Stochastic variation in network epidemic models: implications for the design of community level HIV prevention trials

Abstract

Important sources of variation in the spread of HIV in communities arise from overlapping sexual networks and heterogeneity in biological and behavioral risk factors in populations. These sources of variation are not routinely accounted for in the design of HIV prevention trials. In this paper, we use agent-based models to account for these sources of variation. We illustrate the approach with an agent-based model for the spread of HIV infection among men who have sex with men in South Africa. We find that traditional sample size approaches that rely on binomial (or Poisson) models are inadequate and can lead to underpowered studies. We develop sample size and power formulas for community randomized trials that incorporate estimates of variation determined from agent-based models. We conclude that agent-based models offer a useful tool in the design of HIV prevention trials.

Keywords: HIV; community randomized trials; epidemics; networks; sample size.

Figure 1

Empirical variances of proportions infected in 5 years $\left(\widehat{P}\right)$ for a given θ, versus fitted proportions (from equation 8). The figure shows 162 data points where each data point refers to a different combination of HIV prevention interventions. The empirical variances were based on replicate runs for each of those combinations (the figure is based on 2157 runs of the agent based model). Also shown is the fitted variance function from equation 9 $\left(\mathit{var}\right(\widehat{P}\mid \theta )=0.5205P(\theta )-0.1127P{\left(\theta \right)}^3)$ and the naïve binomial variance. The fitted proportions are based on equation 8 with β₀=−1.086, β₁=−.000936, β₂=−.00266, β₃= −.04137, β₄ =.000642, β₅=−.0000087, β₆=−.00119

Figure 2

The variance of the proportion in the study sample that become infected, $\mathit{var}(\widehat{p}\mid \theta )$, plotted versus fitted proportions (from equation 8). The variance is shown decomposed into the random sampling and stochastic epidemic components with sample sizes n=50, 100 and 200.

Figure 3

Power versus the effect size (percent of infections prevented(100(P₁ – P₂)/P₁)) = (ε × 100) with α=.05, P₁=.264, sample size n=50, 100 and 200 for k= 5 clusters (Panel A) and k=10 clusters (Panel B) in each arm.

Figure 4

Number of clusters per arm (k) needed to obtain 90% power to detect effect sizes (percent infections prevented, ε × 100) of 25%, 35% and 50%, with α=.05 and P1=.264 versus sample size n.