Degree Distributions in Sexual Networks: A Framework for Evaluating Evidence

Objective: We present a likelihood based statistical framework to test the fit of power-law and alternative social process models for the degree distribution, and derive the sexually transmitted infection epidemic predictions from each model. Study Design: Five surveys from the United States are analyzed. Model fit is formally compared via Akaike Information Criterion and Bayesian Information Criterion, and substantively assessed via the prediction of a generalized epidemic. Results: Formal goodness-of-fit tests do not consistently identify any model as the best all around fit to the US data. Power-law models predict a generalized sexually transmitted infection epidemic in the United States, while most alternative models do not. Conclusions: Power-law models do not fit the data better than alternative models, and they consistently make inaccurate epidemic predictions. Better models are needed to represent the behavioral basis of sexual networks and the structures that result, if these data are to be used for disease transmission modeling.

[1]  M. Handcock,et al.  Likelihood-based inference for stochastic models of sexual network formation. , 2004, Theoretical population biology.

[2]  S. Goodreau,et al.  Sexual role and transmission of HIV Type 1 among men who have sex with men, in Peru. , 2005, The Journal of infectious diseases.

[3]  J A P Heesterbeek,et al.  The metapopulation dynamics of an infectious disease: tuberculosis in possums. , 2002, Theoretical population biology.

[4]  J. O. Irwin,et al.  The Place of Mathematics in Medical and Biological Statistics. , 1963 .

[5]  Michel Hubert,et al.  Sexual Behaviour and HIV/AIDS in Europe. Comparisons of national surveys , 1998 .

[6]  Albert,et al.  Topology of evolving networks: local events and universality , 2000, Physical review letters.

[7]  William C Miller,et al.  Prevalence of HIV infection among young adults in the United States: results from the Add Health study. , 2006, American journal of public health.

[8]  H E Stanley,et al.  Classes of small-world networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[9]  R. May,et al.  Epidemiology. How viruses spread among computers and people. , 2001, Science.

[10]  H. Simon,et al.  ON A CLASS OF SKEW DISTRIBUTION FUNCTIONS , 1955 .

[11]  R. May,et al.  How Viruses Spread Among Computers and People , 2001, Science.

[12]  E. Laumann,et al.  Social Network Effects on the Transmission of Sexually Transmitted Diseases , 2002, Sexually transmitted diseases.

[13]  L. Hedges,et al.  Reports of elapsed time: bounding and rounding processes in estimation. , 1990, Journal of experimental psychology. Learning, memory, and cognition.

[14]  T. Heeren,et al.  Transmission of Chlamydia trachomatis and Neisseria gonorrhoeae among men with urethritis and their female sex partners. , 1998, The Journal of infectious diseases.

[15]  R. Perline.  Strong, Weak and False Inverse Power Laws , 2005 .

[16]  W. Miller,et al.  Methods for Detection of Trichomonas vaginalis in the Male Partners of Infected Women: Implications for Control of Trichomoniasis , 2006, Journal of Clinical Microbiology.

[17]  William C Miller,et al.  Prevalence of chlamydial and gonococcal infections among young adults in the United States. , 2004, JAMA.

[18]  H. Akaike.  A new look at the statistical model identification , 1974 .

[19]  Elizabeth R Unger,et al.  Prevalence of HPV infection among females in the United States. , 2007, JAMA.

[20]  M. Morris,et al.  Telling tails explain the discrepancy in sexual partner reports , 1993, Nature.

[21]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[22]  William C Miller,et al.  Sexual and drug behavior patterns and HIV and STD racial disparities: the need for new directions. , 2007, American journal of public health.

[23]  S. Aral,et al.  Sexual network patterns as determinants of STD rates: paradigm shift in the behavioral epidemiology of STDs made visible. , 1999, Sexually transmitted diseases.

[24]  David R. Anderson,et al.  Model Selection and Inference: A Practical Information-Theoretic Approach , 2001 .

[25]  R. Anderson,et al.  For Personal Use. Only Reproduce with Permission from the Lancet Publishing Group , 2022 .

[26]  V. Sadock.  The Social Organization of Sexuality: Sexual Practices in the United States , 1995 .

[27]  Martina Morris,et al.  Consistency of Self-Reported Sexual Behavior in Surveys , 2010, Archives of sexual behavior.

[28]  R. Anderson,et al.  The Natural History of Syphilis: Implications for the Transmission Dynamics and Control of Infection , 1997, Sexually transmitted diseases.

[29]  K. P. Hadeler,et al.  Models for pair formation in bisexual populations , 1988, Journal of mathematical biology.

[30]  L. Amaral,et al.  The web of human sexual contacts , 2001, Nature.

[31]  C. Schofield.  Sexually transmitted disease surveillance. , 1982, British medical journal.

[32]  R. Anderson,et al.  Sexually transmitted diseases and sexual behavior: insights from mathematical models. , 1996, The Journal of infectious diseases.

[33]  G. Mcquillan,et al.  Herpes simplex virus type 2 in the United States, 1976 to 1994. , 1998, The New England journal of medicine.

[34]  A. Barabasi,et al.  Halting viruses in scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  A. Wald,et al.  Effect of condoms on reducing the transmission of herpes simplex virus type 2 from men to women. , 2001, JAMA.

[36]  K. Holmes,et al.  Cohort study of venereal disease. I: the risk of gonorrhea transmission from infected women to men. , 1978, American journal of epidemiology.

[37]  H. Jaffe,et al.  Risk of human immunodeficiency virus transmission from heterosexual adults with transfusion-associated infections. , 1988, JAMA.

[38]  K. Tanfer.  National Survey of Men: design and execution. , 1993, Family planning perspectives.

[39]  A. Raftery.  Bayesian Model Selection in Social Research , 1995 .

[40]  B P Katz,et al.  Estimating transmission probabilities for chlamydial infection. , 1992, Statistics in medicine.

[41]  Mark S Handcock,et al.  Center for Studies in Demography and Ecology Interval Estimates for Epidemic Thresholds in Two-Sex Network Models , 2005 .

[42]  E. Laumann,et al.  Racial/ethnic group differences in the prevalence of sexually transmitted diseases in the United States: a network explanation. , 1999, Sexually transmitted diseases.

[43]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[44]  Martina Morris,et al.  Center for Studies in Demography and Ecology On “ Sexual contacts and epidemic thresholds , ” models and inference for Sexual partnership distributions , 2005 .

[45]  Catherine H Mercer,et al.  Scale-Free Networks and Sexually Transmitted Diseases: A Description of Observed Patterns of Sexual Contacts in Britain and Zimbabwe , 2004, Sexually transmitted diseases.

[46]  J. Yorke,et al.  Gonorrhea Transmission Dynamics and Control , 1984 .

[47]  M. Handcock,et al.  The Prevalence of Trichomoniasis in Young Adults in the United States , 2005, Sexually transmitted diseases.

[48]  M. Kretzschmar,et al.  Concurrent partnerships and the spread of HIV , 1997, AIDS.

[49]  J. C. Thomas,et al.  The development and use of the concept of a sexually transmitted disease core. , 1996, The Journal of infectious diseases.

[50]  M. Lehtinen,et al.  Epidemiology of HPV 16 and Cervical Cancer in Finland and the Potential Impact of Vaccination: Mathematical Modelling Analyses , 2006, PLoS medicine.