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, 35 (15), 2609-34

Estimating Effectiveness in HIV Prevention Trials With a Bayesian Hierarchical Compound Poisson Frailty Model

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Estimating Effectiveness in HIV Prevention Trials With a Bayesian Hierarchical Compound Poisson Frailty Model

Rebecca Yates Coley et al. Stat Med.

Abstract

Inconsistent results in recent HIV prevention trials of pre-exposure prophylactic interventions may be due to heterogeneity in risk among study participants. Intervention effectiveness is most commonly estimated with the Cox model, which compares event times between populations. When heterogeneity is present, this population-level measure underestimates intervention effectiveness for individuals who are at risk. We propose a likelihood-based Bayesian hierarchical model that estimates the individual-level effectiveness of candidate interventions by accounting for heterogeneity in risk with a compound Poisson-distributed frailty term. This model reflects the mechanisms of HIV risk and allows that some participants are not exposed to HIV and, therefore, have no risk of seroconversion during the study. We assess model performance via simulation and apply the model to data from an HIV prevention trial. Copyright © 2016 John Wiley & Sons, Ltd.

Keywords: Bayesian analysis; data augmentation; heterogeneity; latent variable; survival analyisis.

Figures

Figure 1
Figure 1
Estimated effectiveness (upper panel) and coverage of 95% intervals (lower panel) from simulation study, priors from Equation (8).
Figure 2
Figure 2
Prior distribution of average baseline incidence when proportion at risk varies and average seroincidence among those at risk is equal across all sites.
Figure 3
Figure 3
Density of seroincidence in placebo arm under specified priors.
Figure 4
Figure 4
Results of sensitivity analysis for priors on frailty distribution parameters. Plots in left-hand column give the site-specific prior densities for the proportion at risk. Plots in the middle column give prior seroincidence for all combinations of priors (see legend at the bottom of the figure for hyperparameters for π(η)) in comparison to that used in the primary analysis (solid, black line). Posterior distributions for the HR associated with 0.5% PRO 2000 gel are given (on the log-scale) in the right-hand column for each prior. The black, solid line gives the posterior HR from the primary analysis (priors given in (9)), and the vertical dashed line indicates the estimated effectiveness (given in Table 4).
Figure 5
Figure 5
Site-specific estimates of proportion of participants at risk of seroconversion, 1 − exp(−ρj), (left panel), and baseline seroincidence, λj × 100, (right panel) versus observed seroincidence in placebo arm, represented by plotting symbols. Solid lines depict 95% HPD intervals around site-specific estimates.
Figure 6
Figure 6
Kaplan Meier curves for survival data simulated with stratified compound Poisson frailty model estimates (gray lines) and observed survival data (bold, solid line) with a 95% confidence interval around the observed survival (bold, dashed lines).

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