Sexual Network Constraints on STD Flow

1
Sexual Network Constraints on STD Flow The role
of Sexual Networks in HIV spread
by
James Moody The Ohio State University Presente
d at The UNC Center for Aids Research
Conference Methods of Study in Human Sexuality
Relevance to AIDS Research Chapel Hill, May 5,
2001
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Overview

• I. Introduction
• Why networks matter
• Basic network data types
• II. Network Topology
• Mixing Patterns in ego networks
• Reachability properties
• Location properties
• III. Timing Sexual Networks
• Network Development
• Directional Constraint
• IV. Problems, Limitations Future Directions
• Data, Data, Data
• Linking non-sexual relations to sexual networks
• Sampling, Simulation Estimation
• VI. Conclusion

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Why Networks Matter

• Intuitive STDs travel through intimate
  interpersonal contact
• We should do better explaining disease spread if
  we take this into account.
• Less intuitive The pattern of intimate contact
  can have global effects on disease spread that
  could not be detected looking only at individual
  behavior.
• Work making this point
• Klovdahl, A. S. 1985. "Social Networks and the
  Spread of Infectious Diseases The AIDS Example."
  Social Science Medicine 211203-16.
• Morris, M. 1993. "Epidemiology and Social
  Networks Modeling Structured Diffusion."
  Sociological Methods and Research 2299-126.
• Rothenberg, et al. 1997 Using Social Network
  and Ethnographic Tools to Evaluate Syphilis
  Transmission Sexually Transmitted Diseases 25
  154-160

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Basic network data

• People treated as nodes, relations (sex or drug
  use) as lines among nodes.
• Network data are represented in multiple, often
  unfamiliar, ways
• Graphical
• - Often intuitive, but cumbersome to work with
  beyond intuition
• Adjacency Matrix
• - An n by n matrix, X, where Xij 1 if i has had
  sex w. j
• - Can also be valued, with Xij k, where k is a
  count
• Adjacency List
• - An n row list of each actors relations
• - Contains the row information of X
• Edge List
• - An m row list of sender receiver and value of
  the relation
• - Contains each element of X

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Basic network data

• Types of network data
• Ego-network
• Have data on a respondent (ego) and their reports
  of people they are connected to (alters).
• May include estimates of connections among alters
• National Health and Social Life Survey, Laumann
  et al.
• Partial network
• Ego networks plus some amount of tracing to reach
  partners of partners.
• Something less than full account of connections
  among all pairs of actors in the relevant
  population
• Colorado Springs, Potterat, Rothenberg, et al.
• Urban and Rural Networks Project (Trotter,
  Rothenberg, et al.)
• Complete (Udry, Bearman, et al.)
• Data on all actors within a particular (relevant)
  boundary
• Never exactly complete

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Examples linked levels of data
Respondent
Partner
Primary Relation
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Why Sexual Networks Matter
Consider the following (much simplified) scenario

• Probability that actor i infects actor j (pij)is
  a constant over all relations 0.6
• S T are connected through the following
  structure

S
T

• The probability that S infects T through either
  path would be 0.09

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Probability of infection over independent paths

• The probability that an infectious agent travels
  from i to j is assumed constant at pij.
• The probability that infection passes through
  multiple links (i to j, and from j to k) is the
  joint probability of each (link1 and link2 and
  link k) pijd where d is the path distance.
• To calculate the probability of infection passing
  through multiple paths, use the compliment of it
  not passing through any paths. The probability
  of not passing through path l is 1-pijd, and thus
  the probability of not passing through any path
  is (1-pijd)k, where k is the number of paths
• Thus, the probability of i infecting j given k
  independent paths is

Why matter
Distance
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Probability of infection over non-independent
paths
- To get the probability that I infects j given
that paths intersect at 4, I calculate
Using the independent paths formula.
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Why Sexual Networks Matter
Now consider the following (similar?) scenario
S
T

• Every actor but one has the exact same number of
  partners
• The category-to-category mixing is identical
• The distance from S to T is the same (7 steps)
• S and T have not changed their behavior
• Their partners partners have the same behavior
• But the probability of an infection moving from S
  to T is
• 0.148
• Different outcomes different potentials for
  intervention

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Network Topology Ego Networks
Mixing Matters

• The most commonly collected network data are
  ego-centered. While limited in the structural
  features, these do provide useful information on
  broad mixing patterns relationship timing.
• Consider Laumann Youms (1998) treatment of
  sexual mixing by race and activity level, using
  data from the NHSLS, to explain the differences
  in STD rates by race
• They find that two factors can largely explain
  the difference in STD rates
• Intraracially, low activity African Americans are
  much more likely to have sex with high activity
  African Americans than are whites
• Interracially, sexual networks tend to be
  contained within race, slowing spread between
  races

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Network Topology Ego Networks

• In addition to general category mixing,
  ego-network data can provide important
  information on
• Local clustering (if there are relations among
  egos partners. Not usually relevant in
  heterosexual populations, though very relevant to
  IDU populations)
• Number of partners -- by far the simplest network
  feature, but also very relevant at the high end
• Relationship timing, duration and overlap
• By asking about partners behavior, you can get
  some information on the relative risk of each
  relation. For example, whether a respondents
  partner has many other partners (though data
  quality is often at issue).

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Network Topology Ego Networks

• Studies making successful use of ego-network data
  include

• Reinking et al. 1994. Social Transmission
  Routes of HIV. A combined sexual network and
  life course perspective. Patient Education and
  Counseling 24289-297.
• Aral et al. 1999. Sexual Mixing Patterns in
  the Spread of Gonococcal and Chlamydial
  Infections. American Journal of Public Health
  89 825-833.
• Martin and Dean 1990 (Longitudinal AIDS Impact
  Project). Development of a community sample of
  gay men for an epidemiologic study of aids.
  American Behavioral Science 33546-61.
• Morris and Dean. 1994. The effects of sexual
  behavior change on long-term hiv seroprevalence
  among homosexual men. American Journal of
  Epidemiology 140217-32.

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Network Topology Partial and Complete Networks
Once we move beyond the ego-network, we can start
to identify how the pattern of connection changes
the disease risk for actors. Two features of the
networks shape are known to be important
Connectivity and Centrality.

• Connectivity refers to how actors in one part of
  the network are connected to actors in another
  part of the network.
• Reachability Is it possible for actor i to
  infect actor j? This can only be true if there
  is an unbroken (and properly time ordered) chain
  of contact from one actor to another.
• Given reachability, three other properties are
  important
• Distance
• Number of paths
• Distribution of paths through actors
  (independence of paths)

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Reachability example All romantic contacts
reported ongoing in the last 6 months in a
moderate sized high school (AddHealth)
63
(From Bearman, Moody and Stovel, n.d.)
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• 288 People in largest component
• 42 steps maximum distance
• Mean distance between non-connected pairs is 16
  steps
• Mean number within 3 steps is 9.7
• 45 people are biconnected (in the center ring).

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Network Topology Distance number of paths

• Given that ego can reach alter, distance
  determines the likelihood of an infection passing
  from one end of the chain to another.
• Disease spread is never certain, so the
  probability of transmission decreases over
  distance.
• Disease transmission increases with each
  alternative path connecting pairs of people in
  the network.

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Probability of infection
by distance and number of paths, assume a
constant pij of 0.6
1.2
1
10 paths
0.8
5 paths
probability
0.6
2 paths
0.4
1 path
0.2
0
2
3
4
5
6
Path distance
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Probability of infection
by distance and number of paths, assume a
constant pij of 0.3
0.7
0.6
0.5
0.4
probability
0.3
0.2
0.1
0
2
3
4
5
6
Path distance
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Return to our first example
2 paths
4 paths
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Reachability in Colorado Springs (Sexual contact
only)

• High-risk actors over 4 years
• 695 people represented
• Longest path is 17 steps
• Average distance is about 5 steps
• Average person is within 3 steps of 75 other
  people
• 137 people connected through 2 independent paths,
  core of 30 people connected through 4 independent
  paths

(Node size log of degree)
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Network Topology Centrality and Centralization

• Centrality refers to (one dimension of) where an
  actor resides in a sexual network.
• Local compare actors who are at the edge of the
  network to actors at the center
• Global compare networks that are dominated by a
  few central actors to those with relative
  involvement equality

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Centrality example Add Health
Node size proportional to betweenness centrality
Graph is 45 centralized
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Centrality example Colorado Springs
Node size proportional to betweenness centrality
Graph is 27 centralized
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Network Topology Centrality and Centralization
Measures research

• Rothenberg, et al. 1995. "Choosing a Centrality
  Measure Epidemiologic Correlates in the Colorado
  Springs Study of Social Networks." Social
  Networks Special Edition on Social Networks and
  Infectious Disease HIV/AIDS 17273-97.
• Found that the HIV positive actors were not
  central to the overall network
• Bell, D. C., J. S. Atkinson, and J. W. Carlson.
  1999. "Centrality Measures for Disease
  Transmission Networks." Social Networks 211-21.
• Using a data-based simulation on 22 people, found
  that simple degree measures were adequate,
  relative to complexity
• Poulin, R., M.-C. Boily, and B. R. Masse. 2000.
  "Dynamical Systems to Define Centrality in Social
  Networks." Social Networks 22187-220
• Method that allows one to compare across
  non-connected portions of a network, applied to a
  network of 40 people w. AIDS

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Timing Sexual Networks
A focus on contact structure often slights the
importance of network dynamics. Time affects
networks in two important ways 1) The structure
itself goes through phases that are correlated
with disease spread Wasserheit and Aral, 1996.
The dynamic topology of Sexually Transmitted
Disease Epidemics The Journal of Infectious
Diseases 74S201-13 Rothenberg, et al. 1997
Using Social Network and Ethnographic Tools to
Evaluate Syphilis Transmission Sexually
Transmitted Diseases 25 154-160 2) Relationship
timing constrains disease flow a) by spending
more or less time in-host b) by changing the
potential direction of disease flow
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Sexual Relations among A syphilis outbreak
Changes in Network Structure
Rothenberg et al map the pattern of sexual
contact among youth involved in a Syphilis
outbreak in Atlanta over a one year period.
(Syphilis cases in red)
Jan - June, 1995
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Sexual Relations among A syphilis outbreak
July-Dec, 1995
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Sexual Relations among A syphilis outbreak
July-Dec, 1995
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Data on drug users in Colorado Springs, over 5
years
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Data on drug users in Colorado Springs, over 5
years
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Data on drug users in Colorado Springs, over 5
years
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Data on drug users in Colorado Springs, over 5
years
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Data on drug users in Colorado Springs, over 5
years
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What impact does this kind of timing have on
disease flow?
The most dramatic effect occurs with the
distinction between concurrent and serial
relations. Relations are concurrent whenever
an actor has more than one sex partner during the
same time interval. Concurrency is dangerous for
disease spread because a) compared to serially
monogamous couples, and STDis not trapped inside
a single dyad b) the std can travel in two
directions - through ego - to either of his/her
partners at the same time
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Concurrency and Epidemic Size Morris
Kretzschmar (1995)
1200
800
400
0
0
1
2
3
4
5
6
7
Monogamy
Disassortative
Assortative
Random
Population size is 2000, simulation ran over 3
years
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Concurrency and disease spread
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A hypothetical Sexual Contact Network
8 - 9
C
E
3 - 7
2 - 5
B
A
0 - 1
3 - 5
D
F
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The path graph for a hypothetical contact network
E
C
B
A
D
F
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Direct Contact Network of 8 people in a ring
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Implied Contact Network of 8 people in a ring All
relations Concurrent
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Implied Contact Network of 8 people in a
ring Mixed Concurrent
2
3
2
1
1
2
2
3
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Implied Contact Network of 8 people in a
ring Serial Monogamy (1)
1
8
2
7
3
6
5
4
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Implied Contact Network of 8 people in a
ring Serial Monogamy (2)
1
8
2
7
3
6
1
4
45
Implied Contact Network of 8 people in a
ring Serial Monogamy (3)
1
2
2
1
1
2
1
2
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Timing Sexual Networks

• Network dynamics can have a significant impact on
  the level of disease flow and each actors risk
  exposure

This work suggests that a) Disease outbreaks
correlate with phase-shifts in the connectivity
level b) Interventions focused on relationship
timing, especailly concurrency, could have a
significant effect on disease spread c) Measure
and models linking network topography to disease
flow should account for the timing of romantic
relationships
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Problems, Limitations Future Directions
Data

• Theoretically, STDs travel through a complete
  network, and thus that would be the ideal data to
  have.
• Practically, this is extremely difficult and very
  expensive
• Ego-network data are the easiest to collect, but
  limited.
• They cannot capture extended effects of network
  structure
• Partial network data is thus the most realistic
  hope we have for combining network insights with
  data.
• Future strategies should focus on developing
  methods for selecting partial network data that
  maximizes network coverage developing
  statistical and simulation techniques that can
  bridge the local/partial data and global data
  divide

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Problems, Limitations Future Directions
Linking non-sexual relations to sexual networks
Consider another look at the data from Colorado
Springs The circled node is HIV positive.
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Linking non-sexual relations to sexual networks
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Linking non-sexual relations to sexual networks
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