Far from MCAR: Obtaining Population-level Estimates of HIV Viral Suppression : Epidemiology

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Infectious Disease

Far from MCAR

Obtaining Population-level Estimates of HIV Viral Suppression

Balzer, Laura B.a; Ayieko, Jamesb; Kwarisiima, Dalsonec; Chamie, Gabrield; Charlebois, Edwin D.e; Schwab, Joshuaf; van der Laan, Mark J.f; Kamya, Moses R.g; Havlir, Diane V.d; Petersen, Maya L.f

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Epidemiology 31(5):p 620-627, September 2020. | DOI: 10.1097/EDE.0000000000001215



Population-level estimates of disease prevalence and control are needed to assess prevention and treatment strategies. However, available data often suffer from differential missingness. For example, population-level HIV viral suppression is the proportion of all HIV-positive persons with suppressed viral replication. Individuals with measured HIV status, and among HIV-positive individuals those with measured viral suppression, likely differ from those without such measurements.


We discuss three sets of assumptions to identify population-level suppression in the intervention arm of the SEARCH Study (NCT01864603), a community randomized trial in rural Kenya and Uganda (2013–2017). Using data on nearly 100,000 participants, we compare estimates from (1) an unadjusted approach assuming data are missing-completely-at-random (MCAR); (2) stratification on age group, sex, and community; and (3) targeted maximum likelihood estimation to adjust for a larger set of baseline and time-updated variables.


Despite high measurement coverage, estimates of population-level viral suppression varied by identification assumption. Unadjusted estimates were most optimistic: 50% (95% confidence interval [CI] = 46%, 54%) of HIV-positive persons suppressed at baseline, 80% (95% CI = 78%, 82%) at year 1, 85% (95% CI = 83%, 86%) at year 2, and 85% (95% CI = 83%, 87%) at year 3. Stratifying on baseline predictors yielded slightly lower estimates, and full adjustment reduced estimates meaningfully: 42% (95% CI = 37%, 46%) of HIV-positive persons suppressed at baseline, 71% (95% CI = 69%, 73%) at year 1, 76% (95% CI = 74%, 78%) at year 2, and 79% (95% CI = 77%, 81%) at year 3.


Estimation of population-level disease burden and control requires appropriate adjustment for missing data. Even in large studies with limited missingness, estimates relying on the MCAR assumption or baseline stratification should be interpreted cautiously.


The article by Balzer et al.1 in the September 2020 issue of Epidemiology was published without its accompanying Appendix. This Appendix is provided below. The citations in the Erratum refer to the references in the main text of Balzer et al.1

For the moment, assume complete measurement and let HIVt be an indicator of HIV-positive serostatus at time t; Dxt be an indicator of having an HIV diagnosis by time t; ARTt be an indicator of ART use at time t, and Suppt be an indicator of suppressed viral replication at time t. The UNAIDS 90-90-90 targets are a series of proportions or conditional probabilities:5

Percentage of all HIV-positives who are diagnosed (first-90):

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Percentage of diagnosed who are on ART (second-90):

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Percentage on ART who are currently suppressed (third-90):

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Multiplying together the three “90s” yields the proportion of all HIV-positive persons who are currently suppressed (i.e. population-level suppression):

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Since each numerator and denominator is a population-level proportion, we can equivalently express the targets as follows: first-90 = (number previously diagnosed)/(number HIV-positive), second-90 = (number on ART)/(number previously diagnosed), third-90 = (number virally suppressed)/(number on ART), and population-level suppression = (number virally suppressed)/(number HIV-positive).

Therefore, one could directly estimate population-level suppression, as we demonstrated here, or instead estimate each 90-90-90 target and multiply. These two approaches should yield identical results, as demonstrated in our previous work.8,9,27 However, deviations between the direct estimate and the multiplied one can occur when making the MCAR assumption.1–4 Specifically, under MCAR, the denominators of the third-90 and population-level suppression become conditional on having a viral load measured, which is almost always a subset of the population on ART and a subset of the population who is HIV-positive.

Epidemiology. 32(5):e25, September 2021.

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