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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.

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Page 1: 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.
Page 2: 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.

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

Page 3: 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.
Page 4: 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

Page 5: 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.
Page 6: 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.

Colorado Springs, Gonorrhea, 1981Lot 004

Page 7: 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.

Colorado Springs, Gonorrhea, 1981, Lot 004

Page 8: 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.
Page 9: 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.

Modeling disease transmission

A comparison of data from 15 network studies

…well, 13, actually….

Page 10: 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.

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

Page 11: 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.

Study sites

Page 12: 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.

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

Page 13: 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.

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

Page 14: 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.

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

Page 15: 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.

• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity

Page 16: 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.

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)

Page 17: 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.

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)

Page 18: 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.

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 (%)

Page 19: 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.

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 (%)

Page 20: 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.

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

Page 21: 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.

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

Page 22: 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.

• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity• Multiplexity

Page 23: 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.

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

Page 24: 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.

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

Page 25: 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.

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

Page 26: 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.

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.

Page 27: 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.

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

Page 28: 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.

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

Page 29: 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.

• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity

Page 30: 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.

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

Page 31: 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.

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)

Page 32: 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.

Gang-Associated STD Outbreak, Colorado Springs, 1990-1991 N=410

Page 33: 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.

Rockdale county syphilis epidemic:

Late phase

Page 34: 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.

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.

Page 35: 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.

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)

Page 36: 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.

Missing Links:Graphic display

0 5000 10000 15000

Rockdale

Syph318

PPNG

Matrix

GC1981

Chlamydia

HIV

Urban

Houston

Manitoba

Antiviral

Bushwick

Actual numberInterviewed Noninterviewed

Page 37: 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.

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)

Page 38: 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.

• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity

Page 39: 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.

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)

Page 40: 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.

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

Page 41: 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.

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

Page 42: 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.

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

Page 43: 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.

• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity

Page 44: 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.

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

Page 45: 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.

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

Page 46: 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.

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

Page 47: 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.

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

Page 48: 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.

• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity

Page 49: 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.

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

Page 50: 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.

Distribution of componentsThree exceptions

• Rockdale– Contact tracing, single outbreak

• Matrix– Snowball design

• Manitoba– Contact tracing, multiple isolated areas

Page 51: 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.

Bushwick

Page 52: 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.

Manitoba

Page 53: 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.

GC1981

Page 54: 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.

• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity

Page 55: 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.

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

Page 56: 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.

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

Page 57: 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.

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

Page 58: 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.

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

Page 59: 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.

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

Page 60: 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.

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

Page 61: 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.

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

Page 62: 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.

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

Page 63: 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.

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)

Page 64: 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.

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.

Page 65: 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.

• Demographics, Time Frame and Prevalence• Degree distributions• Recursion• Concurrency• Transitivity• Component distribution• Assortativity • Multiplexity

Page 66: 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.

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

Page 67: 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.

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

Page 68: 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.

General Observations--1

• A heterogeneous group of studies

• Considerable variability by:– Demographics– Risk-taking– Disease prevalence

Page 69: 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.

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

Page 70: 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.

General Observations--3

• Considerable variability with regard to connectivity factors:

– Recursion– Concurrency– Transitivity (clustering) – Assortativity (age, ethnicity, degree)– Multiplexity

Page 71: 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.

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

Page 72: 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.

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

Page 73: 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.

Connecting these factors to disease transmission…

Page 74: 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.

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

Page 75: 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.

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

Page 76: 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.

The “Answer”

A need to use theory and simulation, grounded in observation, to understand the influence of fixed and variable factors on transmission.

Page 77: 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.

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