Estimating HIV prevalence from surveys with low individual consent rates: annealing individual and pooled samples

Abstract

: Many HIV prevalence surveys are plagued by the problem that a sizeable number of surveyed individuals do not consent to contribute blood samples for testing. One can ignore this problem, as is often done, but the resultant bias can be of sufficient magnitude to invalidate the results of the survey, especially if the number of non-responders is high and the reason for refusing to participate is related to the individual's HIV status. One reason for refusing to participate may be for reasons of privacy. For those individuals, we suggest offering the option of being tested in a pool. This form of testing is less certain than individual testing, but, if it convinces more people to submit to testing, it should reduce the potential for bias and give a cleaner answer to the question of prevalence. This paper explores the logistics of implementing a combined individual and pooled testing approach and evaluates the analytical advantages to such a combined testing strategy. We quantify improvements in a prevalence estimator based on this combined testing strategy, relative to an individual testing only approach and a pooled testing only approach. Minimizing non-response is key for reducing bias, and, if pooled testing assuages privacy concerns, offering a pooled testing strategy has the potential to substantially improve HIV prevalence estimates.

Figure 1

Comparing the asymptotic properties of the combined estimator to the individuals-only estimator. Ratio of the asymptotic mse for the combined estimator to the ratio of the asymptotic mse for the estimator using only individuals in the low, moderate, and high prevalence settings for two scenarios: (a) pooled testers have a higher prevalence than individual testers, m=1000; (b) the prevalence in the pooled testers equals that in the individual testers (this ratio is independent of m). The combined estimator always has lower mse than the individuals only estimator in these settings.

Figure 2

Comparing the asymptotic properties of the combined estimator to the pooling-only estimator. Ratio of the mse for the combined estimator to the ratio of the mse when everyone is offered pooled testing, as a function of pool size for the low, moderate, and high prevalence settings when pooled testers have a higher prevalence than individual testers. The combined estimator always has lower mse than the estimator where everyone is offered pooled testing in these settings.

Figure 3

Percent bias in the combined estimator. Percent bias in the MLE estimator ${\widehat{p}}_T$ (thin lines) and the Burrows estimator ${\tilde{p}}_T$ (bold lines) for pool size k=7 as a function of sample size for low, moderate, and high prevalence settings. Using the Burrows estimator results in a substantial reduction in finite sample bias.

Figure 4

Confidence interval coverage for the combined estimator. 95% confidence interval coverage for ${\tilde{p}}_T$ as a function of sample size calculated using various pool sizes in the (a) low and (b) high prevalence setting as a function of the sample size.

Figure 5

Assessing the MSE of the combined estimator in simulation. Plot of the ratio of the empirical to the true mse of the combined estimator as a function of sample size for the (a) low and (b) high prevalence settings. When asymptotic results are valid, this ratio will be close to one.