Biostatistical Methods for HIV Monitoring and Prevention
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Part I Pooled-testing methods can greatly reduce the number of tests needed to identify failures in a collection of samples. Existing methodology has focused primarily on binary tests, but there is a clear need for improved efficiency when using expensive quantitative tests, such as tests for HIV viral load in resource-limited settings. We propose a matrix-pooling method which uses the EM algorithm to identify individual samples most likely to be failures. Simulation studies show that the proposed method can improve testing efficiency by a modest amount, and dramatically reduce the total number of testing rounds needed to identify all failures. In settings where the turn-around time for testing services is significant, the EM method can substantial time savings. The EM method does not perform as well when the measurements of interest are highly skewed, as is often the case with viral load concentrations. We therefore propose a second method that accommodates situations where target quantities do not follow a normal distribution. This approach uses Markov Chain Monte Carlo (MCMC) sampling to identify the failure status of individual samples, and is highly flexible in terms of assumptions regarding the distributions of both target quantities and measurement error. This method is further extended to include covariate information. Simulation studies show that the proposed method can substantially reduce turn-around time as compared to existing group-testing methods, particularly when covariate data is available that are highly predictive of failure. The proposed method did not perform as well when applied to a series of real datasets taken from actual pooled specimens. This may be due to measurement error variances for viral load testing that are much higher than anticipated. Part II Discordant partner studies are commonly used to quantify per-act infectivity rates for HIV. Statistical models used to estimate these rates depend on self-reported sexual activity, which is notoriously unreliable. The degree to which misreported sexual activity can affect infectivity estimates has not previously been reported. By using a basic transmission model in the context of measurement error, we show that infectivity estimates can be severely biased, and that the size and direction of bias depends on the underlying infectivity rate and on the mean number of sex acts occurring in the observation window. We show that by modifying the size of this window, in certain circumstances it is possible to avoid measurement-error bias without having to use a more sophisticated statistical model. We also show that, when misreporting is ignored, covariate parameter estimates can be biased, particularly when subgroup differences are large or when sexual frequency is heterogeneous. Recent discordant partner studies have begun collecting sexual history data from both partners. We propose a latent-variable transmission model which incorporates data from both partners, and accounts for the mis-reporting of sex acts as well as non-overlapping recall periods. Bayes-MCMC methods are used to generate parameter estimates. Simulation studies demonstrate that the proposed method can dramatically reduce measurement-error bias for per-act infectivity estimation. We then apply this method to the Partners PrEP study dataset and show that HIV infectivity may be 25% higher than would be estimated with a naive model.
- Biostatistics