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

4. Chlamydia network from Qikiqtarjuaq, Nunavut Canada, 2003 Data courtesy of Andrea Cuschieri

6. Colorado Springs, Gonorrhea, 1981 Lot 004

7. Colorado Springs, Gonorrhea, 1981, Lot 004

9. Modeling disease transmission A comparison of data from 15 network studies …well, 13, actually….

10. 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 Muth John Potterat Rich Rothenberg Bob Trotter TheoreticiansEmpiricists

11. Study sites

12. The Studies—Colorado Springs Site Persons Interviewed Total Dyads DesignDescription Project 905896949 Venue sampling with cross-links. 1988-1993 Recruitment of prostitutes, IDU, and their sex and drug partners at street and institutional venues GC19817091638 Contact tracing of 90% of GC cases from Jan-Jun 1981 Routine case interview and contact investigation, seeking partners of positive persons Chlamydia10821893 Contact tracing of 2/3 of Chlamydia cases, 1996-1997 Routine case interview and contact investigation applied to chlamydial infections HIV8101932 Contact tracing of almost all HIV cases, 1982-2000 Routine case interview and contact investigation applied to HIV infections PPNG2791104 Contact tracing of almost all PPNG cases, 1990-1991 Routine case interview and contact investigation applied to PPNG infections in an outbreak setting

13. The Studies—Atlanta Site Persons Interviewed Total Dyads DesignDescription Urban Networks 2061580 Chain link: random walk vs. nomination Men and women in inner city Atlanta, at risk for HIV because of drug use and sexual activity Matrix112645 Snowball sample of IDU and crack users Using 5 “seeds” a 2-wave snowball sample with all contacts interviewed Antiviral3581830 Clinic 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 Rockdale34197 Syphilis outbreak investigation in a private HS Network-informed contact investigation, with interview of pos and neg persons Syph31875319 Investigation of endemic syphilis Network-informed contact investigation, with interview of contacts, suspects, associates

14. The Studies Site Persons Interviewed Total Dyads DesignDescription Houston2711753 Ethnographic, targeted sampling of IDU Street-based representational sampling of IDU to determine prevalence and factors for HIV Bushwick7033162 Ethnographic, targeted sampling of IDU Street-based sampling of IDU in the Bushwick section of Brooklyn, NY Manitoba21202924 Contact tracing for GC and Chlamydia Routine contact tracing results in Manitoba, primarily among First Nation peoples Baltimore Flagstaff Wash, DC

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

16. Demographic pattern for 13 network studies: Age

18. Demographic pattern for 13 network studies Age, %Male

19. Demographic pattern for 13 network studies Age, %Male, %African American

20. Time frame for 13 network studies

21. Prevalence of STDs and HIV—13 studies

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

23. Selected Power Law curves from network studies

24. Exponents and R 2 associated with power law curves for 13 network studies

25. Degree distributions Cumulative probability distribution for interviewed persons—all 13 studies combined

26. 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.

27. Degree distributions Cumulative probability distribution for interviewed and noninterviewed persons—all 13 studies combined

28. Missing Links Who 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

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

30. 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

31. Recursion: observations from data-- all contacts

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

33. Rockdale county syphilis epidemic: Late phase

34. 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.

35. Missing Links: Calculation Total = Expected * (1-(0.01*Recursion)

36. Missing Links: Graphic display

37. Proportion of Nodes missing from networks

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

39. 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)

40. Estimate of concurrency by study

41. Concurrency—SEXUAL partners StudyEgocentricSociogram Antiviral 3.41.7 Bushwick Chlamydia 2.41.4 GC1981 2.41.5 HIV 3.72.0 Houston 3.01.7 Manitoba 0.80.5 Matrix 3.21.9 PPNG 2.41.8 Project 90 7.64.2 Rockdale 6.24.7 Syph318 2.51.5 Urban 4.52.5

42. Concurrency—NEEDLE partners StudyEgocentricSociogram Antiviral 1.50.7 Bushwick 3.62.1 Chlamydia GC1981 HIV 1.60.8 Houston 4.93.3 Manitoba Matrix PPNG Project 90 8.34.7 Rockdale Syph318 Urban

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

44. 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

45. Transitivity by study (all relationships) Transitivity (percent) AllSexualNeedle Antiviral0.0 Bushwick5.490.06.96 Chlamydia0.0 GC19812.08 HIV5.925.840.0 Houston14.070.032.67 Manitoba0.0 Matrix7.520.85 PPNG23.910.0 Project 906.950.4311.04 Rockdale11.5411.24 Syph31811.390.0 Urban9.145.44

46. Transitivity by study (sexual relationships) Transitivity (percent) AllSexualNeedle Antiviral0.0 Bushwick5.490.06.96 Chlamydia0.0 GC19812.08 HIV5.925.840.0 Houston14.070.032.67 Manitoba0.0 Matrix7.520.85 PPNG23.910.0 Project 906.950.4311.04 Rockdale11.5411.24 Syph31811.390.0 Urban9.145.44

47. Transitivity by study (needle-sharing relationships) Transitivity (percent) AllSexualNeedle Antiviral0.0 Bushwick5.490.06.96 Chlamydia0.0 GC19812.08 HIV5.925.840.0 Houston14.070.032.67 Manitoba0.0 Matrix7.520.85 PPNG23.910.0 Project 906.950.4311.04 Rockdale11.5411.24 Syph31811.390.0 Urban9.145.44

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

49. Distribution of components Study Largest Component Next Largest Antiviral 121 23 Bushwick1261 42 Chlamydia 45 24 GC1981 204 97 HIV 324 28 Houston1091 24 Manitoba 26 25 Matrix 515 0 PPNG 537 15 Project 904223 52 Rockdale 98 0 Syph318 102 79 Urban 913272

50. Distribution of components Three exceptions Rockdale –Contact tracing, single outbreak Matrix –Snowball design Manitoba –Contact tracing, multiple isolated areas

51. Bushwick

52. Manitoba

53. GC1981

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

55. Calculation of Assortativity Using Newman’s approach: –Create a matrix of e ij 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

56. Assortativity by age and ethnicity All contacts AgeEthnicity EgocentricSociometricEgocentricSociometric Antiviral0.2420.2440.719 Bushwick0.2620.2540.7350.736 Chlamydia0.3920.3930.4980.504 GC19810.3260.3320.6160.619 HIV0.2740.2850.573 Houston0.2230.2210.7700.773 Manitoba0.2120.213 Matrix0.1950.1990.5000.501 PPNG0.441 0.3810.380 Project 900.2540.2510.568 Rockdale0.3540.3660.0680.128 Syph3180.2000.202 Urban0.229 0.5370.534

57. Assortativity by age and ethnicity Stratified by degree—all contacts Number of Partners AgeEthnicity 10.3910.571 20.3410.593 3-40.3100.629 5-90.3290.662 10+0.3140.575

58. Assortativity by age and ethnicity Sex contacts AgeEthnicity EgocentricSociometricEgocentricSociometric Antiviral0.2270.2310.6750.676 Bushwick0.2620.2600.7390.738 Chlamydia0.3920.3930.4980.504 GC19810.3260.3320.6160.619 HIV0.2710.2810.573 Houston0.2200.2290.7620.767 Manitoba0.2120.213 Matrix0.1820.1950.4660.471 PPNG0.4480.4510.3600.355 Project 900.2210.2190.4960.495 Rockdale0.3270.3290.0250.074 Syph3180.2330.223 Urban0.2060.2030.4550.457

59. Assortativity by age and ethnicity Stratified by degree—sex contacts Number of Partners AgeEthnicity 10.3870.609 20.3230.584 3-40.3110.566 5-90.3090.532 10+0.2390.420

60. Assortativity by age and ethnicity Needle contacts AgeEthnicity EgocentricSociometricEgocentricSociometric Antiviral0.4420.4580.4330.436 Bushwick0.2720.2610.6930.692 Chlamydia GC1981 HIV0.2860.2980.6310.620 Houston0.2620.2680.654 Manitoba Matrix PPNG Project 900.2770.2750.5800.575 Rockdale Syph318 Urban

61. Assortativity by age and ethnicity Stratified by degree—needle contacts Number of Partners AgeEthnicity 10.3550.759 20.3120.675 3-40.3230.735 5-90.2810.656 10+0.2270.447

62. Assortativity by degree (using respondent-respondent pairs only) Assortativity AllSexNeedle Antiviral0.515 Bushwick0.2960.4510.306 Chlamydia0.458 GC19810.325 HIV0.3450.3500.304 Houston0.3800.4520.326 Manitoba0.337 Matrix0.2260.314 PPNG0.3380.253 Project 900.3540.2310.196 Rockdale0.1470.178 Syph3180.2410.209 Urban0.3260.405

63. Asssortativity Summary by type of contact Assortativity Contacts AgeEthnicityDegree All 0.279 (0.199-0.441) 0.549 (0.128-0.773) 0.330 (0.147-0.515 Sex 0.274 (0.195-0.451) 0.521 (0.074-0.767) 0.330 (0.178-0.458) Needle 0.312 (0.261-0.458) 0.596 (0.436-0.692) 0.283 (0.196-0.326)

64. 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.

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

66. —selected sites A = Acquaintance N = Needle D = Drug S = Sex Proj90HoustonManitoba.. 014 A1900451 N156107 N A16149 D662460 D A90779 D N143120 D N A24546 S8371182924 S A55993 S D323 S D A6514 S D220112 S D A48964 S D N3011 S D N A13824

67. Multiplexity by study site MultiplexitySex + DrugsSex + Needles (percent) Antiviral37.314.70.3 Bushwick75.00.0 Chlamydia0.0 GC19810.0 HIV2.80.02.8 Houston35.711.93.0 Manitoba0.0 Matrix51.023.90.0 PPNG0.0 Project 9045.713.44.0 Rockdale0.0 Syph31812.53.10.0 Urban47.423.00.0

68. General Observations--1 A heterogeneous group of studies Considerable variability by: – Demographics – Risk-taking – Disease prevalence

69. 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

70. General Observations--3 Considerable variability with regard to connectivity factors: –Recursion –Concurrency –Transitivity (clustering) –Assortativity (age, ethnicity, degree) –Multiplexity

71. 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

72. Empirical data support a bottom up approach A rough correspondence…. Social and geographic choices Timing and sequence Specific acts Attribute mixing Recursion Concurrency Transitivity (clustering) Multiplexity Assortativity Local RulesNetwork Properties

73. Connecting these factors to disease transmission…

74. Prevalence of STDs and HIV—13 studies

75. 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

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

77. 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 Muth John Potterat Rich Rothenberg Bob Trotter TheoreticiansEmpiricists