Stationary Diarrhea, Acute Respiratory
Infection, and Malaria Time-Series in Niono,
Mali. PLoS ONE 2(11) e1181.
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Observed malaria consultation rate time-series
are depicted as black lines while red and blue
traces correspond to contemporaneous 2- and
3-month horizon forecasts, respectively their
95 prediction interval bounds are symbolized by
dots of the same colors. Forecasts and prediction
interval bounds are calculated with a
bootstrap-coupled seasonal multiplicative
Holt-Winters method. Panel A 011 months Panel
B 14 years Panel C 515 years and, Panel D
gt15 years. Medina DC et al. (2007) Forecasting
Non-Stationary Diarrhea, Acute Respiratory
Infection, and Malaria Time-Series in Niono,
Mali. PLoS ONE 2(11) e1181.
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Thus, SA3 degenerates faster than the MHW method
as the forecast horizon increases
Medina DC et al. (2007) Forecasting
Non-Stationary Diarrhea, Acute Respiratory
Infection, and Malaria Time-Series in Niono,
Mali. PLoS ONE 2(11) e1181.
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Observed Schistosoma haematobium consultation
rate time-series in the district of Niono, Mali,
are depicted as black lines in this composite
panel while red traces correspond to
contemporaneous h-month horizon forecasts 95
prediction interval bounds are symbolized by red
dots of the same color. Forecasts were generated
with exponential smoothing (ES) methods, which
are encapsulated within the state-space
forecasting framework. Panels A, B, C, and D
correspond to 2-, 3-, 4-, and 5-month horizon
forecasts, respectively. Medina DC et al. (2008)
StateSpace Forecasting of Schistosoma
haematobium Time-Series in Niono, Mali. PLoS Negl
Trop Dis 2(8) e276.
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Mean absolute percentage error (MAPE) values
between Schistosoma haematobium time-series
observations for the district of Niono, Mali, and
their corresponding h-month horizon forecasts
measure external accuracy. MAPE values for 15
month horizon forecasts were circa 25. Therefore,
this panel demonstrates that forecast accuracy is
reasonable for short horizons. Of note, MAPE
assesses the skill of h-month horizon forecasts.
Medina DC et al. (2008) StateSpace Forecasting
of Schistosoma haematobium Time-Series in Niono,
Mali. PLoS Negl Trop Dis 2(8) e276.
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Example 2 Knowledge-driven approach

• ?Fuzzy logic functions (e.g. trigonometric,
  weighted, etc)
• Engineering tradition
• Attempts to assign membership to an item with
  different degrees of certainty
• Knowledge- and or data-driven
• Capture non-linearity (climates, geography,
  demography)
• Learn from experience
• Usually multivariate
• Optimum for spatially extended system with scarce
  data

• ?African continent
• Rift Valley Fever

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Endemic suitability map for Rift Valley fever in
Africa based on ordered weighted averages
analysis. Suitability scores range from 0
(completely unsuitable) to 255 (completely
suitable). Clements et al. International Journal
of Health Geographics 2006 557
Epidemic suitability map for Rift Valley fever in
Africa based on ordered weighted averages
analysis. Suitability scores range from 0
(completely unsuitable) to 255 (completely
suitable).Clements et al. International Journal
of Health Geographics 2006 557
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Overlay of observed serological prevalence and
estimated endemic suitability for Rift Valley
fever in Senegal (ruminant). Suitability
estimates were derived using weighted linear
combination. Clements et al. International
Journal of Health Geographics 2006 557  
Overlay of observed serological prevalence and
estimated epidemic suitability for Rift Valley
fever in Senegal (ruminant). Suitability
estimates were derived using weighted linear
combination. Clements et al. International
Journal of Health Geographics 2006 557
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Example 3 Artificial Intelligence approach

• ?Support vector machines
• Artificial intelligence tradition Kernel
  methods, Support-vector Machines (regression,
  classification, anomaly detection), Neural
  networks
• Solve problems for which analytical treatment is
  lacking or intractable
• Capture non-linearity (climates, geography,
  demography)
• Learn from experience
• Usually univariate or multivariate
• Temporally or spatially-temporally extended

• ?Support Vector Regression (SVR)
• Kernel-Based ? transform data set into a linear
  space
• Large data sets ? automatic regularization
• Highly generalizeable

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Support vector machines is similar to
kernel-transforming a non-linear input data into
a linear high-dimensional feature space where
simple linear regression can be executed. The
output is always in the original dimension.
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• Somalia
• Ruminant IgG sero-prevalence
• Two-stage cluster-randomized serological survey
• Spatial estimates with SVR
• Built-in bootstrap for dispersion estimation

Figure 8. Spatial ruminant serological spatial
prevalence. Centrality and dispersion were
calculated via B 100 ordinary bootstraps of
multivariate observations, SVR-based
spatially-resolved prevalence estimation for each
re-sample, and finally computation of adequate
order statistics. A) median, B) maximum, C) IQR,
and D) minimum. Courtesy of Daniel Medina..
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Conclusion

• Non-parametric approaches may be applied to
  multiple diseases and settings without parametric
  disadvantages such as multi-colinearity and
  sensitivity to outliers.
• Although non-parametric approaches are like a
  black-box approach, they are robust, simply
  interpreted, and easily optimized.
• Fuzzy logic is ideal for spatially extended areas
  for which transmission is epidemic and or data
  are scarce. Thus, minimizing data collection
  needs.
• The general-purpose nature of non-parametric/fuzzy
  logic/artificial intelligence approaches implies
  that studies for multiple diseases and sites
  could be better compared
• Adequate predictions maximize intervention and
  minimize costs

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Acknowledgements
Thanks to the organizers, participants, Malaria
Research Training Center, Mali Columbia
University, US and the District Hospital of
Niono, Mali.