Dynamic Variation in Sexual Contact Rates in a Cohort of HIV-Negative Gay Men

Abstract

Human immunodeficiency virus (HIV) transmission models that include variability in sexual behavior over time have shown increased incidence, prevalence, and acute-state transmission rates for a given population risk profile. This raises the question of whether dynamic variation in individual sexual behavior is a real phenomenon that can be observed and measured. To study this dynamic variation, we developed a model incorporating heterogeneity in both between-person and within-person sexual contact patterns. Using novel methodology that we call iterated filtering for longitudinal data, we fitted this model by maximum likelihood to longitudinal survey data from the Centers for Disease Control and Prevention's Collaborative HIV Seroincidence Study (1992-1995). We found evidence for individual heterogeneity in sexual behavior over time. We simulated an epidemic process and found that inclusion of empirically measured levels of dynamic variation in individual-level sexual behavior brought the theoretical predictions of HIV incidence into closer alignment with reality given the measured per-act probabilities of transmission. The methods developed here provide a framework for quantifying variation in sexual behaviors that helps in understanding the HIV epidemic among gay men.

Keywords: HIV; HIV risk; disease transmission; gay men; iterated filtering; partially observed Markov process; sexual behavior.

Figure 1.

Features of a set of longitudinal data on rates of sexual contact among human immunodeficiency virus (HIV)-negative gay men in the United States, Centers for Disease Control and Prevention Collaborative HIV Seroincidence Study (1992–1995). A) Secular trend from the time of enrollment in the cohort; B) average rate of sexual contact per month; C) rates of sexual contact over time; D) bias-corrected autocorrelation (Web Appendix 1). Black bars show autocorrelation >0, while gray bars show autocorrelation ≤0. The mean (0.076) and standard error (0.0094) of the autocorrelation imply a small but positive autocorrelation (95% confidence interval: 0.057, 0.094).

Figure 2.

A model of rates of sexual contact that accounts for between-person and within-person variation in sexual behavior over time, Centers for Disease Control and Prevention Collaborative HIV Seroincidence Study (1992–1995). The graph shows one possible realization of the model for a single individual, i. The length of behavioral intervals (horizontal lines) over which an individual's contact rate (left axis) is constant is controlled by R_i, having the mean value 1/R_i. At the beginning of a new behavioral interval, a new contact rate is drawn from a gamma distribution mean, μ_X, and standard deviation, σ_X. The box plots illustrate the distribution of the possible number of sexual contacts (right axis) for the given pattern of behavioral intervals shown over each 6-month observation period. The positive latent variable D_i governs the dispersion of the actual number of contacts within a given behavioral interval. As D_i decreases toward zero, the number of contacts observed in each observation period will be more variable. HIV, human immunodeficiency virus.

Figure 3.

Visual representation of the maximum likelihood parameter estimates for a model of variations in sexual behavior among human immunodeficiency virus (HIV)-negative gay men.

Figure 4.

Possible epidemic curves for the human immunodeficiency virus (HIV) epidemic under 3 parameterizations of variation in sexual behavior. The median values from 500 simulations are shown as lines, and the interquartile ranges (25th–75th percentiles) are shown as gray shading surrounding the 3 parameterizations. In the “homogeneous” case (dashed line), the epidemic was simulated with μ_X estimated by the sample mean (1.53 contacts/month) without any sources of between-person or within-person heterogeneity. In the “between heterogeneity” case (dotted line), the epidemic was simulated with μ_X estimated by the sample mean (1.53 contacts/month) and σ_X estimated by the sample standard deviation (3.28 contacts/month). In the “within + between heterogeneity” case (solid line), the epidemic was simulated with each parameter set to the estimated maximum likelihood estimate for total sexual contacts (all types). For all situations, the per-contact probability of transmission was set to 1/120, the average length of infection was set to 10 years, and the infection-free equilibrium population size was set to 3,000. The per-contact probability was selected such that the basic reproduction number in the “homogeneous” case was 1.53. In the “homogeneous,” “between heterogeneity,” and “within + between heterogeneity” cases, respectively, 239 of 500, 172 of 500, and 95 of 500 simulations died out before the 100-year mark.