Download Sexual Network Constraints on STD Flow: The role

Sexual Network Constraints on STD Flow
The role of Sexual Networks in HIV spread
by
James Moody
The Ohio State University
Presented at The UNC Center for Aids Research Conference:
Methods of Study in Human Sexuality: Relevance to AIDS Research
Chapel Hill, May 5, 2001
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
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 21:1203-16.
Morris, M. 1993. "Epidemiology and Social Networks: Modeling
Structured Diffusion." Sociological Methods and Research 22:99-126.
Rothenberg, et al. 1997 “Using Social Network and Ethnographic Tools
to Evaluate Syphilis Transmission” Sexually Transmitted Diseases 25:
154-160
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’
Examples: linked levels of data
Respondent
Partner
Partner’s partner
Primary Relation
Alter Relation
Trace Relation
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
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 partner’s 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
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 & Youm’s (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
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 ego’s 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 partner’s 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).
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 24:289-297.
•Aral et al. 1999. “Sexual Mixing Patterns in the Spread of Gonococcal
and Chlamydial Infections.” American Journal of Public Health 89: 825833.
•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 33:546-61.
•Morris and Dean. 1994. “The effects of sexual behavior change on longterm hiv seroprevalence among homosexual men.” American Journal of
Epidemiology 140:217-32.
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 network’s
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)
Reachability example: All romantic contacts reported ongoing in the last 6 months in
a moderate sized high school (AddHealth)
2
12
9
63
Male
Female
(From Bearman, Moody and Stovel, n.d.)
•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).
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.
Probability of infection
by distance and number of paths, assume a constant p ij of 0.6
1.2
1
probability
10 paths
0.8
5 paths
0.6
2 paths
0.4
1 path
0.2
0
2
3
4
Path distance
5
6
Probability of infection
by distance and number of paths, assume a constant p ij of 0.3
0.7
0.6
probability
0.5
0.4
0.3
0.2
0.1
0
2
3
4
Path distance
5
6
Return to our first example:
S
T
S
T
2 paths
4 paths
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)
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
Centrality example: Add Health
Node size proportional to
betweenness centrality
Graph is 45% centralized
Centrality example: Colorado Springs
Node size proportional to
betweenness centrality
Graph is 27% centralized
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 17:273-97.
•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 21:1-21.
•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 22:187-220
•Method that allows one to compare across non-connected portions of a
network, applied to a network of 40 people w. AIDS
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
74:S201-13
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
Changes in Network
Structure
Sexual Relations among A syphilis outbreak
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
Sexual Relations among A syphilis outbreak
July-Dec, 1995
Sexual Relations among A syphilis outbreak
July-Dec, 1995
Data on drug users in
Colorado Springs, over
5 years
Data on drug users in
Colorado Springs, over
5 years
Data on drug users in
Colorado Springs, over
5 years
Data on drug users in
Colorado Springs, over
5 years
Data on drug users in
Colorado Springs, over
5 years
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
Concurrency and Epidemic Size
Morris & Kretzschmar (1995)
1200
800
400
0
0
Monogamy
1
2
3
Disassortative
Population size is 2000, simulation ran over 3 ‘years’
4
Random
5
6
7
Assortative
Concurrency and disease spread
Adjusting for
other mixing
patterns:
Variable
Constant
Concurrent
K2
Degree Correlation
Bias
Coefficient
84.18
357.07
440.38
-557.40
982.31
Each .1 increase in
concurrency results in
45 more positive cases
A hypothetical Sexual Contact Network
C
A
2-5
8-9
E
B
D
3-5
F
The path graph for a hypothetical contact network
A
C
E
D
F
B
Direct Contact Network of 8 people in a ring
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Implied Contact Network of 8 people in a ring
All relations Concurrent
1
1
2
2
2
2
2
1
1
2
2
2
2
2
2
1
1
2
2
2
2
2
2
1
1
2
2
2
2
2
2
1
1
2
2
2
2
2
2
1
1
2
2
2
2
2
2
1
1
1
2
2
2
2
2
1
Implied Contact Network of 8 people in a ring
Mixed Concurrent
3
2
1
2
1
1
1
1
1
2
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Implied Contact Network of 8 people in a ring
Serial Monogamy (1)
8
1
1
2
7
3
6
5
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Implied Contact Network of 8 people in a ring
Serial Monogamy (2)
8
1
1
2
7
1
1
1
1
1
1
1
1
3
6
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Implied Contact Network of 8 people in a ring
Serial Monogamy (3)
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
Timing Sexual Networks
•Network dynamics can have a significant impact on the level of disease flow
and each actor’s 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
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
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.
Linking non-sexual relations to sexual networks
Linking non-sexual relations to sexual networks