sunbelt conference workshop network modeling of infectious...
TRANSCRIPT
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Network Modeling of Infectious Disease and Social Diffusion Processes with EpiModel
Sunbelt Conference Workshop June 23, 2015
Samuel M. Jenness, PhD MPH University of Washington Department of Epidemiology
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Workshop Materials
http://statnet.github.io/sb/
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EpiModel Authors Samuel Jenness Steven Goodreau Martina Morris
EpiModel Contributors Li Wang Emily Beylerian
EpiModel Users!
Acknowledgements
Statnet Development Team Skye Bender-deMoll Carter Butts Mark Handcock David Hunter Pavel Krivitsky
Funding R00 HD057533 (NICHD) R01 HD68395 (NICHD) T32 HD007543 (NICHD) R24 HD042828 (NICHD)
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EpiModel
• EpiModel is an R software package
• Tools for simulation and analysis of epidemic models
• Supports three model classes - Deterministic compartmental models - Stochastic individual contact models - Stochastic network models
• http://epimodel.org/
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EpiModel
• EpiModel is an R software package
• Tools for simulation and analysis of epidemic models
• Supports three model classes - Deterministic compartmental models - Stochastic individual contact models - Stochastic network models
• http://epimodel.org/
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Workshop Goals
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• Introduce dynamic modeling over networks - Also called mathematical models or systems models
- Contrast with purely statistical models
• Provide hands-on experience using EpiModel software - Estimating statistical models for dynamic networks with temporal ERGMs
- Simulating infectious disease or social phenomenon on top of dynamic networks
• Explain methods to extend EpiModel for your research
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Statistical vs Mathematical Models
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Statistical Models • Start with data
• Choose functional framework for summarizing data
• Fit model to estimate parameters
• Infer population associations or casual effects
0 20 40 60 80 100
0100
200
300
400
500
x
y
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Statistical vs Mathematical Models
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Mathematical Models • Start with the parameters
• Construct the processes to get from micro to macro - Micro: Individual-level biology,
behavior, demography - Macro: Population-level disease
incidence and prevalence0 20 40 60 80 100
0.0
0.2
0.4
0.6
0.8
1.0
Time
Prevalence
s.numi.numr.num
Dynamic = Over Time
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Statistical vs Mathematical Models
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Prevalence
Risk
Incidence
Force of Infection (Rate of contacts) •
(Transmission probability per contact) •
(Probability contacting an infected)
The Epidemic Feedback Loop
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Statistical vs Mathematical Models
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Indirect Effects & Herd Immunity
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Statistical vs Mathematical Models
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Statistical vs Mathematical Models
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Stochastic Network Models • Collect egocentric network
data
• Fit a temporal ERGM with target statistics
• Simulate from that statistical model fit
• Construct the other epidemic or diffusion processes over network
Data
Statistical Model
Mathematical Model
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Introductions
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Please briefly introduce yourself
• Name, department, institution
• Exposure to and experience with:
- Statnet (sna, network, networkDynamic) for network analysis
- ERGMs and TERGMs for network modeling
- Dynamic/mathematical models
- The R programming language
• Related research project or interest
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Workshop Outline
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1. Lecture Introduction
2. Lecture From network data to temporal ERGMs
3. Tutorial An SIS epidemic in a closed population
4. Lecture Considerations for open populations
5. Tutorial An SI epidemic in an open population
6. Lab Adding heterogeneity & interventions
7. Lecture Extending EpiModel for novel research
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From Survey Data to Network Data
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• EpiModel depends on egocentric network data - Random sample of population
- Subjects queried on history of recent (sexual) partnerships
- Date of first and last contact, whether ongoing, with last three partners
- Subjects queried on attributes of those partnerships
• Summary statistics from survey data ➟ simulation of complete network consistent with those statistics - Fit ERGM with target statistics, simulate from that model fit
• A scalable, flexible, data generating model for dynamic networks
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Network Model Parameters
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Degree
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Network Model Parameters
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Assortative Mixing
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Network Model Parameters
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Dissortative Mixing
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Network Model Parameters
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Mixing on Multiple Levels
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Egocentric Inference
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1. Start with Target Population
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Egocentric Inference
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2. Sample Egos
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Egocentric Inference
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3. Query on Alters
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Egocentric Inference
4. Estimate Target Statistics
Stat Value# Edges 4
# Isolate nodes 1# Concurrent nodes 1Age homophily 1 yearShape homophily 2Color homophily 0
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Egocentric Inference
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5. Fit an ERGM with Target StatisticsStat Value# Edges 4# Isolate nodes 1# Concurrent nodes 1Age homophily 1 yearShape homophily 2Color homophily 0
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Egocentric Inference
5. Fit an ERGM with Target Statistics
formula = nw ~ edges + isolates + concurrent + absdiff(“age”) + nodematch(“shape”) + nodematch(“color”)
targets = c(4, 1, 1, 4*1, 2, 0)*100
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Egocentric Inference
6. Simulate from the Model
• MCMC-based simulation similar to that used in estimation
• Simulations generate one network cross-section
• Summary of network stats consistent on average with targets
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Egocentric Inference
7. Add Time!
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Egocentric Inference
7. Add Time!
• Incidence = prevalence / duration • STERGMs fit two ERGMs
- One for formation and one for persistence of edges
• Mean edge duration as fixed (offset) coefficient • Default EpiModel method bypasses full STERGM
- Uses cross-sectional ERGM with manual coefficient adjustment - The “Edges Dissolution Approximation”
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Workshop Outline
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1. Lecture Introduction
2. Lecture From network data to temporal ERGMs
3. Tutorial An SIS epidemic in a closed population
4. Lecture Considerations for open populations
5. Tutorial An SI epidemic in an open population
6. Lab Adding heterogeneity & interventions
7. Lecture Extending EpiModel for novel research
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Workshop Outline
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1. Lecture Introduction
2. Lecture From network data to temporal ERGMs
3. Tutorial An SIS epidemic in a closed population
4. Lecture Considerations for open populations
5. Tutorial An SI epidemic in an open population
6. Lab Adding heterogeneity & interventions
7. Lecture Extending EpiModel for novel research
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Independent vs Dependent Simulations
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• Independent simulations - Network structure does not depend on epidemiology, demography, or
other exogenous processes - The epidemiology still depends on network structure!
- Closed populations and fixed nodal attributes
• Dependent simulations - Network structure does depend on exogenous processes
- Open populations: births, deaths, and migration
- Time-varying attributes: disease status and aging
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Implication 1 Network Resimulation
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Independent Models
Network Simulation
t1 tn
Epidemic Simulation
t1 tn
Dependent Models
Net Epi
t1
• • •Net Epi
t2
Net Epi
t3
Net Epi
tn
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• What happens to mean degree when population size changes? - Growing population = growing mean degree
- Person moving from 10k town to 10k city increases degree by 10-fold
• EpiModel includes a edges coefficient adjustment as a function of population size
- Growing population = shrinking density, preserved mean degree
Implication 2 Formation Model Coefficient Adjustment
✓t2 = ✓t1 + log(Nt1)� log(Nt2)
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• STERGMs with demography - STERGMs assume a fixed node set where edge dissolution is endogenous
- Death is an exogenous method of edge dissolution
- Edge duration usually estimated on living populations
- Without adjustment, mean degree would fall below empirically observed
• Dissolution coefficient adjustment for deaths/exits - Increase the dissolution coefficients (really, edge persistence coefficients)
- Analytically solved for dyadic independent dissolution models
Implication 3 Dissolution Model Coefficient Adjustment
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Workshop Outline
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1. Lecture Introduction
2. Lecture From network data to temporal ERGMs
3. Tutorial An SIS epidemic in a closed population
4. Lecture Considerations for open populations
5. Tutorial An SI epidemic in an open population
6. Lab Adding heterogeneity & interventions
7. Lecture Extending EpiModel for novel research
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Workshop Outline
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1. Lecture Introduction
2. Lecture From network data to temporal ERGMs
3. Tutorial An SIS epidemic in a closed population
4. Lecture Considerations for open populations
5. Tutorial An SI epidemic in an open population
6. Lab Adding heterogeneity & interventions
7. Lecture Extending EpiModel for novel research
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Lab Adding Heterogeneity & Interventions
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• Working in small groups (2 to 3 people) for 30 - 45 minutes - Build off the examples in Tutorial 1 or Tutorial 2
- Use a different network model parameterization
- Model an SIR disease
- Explore different epidemic parameters or initial conditions: - Add an intervention to the model with the inter.eff and inter.start
parameters
- Try a bipartite network (this will be tough)
• Brief report back on findings
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Workshop Outline
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1. Lecture Introduction
2. Lecture From network data to temporal ERGMs
3. Tutorial An SIS epidemic in a closed population
4. Lecture Considerations for open populations
5. Tutorial An SI epidemic in an open population
6. Lab Adding heterogeneity & interventions
7. Lecture Extending EpiModel for novel research
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• Built-in models shown here are for teaching purposes - Epidemiology of real diseases much more complex
- Novel research questions require programming modules controlling mechanics of interest
• EpiModel has a “plug-n-play” API to write modules - Modules may replace existing modules: transmission, mortality, summary
statistics
- New modules may supplement existing modules: aging, disease progression, complex intervention
Extending EpiModel
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Extending EpiModel Resources
• Advanced Extension Models tutorials
• Network Modeling for Epidemics summer courses - Seattle and Belgium in 2015
• Email listserv
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http://epimodel.org/
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Scaling Up with EpiModelHPC
• Extension package for simulating network models on high-performance computing systems
• Designed for Linux-based OpenPBS systems like Moab or Torque
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http://github.com/statnet/EpiModelHPC
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• Extension modules for EpiModel specifically for modeling HIV infection - Modules geared towards heterosexual transmission in Sub-Saharan Africa
• Modules include: - Natural disease progression impact on CD4 and HIV viral load trajectories
- Inter-host transmission risk dependent on disease stage and VL
- Anti-retroviral therapy treatment
• Modules expanded for modeling HIV in MSM next
Coming Soon… EpiModelHIV
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Infectious Diseases & Social Networks Session 10:40 – Noon, Thursday @ Viscount Room
• Deven Hamilton. A Dynamic Transmission Network Simulation Study on the Impact of Assortative Mixing, Concurrency, and the Mitigating Impact of Coital Dilution on the Racial Disparities in the STIs in the United States.
• Samuel Jenness. Effectiveness of Male Circumcision for HIV-1 Prevention Depends on Contact Network Structure.
Research Presentations @ Sunbelt