![Yorke and Hethcote’s logic…
• They concluded that, for gonorrhea to propagate, there must be some areas of intense
transmission and some areas with little transmission (“terminal” cases).
• The observed R0 must therefore be a weighted average of many areas with very low
transmission, and a few areas with intense transmission.
• For example, if 4% of all areas account for most/all cases either directly or
indirectly, then the overall R0 would be:
• R0 = [p1R01] + [p2R02]
• R0 = (0.96)(0.22) + (0.04)(3.0) = 0.33](https://image.slidesharecdn.com/rothenbergmoodyworkshop-190927192911/85/24-The-Evolution-of-Network-Thinking-20-320.jpg)
24 The Evolution of Network Thinking
- 1. The evolution of network thinking (A mole’s eye tour) Richard Rothenberg, MD MPH FACP Regents’ Professor School of Public Health Georgia State University rrothenberg@gsu.edu
- 2. The role of quantitative methods is to provide us with qualitative answers.
- 3. My vote for the starting point: Leonard Euler and The Konigsburg Bridge, 1735 Start and end at the same place. Cross each bridge only once without doubling back. Euler’s insight was to make the land masses nodes (A,B,C,D), and the bridges, edges (a,b,c,d,e,f,g)—the origination of graph theory https://www.maa.org/press/periodicals/convergence/leonard-eulers-solution-to-the-konigsberg-bridge-problem
- 4. Conventional network attribution Conventional wisdom attributes the first network diagrams to Juan Moreno, 1934
- 5. But the origins are far more complex…. Pfeiffer J, Freeman LC. Social Network Visualization, Methods of. In Meyers RA (ed.) Encyclopedia of Complexity and Systems Science. https://doi.org/10.1007/978-3-642-27737-5_496-2
- 6. Network primordia Munson WL . Epidemiology of syphilis and gonorrhea . AJPH 1933 ; 23:797-808
- 8. But an interesting parallel emerged… The Mainstream 1920s—early antecedents 1930s—Moreno, sociograms 1950s—Graph theory (Erdos, Rappaport, Frank, etc. 1960s ff—sociologic theory and mathematical development (many people) 1980s ff—HIV/AIDS, larger studies, theoretical development 1999 ff—Statistical physics “intrudes” 2000s ff—social media, big data, weaponization of networks. 2000s ff—network modeling (esp. ERGMs (many people) A Sidestream 1933—Munson (syphilis and gonorrhea epidemiology 1937—Parran (Shadow on the Land, contact tracing) 1965—Russ Havlak (the lot system) (VCI-> PHI->DIS) 1981—Auerbach et al. (a bicoastal epidemic) 1984—Yorke, Hethcote, Nold— gonorrhea transmission 1985—Klovdahl (network aspects of HIV/AIDS 1988 ff—STD and HIV empirical networks
- 9. Parallel play Graph Theory (1950s- 60s…) Anatol Rapoport Paul Erdos Alfred Renyi Ove Frank Julian Besag Small Empirical Studies Network analytic development Network theory Granovetter Burt Wellman Morris Doreian Focus on social interaction After WWII VD Control Program Contact tracing Interview Epidemiologic Rx Case investigation Administrative structure 63 Project areas 800+ PHAs at peak Forms Lot System AIDS 1930s………………………………………………………………………………………………………………………1970s
- 10. The first network diagram relating persons with a strange new syndrome of immunodeficiency, reproduced from Auerbach M, Darrow WW, Curran JW. Cluster of cases of the acquired immune deficiency syndrome: patients linked by sexual contact. Am J Med 1984; 76:487-492 for this special issue of Connections
- 11. A connected group of persons (Lot 004) identified by contact tracing for Gonorrhea Colorado Springs, CO, 1981
- 12. The same group: Network diagram constructed 20 years later
- 13. How do we connect “micro” to “macro” (1973 version) “…A fundamental weakness of current sociological theory is that it does not relate micro-level interactions to macro-level patterns in any convincing way… …how interactions in small groups aggregate to form large-scale patterns eludes us...” Granovetter MS. The strength of weak ties. Am J Sociol 1973;78:1360-1380.
- 14. How “micro” is aggregated to “macro” Morris suggested that local rules (meaning choices made by people at risk or factors that influence such choices) will generate the global properties of networks. Robins G, Pattison P, Woolcock J. Small and other worlds: global network structures from local processes. Am J Sociology 2005;110(4):894-936 Morris M. Local Rules and Global Properties: Modeling the Emergence of Network Structure. In: Breiger R, Carley K, Pattison P, editors. Dynamic Social Network Modeling and Analysis. Washington, DC: National Academy Press, 2003.
- 15. Local (micro) decisions create global (macro) patterns (2005 version) “Actors do not usually cast their gaze across the entire network, possibly because in most cases they can only “see” what is in their local social neighborhood. On the basis of their localized view, they form strategies and make decisions that intersect with those others who are socially proximate. Combinations of these competing or complementary intentions and actions constitute social processes that make up local patterns of relationships. These local patterns agglomerate to create the global structure.” Robins G, Pattison P, Woolcock J. Small and other worlds: global network structures from local processes. Am J Sociol 2005;110(4):894-936
- 16. Where this leads…. • If we have a set of behaviors… • …and a set of network relationships… • …and a group of people between and among whom diseases are transmitted… • Can we account for observed epidemic and endemic disease spread? • The core group concept
- 18. Yorke and Hethcote’s original logic • In 1976, they consulted on the gonorrhea surveillance program: What had been its effect? • They examined contact tracing data and found that, on average, 3 infected persons generated 1 new case of gonorrhea. • They thus noted that the R0 = 0.33 • They concluded that gonorrhea should have died out.
- 19. Gonorrhea trends around 1976 0 200,000 400,000 600,000 800,000 1,000,000 1,200,000 1940 1950 1960 1970 1980 1990 2000 Year Number of cases 1947 1957 1975 1984 19971965 Gonorrhea was not exactly disappearing…
- 20. Yorke and Hethcote’s logic… • They concluded that, for gonorrhea to propagate, there must be some areas of intense transmission and some areas with little transmission (“terminal” cases). • The observed R0 must therefore be a weighted average of many areas with very low transmission, and a few areas with intense transmission. • For example, if 4% of all areas account for most/all cases either directly or indirectly, then the overall R0 would be: • R0 = [p1R01] + [p2R02] • R0 = (0.96)(0.22) + (0.04)(3.0) = 0.33
- 21. Yorke and Hethcote’s logic… • They then postulated that there exist groups, who constitute less than 5% of gonorrhea transmitters, and who account for most or all of transmission either directly or indirectly. • They designated such groups “Core Groups” and attributed to them the following characteristics • Heterogeneity • Definable demographic and behavioral characteristics • Frequent sexual contact with the potential for transmission • Bounded social or geographically • Stable in the intermediate or long term
- 22. Yorke and Hethcote’s logic… What Core groups are NOT: • Transient, rapidly changing, ephemeral • Marked by impermanent characteristics – e.g., contact to a case – Casual sex partners – Homogeneous, disconnected group YORKE JA, HETHCOTE HW, NOLD A. Dynamics and Control of the Transmission of Gonorrhea. Sexually Transmitted Diseases. 1978;5(2):51–56. Hethcote HW, Yorke JA. Gonorrhea Transmission Dynamics and Control. Lecture Notes in Biomathematics (ed. Levin, S.) Springer-Verlag Berlin, 1984
- 23. How the term “core group” has been used • Groups whose prevalence (of gonorrhea) is at least 20% • Prostitutes • Persons who have many sexual contacts • Very sexually active women and men who are asymptomatic when infectious • Census tracts that are the source of >50% of reported cases • Gonorrhea transmitters: persons with >2 infected contacts • People repeatedly infected • People who have a high rate of acquisition of new partners • Groups of people whose sexual activity provide opportunities for sustained transmission • Smallest possible subpopulation such that removal of its members would bring the the basic reproductive number to < 1. • People who, on average, generate >1 new infection • Drug using prostitutes recurrently infected with STDs • Adolescent males in detention • People with >5 sex partners per year • People with clusters of high risk behaviors Thomas JC, Tucker MJ. The development and use of the concept of a sexually transmitted disease core. J Infec Dis 1996;174(Suppl 2):S134-S43.
- 24. Core groups: competing definitions Core groups Core compartments Core networks Defined by Sociodemographics Behavior Social, temporal or geographic cohesion Examples IDU; CSW; 24 y old male drug dealers West side of Zipcode 30318; Youth gang; Smith St. Characteristics Homogeneous, not necessarily connected (‘core person’) Heterogeneous, tied together (no ‘core person’) How ascertained Traditional sampling Targeted sampling Network sampling methods; ethnography How studied Risk factor epidemiology; Mixing patterns; Compartment modeling Network analysis; Visualization; Ethnographic methods Network modeling
- 25. The Power Law construct
- 26. The Power Law construct 0 5 10 15 20 25 30 35 40 45 0 5 10 15 20 25 Number of partners Frequency (%) Cumulative Probability Distribution (CPD) Combined data sets (N=39,890 dyads) 0.0001 0.001 0.01 0.1 1 1 10 100 log (number of partners) log (CPD)
- 27. The low-degree, high-concurrency construct
- 28. The low-degree, high-concurrency construct Helleringer S, Kohler H. Sexual network structure and the spread of HIV in Africa: evidence from Likoma Island, Malawi. AIDS 2007;21(17):2323-32 Graphic from an earlier working paper.
- 29. Morris M, Goodreau S, Moody J. Chapter 7. Sexual Networks, Concurrency, and STD/HIV. In Sexually Transmitted Disease. Ed. Holmes, KK et al. McGraw Hill 2007 1.68 1.74 1.80 1.87
- 30. Local choices Sexual behavior Drug use Partner selection Global Network Attributes Degree Distribution Small World, Giant Component Cohesion Concurrency Transitivity Assortativity Compound Risk Multiple partners Multiple exposures Multiple channels Geographic proximity Compactness Stability Spatial autocorrelation Personal geographic range Endemic Propagation A conceptual model for endemic urban transmission
- 31. Global Network Attributes Compound Risk Endemic Propagation A conceptual model for endemic urban transmission Local choices Geographic proximity
- 32. A follow up study to see if this works…
- 33. Study Design: Distribution of cumulative AIDS cases, 1998-2003, Atlanta (Fulton County), GA.
- 34. Compound Risk
- 35. Components of compound risk Components of compound risk (total N = 894) Components N % 10 or more total sex partners, 6 m 67 7.5 6 or more male sex partners, 6 m 234 26.2 Ever injected drugs, lifetime 14 1.6 Ever engaged in sex work, lifetime 37 4.1 Ever had sex with an IDU, lifetime 24 2.7 Anal sex, 6 m 80 9 Distribution of component frequency The Percent of persons with a given number of components # % 0 64.1 1 25.1 2 7.4 3 2.8 4 0.6 5 0.1 6 0.0 Comparison of compound risk (2 or more major risks) N % Lower Risk Area 24 5.7 Higher Risk Area 73 15.5 Areas combined 97 10.9
- 37. The relationship of social to geodesic distance Social Distance (# of edges) Geodesic Distance (km) 1 2 3 4 5 6 7 8 9 10 0 19 17 20 4 6 3 3 1 . 6 1 71 113 77 50 45 30 34 15 12 13 2 102 114 120 98 58 49 45 33 17 27 3 95 166 135 119 71 53 51 48 33 47 4 82 118 129 86 84 56 71 47 46 52 5 73 126 115 80 63 72 61 51 37 52 6 55 87 93 62 58 54 67 48 52 49 7 40 54 74 49 55 62 70 57 37 51 8 25 55 69 61 54 37 40 36 38 52 9 13 40 56 44 36 49 42 35 37 39 10 19 30 44 30 32 32 35 26 25 32 The n x n squares contain all the dyads with those boundaries.
- 38. The proportion of dyads enclosed with increasing larger “squares” of the social matrix
- 39. Distribution of geographic distances
- 40. Polygon overlap: a method for determining personal contiguity
- 41. Typical overlap, also showing major centers of activity for participants
- 42. Geographic dispersion: overlap of group members
- 44. Comparison of network characteristics Comparison of network characteristics in higher and lower risk areas Network characteristics Lower risk N=15 Higher risk N=15 HIV PREVALENCE 0.12 0.17 Number of nodes (mean) 248.53 288.27 Number of Ties (mean) 282.20 318.60 Number of components (mean) 4.33 7.27 Size of Largest component (mean) 196.40 218.93 Proportion of persons in the largest component 0.79 0.77 Degree (mean) 2.19 2.13 Degree (variance) 12.71 12.73 Concurrency (mean) 7.00 7.10 Network Centrality (based on degree) 9.32 8.73 Transitivity 0.02 0.01 Betweenness 17.70 24.73 Average distance between nodes (mean) 4.22 4.19 Diameter (largest average distance) (mean) 7.53 7.40 Point connectivity (mean) 0.91 0.98
- 45. Log-log plot of the number of partners (degree) vs. their probability
- 46. Global Network Attributes Compound Risk Endemic Propagation Some tentative conclusions about maintaining endemicity Local choices Geographic proximity ! ! ?
- 47. Next steps: paying attention to “C” Exposure Yes No Outcome Yes a b No C d Why do some people who are exposed NOT get the adverse outcomes?
- 48. C: the complement of risk The Complement of Risk: a few examples Percent Proportion of households with two parents 25.1 Proportion of adult AA men who have not been incarcerated 75.0 Proportion of teenage girls who have not had a pregnancy, ages 15-19 93.2 Proportion of persons 25+ who graduate from high school 22.3 Proportion of high school students who do not smoke 83.0 Proportion of adults who are employed 54.9 Proportion of owner occupied housing units 43.7 Proportion of persons without disabilities 77.7 Proportion of families above poverty line 78.7 Proportion without HIV in the highest risk areas 92.5
- 49. Core-Periphery In these 30 networks, we define “core” as persons who have HIV or are directly connected to someone with HIV. We define “periphery” as persons who are at least two steps away from persons with HIV (everyone else)
- 50. Are people in the “Core” different from those in the “Periphery”? An initial approach: determine whether position (i.e., core-periphery) is as or more important that area (higher-lower risk). There are some 340 variables in this study that describe respondents, contacts, and the dyadic relationships. 871 persons were interviewed and many of them were also named as contacts: 783 were peripheral 88 were core
- 51. The Odds Ratio as a screening tool Using a simple logistic framework… 0 1 2 3log ( ) ( ) ( ) 1 Var area position gender Var …we can screen a large number of variables to determine whether area or position (or gender) has the greatest effect.
- 53. Some critical distinctions: comparing position and area
- 54. Applying this approach to methods of transportation
- 55. The peripheral person—ORs on logarithmic scale
- 56. From quantitative to qualitative: Comparing core and peripheral persons The peripheral person is much less like to: • Have been incarcerated • Ever used heroin or cocaine • Ever injected a drug • Ever had injecting sex partners • Been homeless • Walks, primarily The peripheral person is more like to: • Be in good or excellent health • Drive him/herself primarily • Have a paying job • Be heterosexual • Ever had chlamydia • Have completed 8th grade
- 57. Some tentative conclusions There is an observable difference in persons who occupy different positions in the network. For some of these differences, position in the network appears to be more important that the risk area of residence. For some characteristics, being female is more important than either area or position. Where does this lead?
- 58. The role of quantitative methods is to provide us with qualitative answers.
- 59. Crime Racism Poverty Violence Joblessness Homelessness Family Disintegration Community Disintegration Withdrawal of Infrastructure Nonfunctional Public Education Poor Health Care Access Desertification Early Pregnancy Vaccine-Preventable Diseases Low Birth Weight Infant Mortality Substance Abuse Tuberculosis Inner City Syndemics STDs HIV
- 60. The locked-in syndrome The glass walls of geographic immobility. Economic Educational