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A Method for Estimating the Proportion of HIV-Infected Persons That Have Been Diagnosed and Application to China

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Abstract

Estimation of the proportion of living HIV-infected persons that have been diagnosed is critical for tracking progress toward meeting the UNAIDS goal that all persons who need HIV treatment receive it. The objective of this article is to develop a method for estimating that proportion. The methodological problem is that persons with undiagnosed HIV infection are not directly observable and are a “hidden” population. Here, we propose a methodology for estimating the proportion diagnosed that is relatively simple to implement. The key idea is that in many settings certain health conditions such as pregnancy or an upcoming surgery lead to mandatory HIV tests. The size of the undiagnosed infected population can be estimated from the numbers of infected persons diagnosed by mandatory tests and an estimate of the rate that persons in the undiagnosed infected population receive mandatory tests. We discuss approaches for estimating the rate of mandatory testing in the undiagnosed population, such as surgical or pregnancy rates. We develop estimators of the proportion diagnosed and confidence interval procedures. Sample size considerations and sensitivity analyses to underlying assumptions are considered. The proposed methods can be performed at a local level and within demographic strata. Implementation of the method is simple and requires neither historical HIV/AIDS surveillance data nor biomarkers such as CD4 cell counts. The methods are applied to data from Dehong Prefecture in Yunnan Province, China.

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References

  1. Abramowitz M, Stegun I (1970) Handbook of Mathematical Functions with Formulas Graphs and Mathematical Tables (Applied Mathematics Series). National Bureau of Standards, Washington DC

    MATH  Google Scholar 

  2. Blumenthal S, Dahiya RC (1981) Estimating the binomial parameter n. J Am Stat Assoc 76:903–909

    MathSciNet  MATH  Google Scholar 

  3. Brookmeyer R, Gail MH (1988) A method for obtaining short-term projections and lower bounds on the size of the AIDS epidemic. J Am Stat Assoc 83:301–308

    Article  Google Scholar 

  4. Cheng S, Eck D, Crawford F (2018) Estimating the size of a hidden finite set: large sample behavior of estimators. Cornell University Library, https://arxiv.org/abs/1808.04753

  5. Dailey AF, Hoots BE, Hall HI, Song R, Hayes D,Fulton P Jr, Prejean J, Hernandez A, Koenig L, Valleroy LA (2017) Vital Signs: human immunodeficiency virus testing and diagnosis delays—United States. MMWR Morb Mortal Wkly Rep 66:1300

    Article  Google Scholar 

  6. De Cock KM, Rutherford GW, Akhwale W (2014) Kenya AIDS indicator survey 2012. JAIDS J Acquir Immune Defic Syndr 66:S1–S2

    Article  Google Scholar 

  7. Granich R, Gupta S, Hall I, Aberle-Grasse J, Hader S, Mermin J (2017) Status and methodology of publicly available national HIV care continua and 90-90-90 targets: a systematic review. PLoS Med 14(4):e1002253

    Article  Google Scholar 

  8. Hall HI, Song R, Rhodes P, Prejean J, An Q, Lee LM, Karon J, Brookmeyer R, Kaplan EH, McKenna MT, Janssen RS (2008) Estimation of HIV incidence in the United States. JAMA 6:520–529

    Article  Google Scholar 

  9. Hall HI, Song R, Szwarcwald CL, Green T (2015) Brief report: time from infection with the human immunodeficiency virus to diagnosis, United States. JAIDS J Acquir Immune Defic Syndr 69(2):248–251

    Article  Google Scholar 

  10. Kendall M, Stuart A, Ord JK, O’Hagan A (1994) Kendall’s Advanced Theory of Statistics, Distribution Theory, vol 1, 6th edn. Arnold, London

    Google Scholar 

  11. Lodwick RK, Nakagawa F, van Sighem A, Sabin CA, Phillips AN (2015) Use of surveillance data on HIV diagnoses with HIV-related symptoms to estimate the number of people living with undiagnosed HIV in need of antiretroviral therapy. PLoS ONE 10(3):e0121992

    Article  Google Scholar 

  12. Ma Y, Li Z, Zhang K, Yang W, Ren X, Yang R et al (1990) HIV was first discovered among injection drug users in China. Chin J Epidemiol 11(3):184–185

    Google Scholar 

  13. Mao Y, Wu Z, Poundstone K, Wang C, Qin Q, Ma Y, Ma W (2010) Development of a unified web-based national HIV/AIDS information system in China. Int J Epidemiol 39:79–89

    Google Scholar 

  14. Sanathanan L (1972) Estimating the size of a multinomial population. Ann Math Stat 43:142–152

    Article  MathSciNet  Google Scholar 

  15. Singh S, Song R, Johnson AS, McCray E, Hall HI (2018) HIV incidence, prevalence, and undiagnosed infections in US men who have sex with men. Ann Intern Med 168(10):685–694

    Article  Google Scholar 

  16. Song R, Hall HI, Green TA, Szwarcwald CL, Pantazis N (2017) Using CD4 data to estimate HIV incidence, prevalence, and percent of undiagnosed infections in the United States. JAIDS J Acquir Immune Defic Syndr 74(1):3–9

    Article  Google Scholar 

  17. Stover J, Brown T, Marston M (2012) Updates to the spectrum/estimation and projection package (EPP) model to estimate HIV trends for adults and children. Sex Transm Infect 88(Suppl 2):i11–i16

    Article  Google Scholar 

  18. UNAIDS (2014) 90-90-90 An ambitious treatment target to help end the AIDS epidemic, Geneva, Switzerland. http://www.unaids.org/sites/default/files/media_asset/90-90-90_en_0.pdf

  19. Working Group on Estimation of HIV Prevalence in Europe (2011) HIV in hiding: methods and data requirements for the estimation of the number of people living with undiagnosed HIV. Aids 25(8):1017–1023

    Google Scholar 

Download references

Acknowledgements

Authors would like to thank Song Duan of the Dehong Prefecture Center for Disease Control and Prevention, Mangshi, China, for providing the surgery and pregnancy data from Dehong Prefecture. This work was also supported by the Center for HIV Identification, Prevention, and Treatment Services (CHIPTS) NIMH Grant MH58107 and NIH Grant R01-AI095068. The content is solely the responsibility of the authors and does not necessarily represent the official views of NIH.

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Correspondence to Ron Brookmeyer.

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Brookmeyer, R., Wu, Z. A Method for Estimating the Proportion of HIV-Infected Persons That Have Been Diagnosed and Application to China. Stat Biosci 12, 267–278 (2020). https://doi.org/10.1007/s12561-019-09240-8

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