reported female genital chlamydia rates per 100,000 in canada by province/territory, 1997 to 1999...
TRANSCRIPT
Reported Female Genital Chlamydia Rates per 100,000 in Canada by Province/Territory,
1997 to 1999
Health Canada, Bureau of HIV/AIDS, STD and TB, 2000
Chlamydia network from Qikiqtarjuaq, NunavutCanada, 2003
Data courtesy of Andrea Cuschieri
Colorado Springs, Gonorrhea, 1981Lot 004
Colorado Springs, Gonorrhea, 1981, Lot 004
Modeling disease transmission
A comparison of data from 15 network studies
…well, 13, actually….
Dramatis personae
Martina Morris Mark S. Handcock Francesca Chiaromonte Julian Besag David Hunter Steve Goodreau James Moody Philippa Pattison
David Bell
Sam Friedman
Ann Jolly
Al Klovdahl
Stephen MuthJohn Potterat
Rich Rothenberg
Bob Trotter
Theoreticians Empiricists
Study sites
The Studies—Colorado Springs
Site Persons Interviewed
Total Dyads Design Description
Project 90 589 6949Venue sampling with cross-links. 1988-1993
Recruitment of prostitutes, IDU, and their sex and drug partners at street and institutional venues
GC1981 709 1638Contact tracing of 90% of GC cases from Jan-Jun 1981
Routine case interview and contact investigation, seeking partners of positive persons
Chlamydia 1082 1893Contact tracing of 2/3 of Chlamydia cases, 1996-1997
Routine case interview and contact investigation applied to chlamydial infections
HIV 810 1932Contact tracing of almost all HIV cases, 1982-2000
Routine case interview and contact investigation applied to HIV infections
PPNG 279 1104Contact tracing of almost all PPNG cases, 1990-1991
Routine case interview and contact investigation applied to PPNG infections in an outbreak setting
The Studies—Atlanta
Site Persons Interviewed
Total Dyads Design Description
Urban Networks 206 1580
Chain link: random walk vs. nomination
Men and women in inner city Atlanta, at risk for HIV because of drug use and sexual activity
Matrix 112 645Snowball sample of IDU and crack users
Using 5 “seeds” a 2-wave snowball sample with all contacts interviewed
Antiviral 358 1830Clinic and community based representative samples
A study of persons on and not on HAART in the clinic, and with and without HIV in the community
Rockdale 34 197Syphilis outbreak investigation in a private HS
Network-informed contact investigation, with interview of pos and neg persons
Syph318 75 319 Investigation of endemic syphilis
Network-informed contact investigation, with interview of contacts, suspects, associates
The Studies
Site Persons Interviewed
Total Dyads Design Description
Houston 271 1753Ethnographic, targeted sampling of IDU
Street-based representational sampling of IDU to determine prevalence and factors for HIV
Bushwick 703 3162Ethnographic, targeted sampling of IDU
Street-based sampling of IDU in the Bushwick section of Brooklyn, NY
Manitoba 2120 2924Contact tracing for GC and Chlamydia
Routine contact tracing results in Manitoba, primarily among First Nation peoples
Baltimore
Flagstaff
Wash, DC
• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity
Demographic pattern for 13 network studies:Age
Age (mean)
0
20
40
60Antiviral
Bushwick
Chalmydia
GC1981
HIV
Houston
ManitobaMatrix
PPNG
Project90
Rockdale
Syph318
Urban
Age (mean)
Demographic pattern for 13 network studies:Age
Age (mean)
0
20
40
60Antiviral
Bushwick
Chalmydia
GC1981
HIV
Houston
ManitobaMatrix
PPNG
Project90
Rockdale
Syph318
Urban
Age (mean)
Demographic pattern for 13 network studiesAge, %Male
0
20
40
60
80
100Antiviral
Bushwick
Chalmydia
GC1981
HIV
Houston
ManitobaMatrix
PPNG
Project90
Rockdale
Syph318
Urban
Age (mean)Male (%)
Demographic pattern for 13 network studiesAge, %Male, %African American
0
20
40
60
80
100Antiviral
Bushwick
Chalmydia
GC1981
HIV
Houston
ManitobaMatrix
PPNG
Project90
Rockdale
Syph318
Urban
Age (mean)AA (%)Male (%)
Time frame for 13 network studies
1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
Antiviral
Bushwick
Chalmydia
GC1981
HIV
Houston
Manitoba
Matrix
PPNG
Project90
Rockdale
Syph318
Urban
Prevalence of STDs and HIV—13 studies
0
20
40
60
80
100
Antivir
al
Bushw
ick
Chalm
ydia
GC1981 HIV
Housto
n
Manito
baMatr
ix
PPNG
Projec
t90
Rockd
ale
Syph3
18Urba
n
%
HIV Gonorrhea Chlamydia Syphilis HBV
• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity• Multiplexity
0.01
0.1
11 10 100
log (Number of partners)
log (Cumulative probability)
Antiviral
Selected Power Law curves from network studies
0.0001
0.001
0.01
0.1
11 10 100
log (Number of partners)
log (Cumulative probability)
Chlamydia
0.001
0.01
0.1
11 10 100
log (Number of partners)
log (Cumulative probability)
Bushwick
0.01
0.1
11 10
log (Number of partners)
log (Cumulative probability)
Matrix
Exponents and R2 associated with power law curves for 13 network studies
0.87
0.54
0.98
0.91
0.92
0.76
0.94
0.73
0.93
0.77
0.86
0.920.65
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
Antivir
al
Bushwick
Chalmyd
ia
GC1981 HIV
Houston
Manito
baMatr
ix
PPNG
Projec
t90
Rockda
le
Syph31
8Urb
an
exponent
r-squared
Degree distributionsCumulative probability distribution for
interviewed persons—all 13 studies combinedInterviewed
0.0001
0.001
0.01
0.1
11 10 100
log (Number of partners)
log (Cumulative probability) Interviewed
y=5.1x-2.2, R2=0.86
Uninterviewed person
• The construction of a sociogram permits examination of the degree distribution for persons named but never interviewed.
• Their degree distribution says something about the interconnectedness of the network.
Degree distributionsCumulative probability distribution for interviewed and
noninterviewed persons—all 13 studies combined
0.0001
0.001
0.01
0.1
11 10 100
log (Number of partners)
log (Cumulative probability)
Interviewed
Not interviewed
y=5.1x-2.2, R2=0.86
y=0.05x-2.2, R2=0.99
Missing LinksWho has not been named?
• What does the space between these two curves represent, and how can it be measured?
• Assume that the Non-interviewed actually have the same degree distribution as the Interviewed.
• Assume that “Recursion” is the same for Non-interviewed and Interviewed persons
• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity
Recursion: definition
• Number of persons in network in the absence of interaction (all respondents provide only egocentric information):Respondents + Contacts = Expected nodes
• With de-duplication, we get the actual number of nodes in the network
• Recursion is the proportionate decrease in network nodes that occurs because of interaction:[Expected nodes – Actual nodes]/Expected nodes
Recursion: observations from data--all contacts
1.5
16.8
20.8
28.1
14.3
23.9
10.6
32.0
56.9
20.8
57.6
28.4
26.5
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0
Antiviral
Bushwick
Chlamydia
GC1981
HIV
Houston
Manitoba
Matrix
PPNG
Proj90
Rockdale
Syph318
Urban
Recursion (percent)
Gang-Associated STD Outbreak, Colorado Springs, 1990-1991 N=410
Rockdale county syphilis epidemic:
Late phase
Missing Links:Estimation of the missing
• Calculate the expected number of partnerships from the number of contacts named and not interviewed by applying the degree distribution of the Interviewed persons.
• Calculated the expected number of persons, given no interaction.
• Apply the observed proportion of Recursion, to get the expected total of persons associated with the Non-interviewed.
• Sum the expected persons associated with the Noninterviewed with the observed persons associated with the Interviewed.
• STILL MISSING: The proportion of ties between Noninterviewed persons that occurred with Interviewed persons and their contacts.
Missing Links:Calculation
Non-interviewed (Ni) Study
Respondents Contacts Expected persons Recursion Total Interviewed
(I) Total
(Ni + I) Antiviral 370 9322 9692 1.5 9550 2156 11706 Bushwick 709 11966 12675 16.8 10540 3214 13754 Chlamydia 1096 2858 3954 20.8 3130 2355 5485 GC1981 760 2961 3721 28.1 2676 1688 4364 HIV 858 4133 4991 14.3 4279 2351 6630 Houston 427 9551 9978 23.9 7592 1540 9132 Manitoba 2304 3900 6204 10.6 5546 4509 10055 Matrix 132 2658 2790 32.0 1898 515 2413 PPNG 454 2559 3013 56.9 1298 596 1894 Proj90 1070 62596 63666 20.8 50431 5651 56082 Rockdale 42 542 584 57.6 248 98 346 Syph318 107 1097 1204 28.4 861 282 1143 Urban 244 9217 9461 26.5 6955 1313 8268
Total = Expected * (1-(0.01*Recursion)
Missing Links:Graphic display
0 5000 10000 15000
Rockdale
Syph318
PPNG
Matrix
GC1981
Chlamydia
HIV
Urban
Houston
Manitoba
Antiviral
Bushwick
Actual numberInterviewed Noninterviewed
Proportion of Nodes missing from networks
0.0 20.0 40.0 60.0 80.0 100.0
Rockdale
Syph318
PPNG
Matrix
GC1981
Chlamydia
HIV
Urban
Houston
Manitoba
Antiviral
Bushwick
Overall
Missing Nodes (percent)
• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity
Calculating Kappa from egocentric data
• Determine mean and variance of degree distribution:
kappa = (var/mean) + mean – 1
• For these data, sociometric information is available, so the connection formed by Non-interviewed persons can be included (net effect of decreasing estimate of concurrency)
Estimate of concurrency by study
0.0 2.0 4.0 6.0 8.0 10.0 12.0
Antiviral
Bushw ick
Chlamydia
GC1981
HIV
Houston
Manitoba
Matrix
PPNG
Proj90
Rockdale
Syph318
Urban
Kappa
Concurrency—SEXUAL partners
Study Egocentric Sociogram
Antiviral 3.4 1.7Bushwick
Chlamydia 2.4 1.4GC1981 2.4 1.5
HIV 3.7 2.0Houston 3.0 1.7Manitoba 0.8 0.5
Matrix 3.2 1.9PPNG 2.4 1.8
Project 90 7.6 4.2Rockdale 6.2 4.7Syph318 2.5 1.5
Urban 4.5 2.5
Concurrency—NEEDLE partners
Study Egocentric Sociogram
Antiviral 1.5 0.7Bushwick 3.6 2.1Chlamydia
GC1981
HIV 1.6 0.8Houston 4.9 3.3Manitoba
Matrix
PPNG
Project 90 8.3 4.7Rockdale
Syph318
Urban
• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity
Transitivity (Clustering)
• Using the definition of completed triangles• Algorithm implemented in UCI-6• Note the absence (by definition) of
clustering in sexual networks that are strictly heterosexual
• Conversely, networks involving MSM or IDU can demonstrate considerable clustering
Transitivity by study(all relationships)
Transitivity (percent)All Sexual Needle
Antiviral 0.0 0.0 0.0
Bushwick 5.49 0.0 6.96
Chlamydia 0.0 0.0
GC1981 2.08 2.08
HIV 5.92 5.84 0.0
Houston 14.07 0.0 32.67
Manitoba 0.0 0.0
Matrix 7.52 0.85
PPNG 23.91 0.0
Project 90 6.95 0.43 11.04
Rockdale 11.54 11.24
Syph318 11.39 0.0
Urban 9.14 5.44
Transitivity by study(sexual relationships)
Transitivity (percent)All Sexual Needle
Antiviral 0.0 0.0 0.0
Bushwick 5.49 0.0 6.96
Chlamydia 0.0 0.0
GC1981 2.08 2.08
HIV 5.92 5.84 0.0
Houston 14.07 0.0 32.67
Manitoba 0.0 0.0
Matrix 7.52 0.85
PPNG 23.91 0.0
Project 90 6.95 0.43 11.04
Rockdale 11.54 11.24
Syph318 11.39 0.0
Urban 9.14 5.44
Transitivity by study(needle-sharing relationships)
Transitivity (percent)All Sexual Needle
Antiviral 0.0 0.0 0.0
Bushwick 5.49 0.0 6.96
Chlamydia 0.0 0.0
GC1981 2.08 2.08
HIV 5.92 5.84 0.0
Houston 14.07 0.0 32.67
Manitoba 0.0 0.0
Matrix 7.52 0.85
PPNG 23.91 0.0
Project 90 6.95 0.43 11.04
Rockdale 11.54 11.24
Syph318 11.39 0.0
Urban 9.14 5.44
• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity
Distribution of components
Study Largest Component
Next Largest
Antiviral 121 23
Bushwick 1261 42
Chlamydia 45 24
GC1981 204 97
HIV 324 28
Houston 1091 24
Manitoba 26 25
Matrix 515 0
PPNG 537 15
Project 90 4223 52
Rockdale 98 0
Syph318 102 79
Urban 913 272
HIV-C. Springs
1
10
100
1000
0 100 200 300 400
Component size
logFrequency
Distribution of componentsThree exceptions
• Rockdale– Contact tracing, single outbreak
• Matrix– Snowball design
• Manitoba– Contact tracing, multiple isolated areas
Bushwick
Manitoba
GC1981
• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity
Calculation of Assortativity
• Using Newman’s approach:– Create a matrix of eij for proportion of category
interactions• Assortativity is given by
(Tr(e) - |e|2) (1 - |e|2)• These data permit estimation by age,
ethnicity and degree
Assortativity by age and ethnicityAll contactsAge Ethnicity
Egocentric Sociometric Egocentric Sociometric
Antiviral 0.242 0.244 0.719 0.719
Bushwick 0.262 0.254 0.735 0.736
Chlamydia 0.392 0.393 0.498 0.504
GC1981 0.326 0.332 0.616 0.619
HIV 0.274 0.285 0.573 0.573
Houston 0.223 0.221 0.770 0.773
Manitoba 0.212 0.213
Matrix 0.195 0.199 0.500 0.501
PPNG 0.441 0.441 0.381 0.380
Project 90 0.254 0.251 0.568 0.568
Rockdale 0.354 0.366 0.068 0.128
Syph318 0.200 0.202
Urban 0.229 0.229 0.537 0.534
Assortativity by age and ethnicityStratified by degree—all contacts
Number of Partners
Age Ethnicity
1 0.391 0.571
2 0.341 0.593
3-4 0.310 0.629
5-9 0.329 0.662
10+ 0.314 0.575
Assortativity by age and ethnicitySex contactsAge Ethnicity
Egocentric Sociometric Egocentric Sociometric
Antiviral 0.227 0.231 0.675 0.676
Bushwick 0.262 0.260 0.739 0.738
Chlamydia 0.392 0.393 0.498 0.504
GC1981 0.326 0.332 0.616 0.619
HIV 0.271 0.281 0.573 0.573
Houston 0.220 0.229 0.762 0.767
Manitoba 0.212 0.213
Matrix 0.182 0.195 0.466 0.471
PPNG 0.448 0.451 0.360 0.355
Project 90 0.221 0.219 0.496 0.495
Rockdale 0.327 0.329 0.025 0.074
Syph318 0.233 0.223
Urban 0.206 0.203 0.455 0.457
Assortativity by age and ethnicityStratified by degree—sex contacts
Number of Partners
Age Ethnicity
1 0.387 0.609
2 0.323 0.584
3-4 0.311 0.566
5-9 0.309 0.532
10+ 0.239 0.420
Assortativity by age and ethnicityNeedle contacts
Age Ethnicity
Egocentric Sociometric Egocentric Sociometric
Antiviral 0.442 0.458 0.433 0.436
Bushwick 0.272 0.261 0.693 0.692
Chlamydia
GC1981
HIV 0.286 0.298 0.631 0.620
Houston 0.262 0.268 0.654 0.654
Manitoba
Matrix
PPNG
Project 90 0.277 0.275 0.580 0.575
Rockdale
Syph318
Urban
Assortativity by age and ethnicityStratified by degree—needle contacts
Number of Partners
Age Ethnicity
1 0.355 0.759
2 0.312 0.675
3-4 0.323 0.735
5-9 0.281 0.656
10+ 0.227 0.447
Assortativity by degree(using respondent-respondent pairs only)
Assortativity
All Sex Needle
Antiviral 0.515
Bushwick 0.296 0.451 0.306
Chlamydia 0.458 0.458
GC1981 0.325 0.325
HIV 0.345 0.350 0.304
Houston 0.380 0.452 0.326
Manitoba 0.337 0.337
Matrix 0.226 0.314
PPNG 0.338 0.253
Project 90 0.354 0.231 0.196
Rockdale 0.147 0.178
Syph318 0.241 0.209
Urban 0.326 0.405
AsssortativitySummary by type of contact
Assortativity
Contacts Age Ethnicity Degree
All0.279
(0.199-0.441)0.549
(0.128-0.773)0.330
(0.147-0.515
Sex0.274
(0.195-0.451)0.521
(0.074-0.767)0.330
(0.178-0.458)
Needle0.312
(0.261-0.458)0.596
(0.436-0.692)0.283
(0.196-0.326)
Summary of Assortativity findings
• Egocentric and sociometric estimates agree• Assortativity by sex and degree moderate
(~30%)• Assortativity by ethnicity high (~60-70%)• All assortativity estimates vary considerably
by study.
• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity
Multiplexity—selected sites
A = AcquaintanceN = NeedleD = DrugS = Sex
Proj90 Houston Manitoba
. . . . 0 14
A 1900 451
N 156 107
N A 161 49
D 662 460
D A 907 79
D N 143 120
D N A 245 46
S 837 118 2924
S A 559 93
S D 32 3
S D A 65 14
S D 220 112
S D A 489 64
S D N 30 11
S D N A 138 24
Multiplexity by study siteMultiplexity Sex + Drugs Sex + Needles
(percent)
Antiviral 37.3 14.7 0.3
Bushwick 75.0 0.0 0.0
Chlamydia 0.0 0.0 0.0
GC1981 0.0 0.0 0.0
HIV 2.8 0.0 2.8
Houston 35.7 11.9 3.0
Manitoba 0.0 0.0 0.0
Matrix 51.0 23.9 0.0
PPNG 0.0 0.0 0.0
Project 90 45.7 13.4 4.0
Rockdale 0.0 0.0 0.0
Syph318 12.5 3.1 0.0
Urban 47.4 23.0 0.0
General Observations--1
• A heterogeneous group of studies
• Considerable variability by:– Demographics– Risk-taking– Disease prevalence
General Observations--2
• Nevertheless, considerable similarity with regard to structural factors:
• Right-skewed degree distribution (scale-free or close)
• “Giant” component with numerous small components
General Observations--3
• Considerable variability with regard to connectivity factors:
– Recursion– Concurrency– Transitivity (clustering) – Assortativity (age, ethnicity, degree)– Multiplexity
Modeling approaches
A model that produces a specific network configuration
Top down
Bottom up
Social and geographic choices
Timing and sequence
Specific acts
Attribute mixing
Small world
Scale free
Giant component
Local rules yield global structure
From Morris, July 2003
Empirical data support a bottom up approach
A rough correspondence….
Social and geographic choices
Timing and sequence
Specific acts
Attribute mixing
Recursion
ConcurrencyTransitivity (clustering)Multiplexity Assortativity
Local Rules Network Properties
Connecting these factors to disease transmission…
Prevalence of STDs and HIV—13 studies
0
20
40
60
80
100
Antivir
al
Bushw
ick
Chalm
ydia
GC1981 HIV
Housto
n
Manito
baMatr
ix
PPNG
Projec
t90
Rockd
ale
Syph3
18Urba
n
%
HIV Gonorrhea Chlamydia Syphilis HBV
The challenge• Insufficient data points• Confounding by study design• Confounding by variability in missing data
– The boundary problem– Missing nodes– Incorrect information
• Basic inadequacies of regression approach– e.g. Logistic regression to tie a network configuration to
a prevalence or incidence level– The inadequacy of a Relative Risk
The “Answer”
A need to use theory and simulation, grounded in observation, to understand the influence of fixed and variable factors on transmission.
Dramatis personae
Martina Morris Mark S. Handcock Francesca Chiaromonte Julian Besag David Hunter Steve Goodreau James Moody Philippa Pattison
David Bell
Sam Friedman
Ann Jolly
Al Klovdahl
Stephen MuthJohn Potterat
Rich Rothenberg
Bob Trotter
Theoreticians Empiricists