Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: <i>A Case Study of Tanzania</i>

Theresia Bonifasi Mkenda; Kaku Sagary Nokoe; Samuel Githinji Karoki

doi:doi:10.11648/j.ajtas.20190804.11

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Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: A Case Study of Tanzania

Theresia Bonifasi Mkenda, Kaku Sagary Nokoe, Samuel Githinji Karoki

Published in American Journal of Theoretical and Applied Statistics (Volume 8, Issue 4)

Received: 25 June 2019 Accepted: 18 July 2019 Published: 10 August 2019

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Abstract

Estimation of HIV infection time is a crucial step in HIV/AIDS management as it can help to make informed decisions on the best intervention strategies for controlling new infections, and for taking care of the infected individuals. This study demonstrates three approaches for estimating the age at HIV infection in limited resource settings. Using HIV testing history data collected from a sample of 88 HIV positive women in Kilimanjaro region-Tanzania, we developed a model for estimating the most likely age at which HIV infection occurs for women under reproductive age. The sampled data were collected from typical poor resource settings where access to data is very challenging and the gap between last HIV negative test and first HIV positive test is wide. Formulation of the proposed model involved three steps. Through Modified Midpoint approach, we first determined the midpoint of the age at last negative HIV test and the age at first positive HIV test for each subject. Then, the average time at risk prior to infection, taken over all individuals was subtracted from each midpoint value to obtain the distribution of their estimated age at HIV infection (T). In the second step, survival analysis techniques were used to obtain the Kaplan Meier plots and Nelson Aalen cumulative hazards estimates in which the median age for HIV infection and the most risky age were estimated. The plots of Kaplan Meir survival curves for women with different marital status and levels of education helped to assess whether their age at infection were significantly different. In the third step, we used bootstrap estimation procedures to generate 200 samples of random data and obtain the bootstrap median age at HIV infection and its confidence intervals. The estimated median age at HIV infection from survival analysis approach was 28 years while from bootstrap estimation procedures was 27 years. Likewise, the Nelson Aalen cumulative hazards plot indicated that the most risky age for HIV infection is between 18-40 years while the most risky age from bootstrap estimation was 25 to 27 years. The confidence intervals obtained through bootstrap estimation approach was narrower than that obtained from the survival analysis approach, implying that the bootstrap approach gives more precise estimates. Generally, the study findings provide useful information towards the attainment of the 90-90-90 global HIV/AIDS target as it shows where to allocate more resources and establish more focused interventions for HIV/AIDS management and control.

Published in	American Journal of Theoretical and Applied Statistics (Volume 8, Issue 4)
DOI	10.11648/j.ajtas.20190804.11
Page(s)	125-135
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Age at HIV Infection, Modified Midpoint Method, Survival Analysis, Bootstrap Estimation Method

References

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[2]	Chinomona, A and Hendry, M (2015): MultipleImputation for Non-response when EstimatingHIV Prevalence Using Survey. BMC Public Health, doi: 10. 1186/s12889-015-2390-1.
[3]	Hanson DL, S. R. (2016). Mean Recency Period for Estimation of HIV-1 Incidence with the BED - Capture EIA and Bio-Rad Avidity in Persons Diagnosed in the United States with Subtype B. PLos ONE, DOI: 10. 1371/journal. pone, 0152327.
[4]	Kleinbaum and Klein (2012). Survival Analysis: A Self Learning Text, third edition. New York: Springer Science + Business Media, LLC. DOI 10. 1007/978-1-4419-6646-9.
[5]	Ngai s, e. a. (2016). Estimation of Undiagnosed intervals of HIV Infected Individuals by a modified Back Calculation Method for Reconstructing the Epidem Curves. Public Library of Science, DOI: 10. 1371/journal. pone. 0159021.
[6]	Omondi, E., mbogo, R., & Luboobi, L. (2018). Mathematical Modelling of the Impact of Testing, Treatment and Control of HIV Transmission in Kenya. cogent mathematics and Statistics. https://doi.org/10.1080/25742558.2018.1475590.
[7]	Pilcher, et al. (2019). A Generalizable Method for Estimating Duration of HIV Infections Using Clinical Testing History and HIV Testing Results. AIDS, DOI: 10. 1097/QAD. 0000000000002190.
[8]	Puller V, N. R. (2017). Estimating Time of HIV-1 Infection from Next -Generation Sequence Diversity. PLoS Comput Biol, DOI: 10. 1371/JOURNAL. pcbi. 1005775.
[9]	Priyanka, K and R, Mittal (2015): Estimation of Population Medianin Two Occasion Rotation Sampling, Journal of Statistics Application and Probability letters, doi. org/10. 12785/jsapl/020304.
[10]	Skar H, A. J. (2013). Towards Estimation of HIV-1 Date of Infection: A Time Continuous IgG-Model Shows That Seroconversion Does Not Occur at the Midpoint between Negative and Positive Tests. PLOS Public Library of Science, DOI: 10. 1371/JOURNAL. PONE. 0060906.
[11]	Stirrup, D. a. (2018). Estimation of Delay to Diagnosis and Incidence in HIV Using Indirect evidences of Infection Dates. BMC Medical Research Methodology, https//doi.org/10.1186/s12874-018-0522-x.
[12]	Sweeting, M. J, D. Angelis, John P andBarbara S (2014): Estimating the Distribution of the window Period for Recent HIV infections: Acomparison of Statistical Methods, Wiley &Sons Ltd. DOI: 10. 1002/SIM. 3941.
[13]	The URT (2013). National Comprehensive Guidelines for HIV Testing and Counselling. Dar Es Salaam, Tanzania: National AIDS Control Program (NACP).
[14]	Thomas, X. V. (2013). Estimating the time point of acute HCV infection. Journal of Hepatology, volume 58, S 206.
[15]	Tsokos, R. K. (2009). Mathematical Statistics with Applications. United States of America: Elsevier Academic Press Publications.
[16]	Wills, K. (2017). Mathematical Modelling Uncovers Mysteriesof HIV Infection in the Brain. Journal of Neurovirology.
[17]	Zhuo, S (2013): Order Statistics-based Inferences for Censored Lifetime Data and Financial Risk Analysis, PhD Thesis.

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Theresia Bonifasi Mkenda, Kaku Sagary Nokoe, Samuel Githinji Karoki. (2019). Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: A Case Study of Tanzania. American Journal of Theoretical and Applied Statistics, 8(4), 125-135. https://doi.org/10.11648/j.ajtas.20190804.11

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Theresia Bonifasi Mkenda; Kaku Sagary Nokoe; Samuel Githinji Karoki. Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: A Case Study of Tanzania. Am. J. Theor. Appl. Stat. 2019, 8(4), 125-135. doi: 10.11648/j.ajtas.20190804.11

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AMA Style

Theresia Bonifasi Mkenda, Kaku Sagary Nokoe, Samuel Githinji Karoki. Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: A Case Study of Tanzania. Am J Theor Appl Stat. 2019;8(4):125-135. doi: 10.11648/j.ajtas.20190804.11

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@article{10.11648/j.ajtas.20190804.11,
  author = {Theresia Bonifasi Mkenda and Kaku Sagary Nokoe and Samuel Githinji Karoki},
  title = {Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: A Case Study of Tanzania},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {8},
  number = {4},
  pages = {125-135},
  doi = {10.11648/j.ajtas.20190804.11},
  url = {https://doi.org/10.11648/j.ajtas.20190804.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20190804.11},
  abstract = {Estimation of HIV infection time is a crucial step in HIV/AIDS management as it can help to make informed decisions on the best intervention strategies for controlling new infections, and for taking care of the infected individuals. This study demonstrates three approaches for estimating the age at HIV infection in limited resource settings. Using HIV testing history data collected from a sample of 88 HIV positive women in Kilimanjaro region-Tanzania, we developed a model for estimating the most likely age at which HIV infection occurs for women under reproductive age. The sampled data were collected from typical poor resource settings where access to data is very challenging and the gap between last HIV negative test and first HIV positive test is wide. Formulation of the proposed model involved three steps. Through Modified Midpoint approach, we first determined the midpoint of the age at last negative HIV test and the age at first positive HIV test for each subject. Then, the average time at risk prior to infection, taken over all individuals was subtracted from each midpoint value to obtain the distribution of their estimated age at HIV infection (T). In the second step, survival analysis techniques were used to obtain the Kaplan Meier plots and Nelson Aalen cumulative hazards estimates in which the median age for HIV infection and the most risky age were estimated. The plots of Kaplan Meir survival curves for women with different marital status and levels of education helped to assess whether their age at infection were significantly different. In the third step, we used bootstrap estimation procedures to generate 200 samples of random data and obtain the bootstrap median age at HIV infection and its confidence intervals. The estimated median age at HIV infection from survival analysis approach was 28 years while from bootstrap estimation procedures was 27 years. Likewise, the Nelson Aalen cumulative hazards plot indicated that the most risky age for HIV infection is between 18-40 years while the most risky age from bootstrap estimation was 25 to 27 years. The confidence intervals obtained through bootstrap estimation approach was narrower than that obtained from the survival analysis approach, implying that the bootstrap approach gives more precise estimates. Generally, the study findings provide useful information towards the attainment of the 90-90-90 global HIV/AIDS target as it shows where to allocate more resources and establish more focused interventions for HIV/AIDS management and control.},
 year = {2019}
}

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TY  - JOUR
T1  - Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: A Case Study of Tanzania
AU  - Theresia Bonifasi Mkenda
AU  - Kaku Sagary Nokoe
AU  - Samuel Githinji Karoki
Y1  - 2019/08/10
PY  - 2019
N1  - https://doi.org/10.11648/j.ajtas.20190804.11
DO  - 10.11648/j.ajtas.20190804.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 125
EP  - 135
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20190804.11
AB  - Estimation of HIV infection time is a crucial step in HIV/AIDS management as it can help to make informed decisions on the best intervention strategies for controlling new infections, and for taking care of the infected individuals. This study demonstrates three approaches for estimating the age at HIV infection in limited resource settings. Using HIV testing history data collected from a sample of 88 HIV positive women in Kilimanjaro region-Tanzania, we developed a model for estimating the most likely age at which HIV infection occurs for women under reproductive age. The sampled data were collected from typical poor resource settings where access to data is very challenging and the gap between last HIV negative test and first HIV positive test is wide. Formulation of the proposed model involved three steps. Through Modified Midpoint approach, we first determined the midpoint of the age at last negative HIV test and the age at first positive HIV test for each subject. Then, the average time at risk prior to infection, taken over all individuals was subtracted from each midpoint value to obtain the distribution of their estimated age at HIV infection (T). In the second step, survival analysis techniques were used to obtain the Kaplan Meier plots and Nelson Aalen cumulative hazards estimates in which the median age for HIV infection and the most risky age were estimated. The plots of Kaplan Meir survival curves for women with different marital status and levels of education helped to assess whether their age at infection were significantly different. In the third step, we used bootstrap estimation procedures to generate 200 samples of random data and obtain the bootstrap median age at HIV infection and its confidence intervals. The estimated median age at HIV infection from survival analysis approach was 28 years while from bootstrap estimation procedures was 27 years. Likewise, the Nelson Aalen cumulative hazards plot indicated that the most risky age for HIV infection is between 18-40 years while the most risky age from bootstrap estimation was 25 to 27 years. The confidence intervals obtained through bootstrap estimation approach was narrower than that obtained from the survival analysis approach, implying that the bootstrap approach gives more precise estimates. Generally, the study findings provide useful information towards the attainment of the 90-90-90 global HIV/AIDS target as it shows where to allocate more resources and establish more focused interventions for HIV/AIDS management and control.
VL  - 8
IS  - 4
ER  -

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Author Information

Theresia Bonifasi Mkenda

Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi, Kenya
Kaku Sagary Nokoe

Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi, Kenya
Samuel Githinji Karoki

Department of Mathematics, School of Science and Technology, United States International University–Africa, Nairobi, Kenya

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Theresia Bonifasi Mkenda, Kaku Sagary Nokoe, Samuel Githinji Karoki. (2019). Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: A Case Study of Tanzania. American Journal of Theoretical and Applied Statistics, 8(4), 125-135. https://doi.org/10.11648/j.ajtas.20190804.11

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ACS Style

Theresia Bonifasi Mkenda; Kaku Sagary Nokoe; Samuel Githinji Karoki. Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: A Case Study of Tanzania. Am. J. Theor. Appl. Stat. 2019, 8(4), 125-135. doi: 10.11648/j.ajtas.20190804.11

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AMA Style

Theresia Bonifasi Mkenda, Kaku Sagary Nokoe, Samuel Githinji Karoki. Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: A Case Study of Tanzania. Am J Theor Appl Stat. 2019;8(4):125-135. doi: 10.11648/j.ajtas.20190804.11

Copy | Download

@article{10.11648/j.ajtas.20190804.11,
  author = {Theresia Bonifasi Mkenda and Kaku Sagary Nokoe and Samuel Githinji Karoki},
  title = {Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: A Case Study of Tanzania},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {8},
  number = {4},
  pages = {125-135},
  doi = {10.11648/j.ajtas.20190804.11},
  url = {https://doi.org/10.11648/j.ajtas.20190804.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20190804.11},
  abstract = {Estimation of HIV infection time is a crucial step in HIV/AIDS management as it can help to make informed decisions on the best intervention strategies for controlling new infections, and for taking care of the infected individuals. This study demonstrates three approaches for estimating the age at HIV infection in limited resource settings. Using HIV testing history data collected from a sample of 88 HIV positive women in Kilimanjaro region-Tanzania, we developed a model for estimating the most likely age at which HIV infection occurs for women under reproductive age. The sampled data were collected from typical poor resource settings where access to data is very challenging and the gap between last HIV negative test and first HIV positive test is wide. Formulation of the proposed model involved three steps. Through Modified Midpoint approach, we first determined the midpoint of the age at last negative HIV test and the age at first positive HIV test for each subject. Then, the average time at risk prior to infection, taken over all individuals was subtracted from each midpoint value to obtain the distribution of their estimated age at HIV infection (T). In the second step, survival analysis techniques were used to obtain the Kaplan Meier plots and Nelson Aalen cumulative hazards estimates in which the median age for HIV infection and the most risky age were estimated. The plots of Kaplan Meir survival curves for women with different marital status and levels of education helped to assess whether their age at infection were significantly different. In the third step, we used bootstrap estimation procedures to generate 200 samples of random data and obtain the bootstrap median age at HIV infection and its confidence intervals. The estimated median age at HIV infection from survival analysis approach was 28 years while from bootstrap estimation procedures was 27 years. Likewise, the Nelson Aalen cumulative hazards plot indicated that the most risky age for HIV infection is between 18-40 years while the most risky age from bootstrap estimation was 25 to 27 years. The confidence intervals obtained through bootstrap estimation approach was narrower than that obtained from the survival analysis approach, implying that the bootstrap approach gives more precise estimates. Generally, the study findings provide useful information towards the attainment of the 90-90-90 global HIV/AIDS target as it shows where to allocate more resources and establish more focused interventions for HIV/AIDS management and control.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Estimating the Age at HIV Infection Retroactively in Limited Resource Settings: A Case Study of Tanzania
AU  - Theresia Bonifasi Mkenda
AU  - Kaku Sagary Nokoe
AU  - Samuel Githinji Karoki
Y1  - 2019/08/10
PY  - 2019
N1  - https://doi.org/10.11648/j.ajtas.20190804.11
DO  - 10.11648/j.ajtas.20190804.11
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 125
EP  - 135
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20190804.11
AB  - Estimation of HIV infection time is a crucial step in HIV/AIDS management as it can help to make informed decisions on the best intervention strategies for controlling new infections, and for taking care of the infected individuals. This study demonstrates three approaches for estimating the age at HIV infection in limited resource settings. Using HIV testing history data collected from a sample of 88 HIV positive women in Kilimanjaro region-Tanzania, we developed a model for estimating the most likely age at which HIV infection occurs for women under reproductive age. The sampled data were collected from typical poor resource settings where access to data is very challenging and the gap between last HIV negative test and first HIV positive test is wide. Formulation of the proposed model involved three steps. Through Modified Midpoint approach, we first determined the midpoint of the age at last negative HIV test and the age at first positive HIV test for each subject. Then, the average time at risk prior to infection, taken over all individuals was subtracted from each midpoint value to obtain the distribution of their estimated age at HIV infection (T). In the second step, survival analysis techniques were used to obtain the Kaplan Meier plots and Nelson Aalen cumulative hazards estimates in which the median age for HIV infection and the most risky age were estimated. The plots of Kaplan Meir survival curves for women with different marital status and levels of education helped to assess whether their age at infection were significantly different. In the third step, we used bootstrap estimation procedures to generate 200 samples of random data and obtain the bootstrap median age at HIV infection and its confidence intervals. The estimated median age at HIV infection from survival analysis approach was 28 years while from bootstrap estimation procedures was 27 years. Likewise, the Nelson Aalen cumulative hazards plot indicated that the most risky age for HIV infection is between 18-40 years while the most risky age from bootstrap estimation was 25 to 27 years. The confidence intervals obtained through bootstrap estimation approach was narrower than that obtained from the survival analysis approach, implying that the bootstrap approach gives more precise estimates. Generally, the study findings provide useful information towards the attainment of the 90-90-90 global HIV/AIDS target as it shows where to allocate more resources and establish more focused interventions for HIV/AIDS management and control.
VL  - 8
IS  - 4
ER  -

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