The limit of sexual networks data: Implications for mathematical modelling of STI Marie-Claude Boily Department of Infectious Disease Epidemiology + le singe Page 1 © Imperial.
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The limit of sexual networks data: Implications for mathematical modelling of STI Marie-Claude Boily Department of Infectious Disease Epidemiology + le singe Page 1 © Imperial College London Thanks to Roel Bakker for network picture We know Network structure is important On disease transmission: • Individual level • risk of infection • risk of transmission • Population level • establishment • persistence Page 2 © Imperial College London • Mean, Variance, Core group Yorke&Hetcothe&Nold (1978), Anderson&May(1991) • Mixing by sexual activity, age,race, etc Blythe&Castillo-Chavez(1989),Gupta et al(1989), Sattenspiel et al(1990), Boily&Anderson(1991), Garnett et al(1996), Aral et al(1999), Gregson et al(2002) • Duration • Interval between partnerships Kretzschmar&Dietz(1998), Hadeler(1992), Kraut-Becher&Aral (2003), Riolo et al (2001) • Concurrency Watts&May(1992), Kreztchmar & Morris(1996), Altmann(1998), Kelley et al (2003), Rosenberg et al (1999), Lagarde et al (2002), Lepont et al (2003) Koumans et al(2001) • Local centrality,Global centrality Ghani et al (2000), Potterat (1999) Rothenberg et al (1995), Bell (1999). Page 3 © Imperial College London • Mean, Variance, Core group Yorke&Hetcothe&Nold (1978), Anderson&May(1991) Critical level of sexual activity 45 infectivity=10% infectivity= 30% Infectivity= 50% infectivity = 80% Mimimum number of partners(Cc) 40 Ro= B c D >1 Cc = 1/ (B c) 35 30 25 20 15 10 5 0 3 4 5 6 7 8 9 10 11 12 Duration of infectiousness (D) (months) Page 4 © Imperial College London 36 60 120 • Mean, Variance, Core group Yorke&Hetcothe&Nold (1978), Anderson&May(1991) Garnett (2002), STI Page 5 © Imperial College London • Mean, Variance, Core group Yorke&Hetcothe&Nold (1978), Anderson&May(1991) • Mixing by sexual activity, age,race, etc Blythe&Castillo-Chavez(1989),Gupta et al(1989), Sattenspiel et al(1990), Boily&Anderson(1991), Garnett et al(1996), Aral et al(1999), Gregson et al(2002) Yaounde Cotonou Page 6 © Imperial College London • Mean, Variance, Core group Yorke&Hetcothe&Nold (1978), Anderson&May(1991) • Mixing by sexual activity, age,race, etc Blythe&Castillo-Chavez(1989),Gupta et al(1989), Sattenspiel et al(1990), Boily&Anderson(1991), Garnett et al(1996), Aral et al(1999), Gregson et al(2002) Page 7 © Imperial College London Detailed micro-simulation/network models • • More intuitive More realistic? – Full network structure, sexual behaviour – Dynamics of infection • Flexibility – Easy to introduce complexity – Wide range of research questions • • Page 8 Epidemiological and methodological Individual and population level © Imperial College London Population Individual behaviour Population Network Sampled network Incomplete understanding of human behaviour Network model Simulated Network Validation Individual rules infected population Behavioural process Partnership formation Concurrent partners Partnership duration Preferred partner type etc Page 9 © Imperial College London Impact of disease on network over time Incomplete network data Biology of Infection + Thanks to Roel Bakker for network pictures Outline • Do not know if network simulated representative of the REAL population network 1. Incomplete understanding of human behaviour 2. Limited data on sexual behaviour 3. Change in the network structure over time – due to the spread of disease itself Page 10 © Imperial College London Defining behavioural process • Do not know which set of individual rules determine real sexual population networks completely – Most obvious rules: • Observed behaviour – More subtle rules: • Intuition Influence on network structure? Page 11 © Imperial College London Simulation of Large Static Multi-Component Networks 900 simulated networks Between components 60 % Monogamous Centrality: within largest component 800 % in largest component % single 700 50 Average(distance)/10000 600 500 40 Percent (%) Eccentricity 400 30 300 20 200 10 0 25000 100 0 27000 29000 31000 33000 35000 0 Number of components (nc) Fixed number of links between activity classes: •Fixed size = 100 000 •Fixed distribution in sexual activity (m1-15=1.5, v=3) •Fixed Mixing (Proportionate) Page 12 © Imperial College London 10000 20000 30000 40000 Size of largest component (# individuals) 50000 Between components Number of components Size of largest component 300 simulated networks 45 34000 40 Size of largest components (%) Number of components (nc) 33000 32000 31000 30000 29000 28000 27000 26000 25000 -0.6 Individual selection rule:Old -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 Partenrship formation (L2) low-low random Partnership selection rule (L2) Page 13 © Imperial College London high-high 35 30 25 20 15 10 5 0 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 L2 Size of largest component 300 simulated networks Individual selection rule:Old 45 Size of largest components (%) 40 35 30 25 20 15 10 5 0 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 low-low Page 14 © Imperial College London 0 0.1 0.2 0.3 0.4 0.5 0.6 L2 random Partnership selection rule (L2) high-high Size of largest component 600 simulated networks Individual selection rule:Old 45 Individual selection rule: New Size of largest components (%) 40 35 30 25 20 15 10 5 0 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 low-low Page 15 © Imperial College London 0 0.1 0.2 0.3 0.4 0.5 0.6 L2 random Partnership selection rule (L2) high-high Size of largest component 900 simulated networks Individual selection rule:Old Individual selection rule: New Individual selection rule: random 45 Size of largest components (%) Proportionate mixing 40 35 30 25 20 15 10 5 0 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 low-low Page 16 © Imperial College London 0 0.1 0.2 0.3 0.4 0.5 0.6 L2 random Partnership selection rule (L2) high-high Implications • Choice of rules/algorithm – Can biased simulated networks toward a region of networks with specific structural properties – Random variation small: • Difficult to create a large variety of network structures • Too restraint variety of network structures Miss impact of risk factors – Random variation large: • Can obtain various network structures • Too restraint variety of network structures Miss impact of risk factors Page 17 © Imperial College London Outline • Do not know if network simulated representative of the REAL population network 1. Incomplete understanding of human behaviour 2. Limited data on sexual behaviour 3. Change in the network structure over time – due to the spread of disease itself Page 18 © Imperial College London Behavioural data ↑ Empirical studies on sexual behaviour, sexual network Key words Number of "hits" on Medline Cumulative number of studies with some info on numbers of sexual partners 1800 Number of sexual partners • Number of sexual partners 180 • Representative study (ies), survey(s), sexual behaviour, sexual activity level 1600 Representative study on sexual behaviour Mixing 160 1400 Sexual networks 140 1200 120 1000 100 800 80 600 60 400 40 200 20 0 0 <=1960 <=1970 <=1980 <=1985 <=1990 <=1995 <=2000 <=2005 Year of publication Page 19 200 © Imperial College London Cumulative number of studies 2000 • Number of sexual partners in general population, homosexual (heterosexual) population, representative sample • Sexual activity in homosexual, heterosexual population • Sexual mixing, mixing patterns • (Empirical) sexual networks, sexual partnership (s), partner (s) network (s) Individual based data • Detailed representative sexual behaviour still limited for many population – Low risk population often under-documented – Unbalanced sexual activity between sexes when reported by men or female • Sampling bias • Misreporting bias – Culture specific Potterat et al, Int J STD AIDS. 2001 Page 20 © Imperial College London – Behaviour crudely reported: categories Page 21 © Imperial College London • Sexual activity distribution and mixing does not define the network uniquely Log (Mean component size) Assortative Proportionate Disassortative • Page 22 Good fit does not mean we have simulated the right population network © Imperial College London Network data Year Objective Sample Alden and Klovdhal et al, 1992 1985 Study a network of HIV infected persons 44 homosexuals egocentric, sociocentric Study cluster of HIV infection 44 homosexuals egocentric sociocentric Auerbach, et al, 1984 Location Network characterstics Authors Rothenberg et al, 1998 19881992 Assess the stability of network over 3 years 595 (CSW+ IDU + sexual partners) 6000 contacts Colorado Springs, US sociocentric Potterat et al, 1999 19881992 Exploration of change in structural change in 2 different population networks •99 adolescents •Atlanta, Georgia, US •Colorado Spring egocentric sociocentric •595 heterosexual at risk of HIV Friedman et al, 1997 19911993 To assess association between network characteristics and HIV 767 IDU New-York, US sociocentric Friedman et al, 2000 19911993 To study reasons of HIV prevalence saturation in IDU 767 IDU over 30 days, 2 years New-York, US egocentric but mainly sociocentric Day et al, 1998 19941996 Describe sexual networks of Gc patients from 2 UK departments of genitourinary medicine •Heterosexual and homosexuals •510 Gc cases+ 1228 contacts •235 Gc cases+ 335 contacts •over 3 months Page 23 © Imperial College London egocentric sociocentric •London, UK •Sheffield, UK Authors Year Objective Sample Location Network characterstics Potterat et al, 1999 19961997 Identify individual and population-level determinants of Ct transmission 1309 Gc cases + 2409 contacts over 6 months Colorado Springs, US egocentric sociocentric Wylie & Jolly, 2001 19971998 To study patterns of Gc and Ct 4544 Gc or Ct male and female cases + contacts Manitoba, Canada sociocentric Jolly et al, 2001 1996, and 19971998 Compare network structure between 2 cities Manitoba: 571 cases+ 663 contacts C.Spring: 468 cases+700 contacts Colorado Springs and Manitoba sociocentric To “test”the use of genetic serotyping data for the study of sexual netowrks 17 individuals over 6 months Sheffield, Derby, Southampton, UK limited sociocentric 48 CSW + 38 clients over 12 weeks Fishing villages, Uganda egocentric Study relation between HIV prevalence and network size Females in pre or post maternal care: 75 HIV+ 41partners & 137 HIV+ 70 partners over 1 year, 5 years, lifetime Lima, Peru egocentric To study the network strucutre+ behaviour among persons at risk of HIV over 6 months, 2 years Atlanta, Georgia, US egocentric sociocentric Day et al, 1998 Pickering et al, 1997 ? Johnson et al, 2003 19961997 Rothenberg et al, 2000 Page 24 © Imperial College London Contact tracing data • Sample of infected individuals + contacts – Completeness of data: • Diagnosis, sensitivity, number of contacts – Not necessarily representative of population networks • Initial sample: high-risk population • Following waves: not representative of populations of links Page 25 © Imperial College London Frequency (percent) Sexual behaviour of gonorrhoea patients compared with ‘general’ US population 80 Newark Men NHSLS Men 60 40 20 0 0 1 2 to 4 5+ Frequency (percent) Number of sex partners over 1 year 80 Newark Women 60 NHSLS Women 40 20 0 0 1 2 to 4 5+ Number of sex partners over 1 year Page 26 © Imperial College London Garnett et al, 1999 Laumann et al, 1994 Changes in sample composition over time • Contact tracing sample depends on the stage of the epidemic Blanchard, STI, (2002) Page 27 © Imperial College London True Mean = 1.5 partner Bias (Estimate-True) Bias (Estimate-True) Bias Page 28 © Imperial College London Example: Estimation of mixing pattern based on snowball sampling Male activity classes j= 1 2 3 4 Mixing Matrice elements Female activity classes Q=0 proportionate Q>0 assortative Q<0 disassortative Page 29 © Imperial College London 5 i= 1 P11 P12 P13 P14 P15 2 P21 P22 P23 P24 P25 3 P31 P32 P33 P34 P35 4 P41 P42 P43 P44 P45 5 P51 P52 P53 P54 P55 Q Bias on assortativity indice = (Estimated Q – True Q= 37) Page 30 © Imperial College London Centrality measures estimates Ghani et al, STD, (2000) Fig. 3. Errors in measures of network position in sampled networks. High values of p1-p2 indicate good estimates, whereas values close to or less than zero indicate poor estimates; error in measures of global centrality by snowball sampling continuously Page 31 © Imperial College London Implications • Structural properties of network ill represented: – For unbiased estimates use sample “strategically” • Distribution in sexual activity: index cases • Mixing: 1 cycle, random selection of links • Measures of centrality (closeness, information centrality, etc): long chains (Ghani et al (2000)) Page 32 © Imperial College London Outline • Do not know if network simulated representative of the REAL population network 1. Incomplete understanding of human behaviour 2. Limited data on sexual behaviour 3. Change in the network structure over time Page 33 © Imperial College London Changes over time • Available behavioural or Network data – One point in time (Cross-sectional studies) • Changes in behaviour and network structure over time Distribution per Sexual Activity Level – Even in absence of prevention – For lethal infectious diseases 0.6 Class 1 Class 2 Class 3 Class 4 Class 5 Class 6 0.5 • Differential mortality (e.g. AIDS) Percentage 0.4 0.3 0.2 0.1 0 Page 34 © Imperial College London 1975 Time (year) •Blower et al(1993) Closed cohort of MSM in Amsterdam over 7 years 21% reduction in mean number of partners (m) 33% reduction in variance (v) 29% reduction in effective mean rate (c=m+ v/m) Variance in sexual activity 80 Initial sample 70 Expected if no individual change Variance (Numer of partners) Total Change 60 Differential Mortality = -33% 50 40 Observed Individual Change 30 20 10 83 84 85 86 87 89 90 91 Final sample 0 Page 35 88 © Imperial College London Time (Year) 92 Example: Impact of wide-scale use of antiretroviral therapy on STI Sexual behaviour and STI Effect of ART at the individual level 0.05 5 0.045 4.5 4 ART 3.5 0.03 3 Sexual activity 0.025 2.5 0.02 2 0.015 1.5 0.01 1 STI 0.005 0.5 0 – Slows disease progression prolong incubation period – Potentially reduce infectivity of HIV+ treated →Differential replenishment HIV 0 0 20 40 60 80 100 Time (Years) STI prevalence: with ART STI prevalence: no ART Risky sex: no ART Risky sex: with ART 0.2 0.18 0.16 0.14 Proportion Proportion 0.035 Mean risky sex (new partners/year) 0.04 – Prolongs survival of AIDS patients+ improve quality of life 0.12 0.1 0.08 0.06 0.04 0.02 Boily et al , STD (in press) Page 36 © Imperial College London 0 0 20 40 60 Time (Years) 80 HIV Prevalence: no ART HIV prevalence: with ART HIV incidence: with ART HIV incidence: no ART 100 STI vs sexual behaviour Over 10 years after ART Page 37 © Imperial College London HIV vs STI Over 10 years after ART Page 38 © Imperial College London STD clinic: gonorrhoea 1981 - 2001 homosexual men in Amsterdam anorectal other 19 81 19 83 19 85 19 87 19 89 19 91 19 93 19 95 19 97 19 99 20 01 1400 1200 1000 800 600 400 200 0 Page 39 © Imperial College London Unprotected anal sex (%) young (<35 years) homosexual men in cohort Reported at cohort visits Time periods: % 100 October ’84 - April ’87 90 May ‘87 - February ’92 80 March ’92 - June ’96 70 Ref. * 60 July ’96 - December ’99 Ref. 50 40 30 Page 40 HIV-1 neg. © Imperial College London HIV-1 pos. Dukers, AIDS 2001 Implications (2) • Interpret current trends • Prevention – Differential AIDS mortality: • Overestimate impact of prevention at the beginning of the HIV epidemic – Differential ART replenishment: • Overestimate relapse to risky sex after treatment availability – Developing countries largely afflicted by HIV/AIDS where ART as yet to become widely available • Increase in STI and sexual behaviour expected • Important considerations – Impact of population-level changes on individual behaviour – Risk of trying altering the network as preventive measures Page 41 © Imperial College London Impact of AIDS mortality on individual behaviour and network structure Ind 1 Ind 1 ? Ind 2 ? Ind 4 Ind new ? Ind 3 ? Ind 2 Ind 3 Ind 4 Ind 4 Goes back to uncertainty in behavioural rules Page 42 © Imperial College London Discussion Model limitations - Causes for concerns? • Do not know if network simulated representive of the population network • Does it really matter? – If presuppose network are important yes – More complex model ≠ Necessarily betterFalse sense of security • Assessment of the impact of network characteristics on disease transmission depends on the characteristic of network simulated – Too restraint variety of network structures Miss impact of risk factors – Too large variety of network structures Find non relevant risk factors – Unfortunately with most complex network models: Page 43 • Behavioural process not always thoroughly described – Non Reproducible • A description of the structure of network not always presented – Non Comparable © Imperial College London Ackowledgments • Special thanks to Martina Morris and Claudia Neuhauser • • • • • Page 44 Robert Poulin (ABB) Roel Bakker (Erasmus University) Azra Ghani (Imperial College) Geoff Garnett (Imperial College) Anu Gupta (MHRC) © Imperial College London End Page 45 © Imperial College London