Joint Survival Model of CD4 Outcome for HIV/TB Coinfected: Data from Kenya AIDS Indicator Survey

Bernadette Ikandi; Samuel Musili Mwalili; Anthony Wanjoya

doi:doi:10.11648/j.ijdsa.20190505.12

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Joint Survival Model of CD4 Outcome for HIV/TB Coinfected: Data from Kenya AIDS Indicator Survey

Bernadette Ikandi, Samuel Musili Mwalili, Anthony Wanjoya

Published in International Journal of Data Science and Analysis (Volume 5, Issue 5)

Received: 24 September 2019 Accepted: 22 October 2019 Published: 28 October 2019

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Abstract

HIV infection leads to immune deficiency, increasing the risk of TB in people with HIV. HIV/TB co-infection increases the risk of death from TB or other opportunist infections. CD4 cell counts (cells/mm3) along with viral load are measures of treatment failure. This study purposed to apply shared frailty model in analyzing the survival and hazard rates of the TB/HIV co-infected persons. This work is very important because co-morbidity with TB and HIV is a rambling cause of death in Africa. The research employed a bivariate Gamma Frailty model to get the correlation amongst the HIV/TB outcomes to necessitate valid and reliable statistical inferencing. A survival frailty model on the CD4 counts is developed and fitted to factor in the unobserved heterogeneity that might occur in some observations. Ignoring some unobserved or unmeasured effects gives misguided estimates of survival. Thus, correcting these overdispersion or under-dispersion helps adjust these frailties. Frailty model provided a solid statistical analysis to CD4 data accounting for TB/HIV co-infection. The study also carried out some simulations along with the standard errors to compare the true values of the parameters. From the simulation findings, it is evident that precision and coverage improves with increase in sample size. Data used in this paper is from Kenya AIDS Indicator Survey (2012) which comprised of 648 HIV-positive patients, 10978 HIV-negative, and 2094 whose status was unknown. From the results, it is evident that the survival rate for the HIV positive individuals who are TB negative, with CD4 ≤ 310 is higher, at 0.9963 than that of the TB positive persons, at 0.975. The research finding points TB/HIV co-infection as a key factor for predicting immunological failure as measured by CD4 counts. The Kenyan government, and in particular the ministry of health should develop policies that mandate TB diagnosis among the PLHIV and linkage to TB treatment for the positive cases.

Published in	International Journal of Data Science and Analysis (Volume 5, Issue 5)
DOI	10.11648/j.ijdsa.20190505.12
Page(s)	86-91
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

HIV/TB Coinfection, CD4 Counts, Heterogeneity, Frailty Model, People Living with HIV

References

[1]	Kaplan, R., Hermans, S., Caldwell, J., Jennings, K., Bekker, L. G., & Wood, R. (2018). HIV and TB co-infection in the ART era: CD4 count distributions and TB case fatality in Cape Town. BMC infectious diseases, 18 (1), 356.
[2]	Pinto, C. M., & Carvalho, A. R. (2017). The HIV/TB coinfection severity in the presence of TB multi-drug resistant strains. Ecological complexity, 32, 1-20.
[3]	Esmail, H., Riou, C., du Bruyn, E., Lai, R. P. J., Harley, Y. X., Meintjes, G.,... & Wilkinson, R. J. (2018). The immune response to Mycobacterium tuberculosis in HIV-1-coinfected persons. Annual review of immunology, 36, 603-638.
[4]	Gleiss, A., Gnant, M., & Schemper, M. (2018). Explained variation in shared frailty models. Statistics in medicine, 37 (9), 1482-1490.
[5]	Gasparini, A., Clements, M. S., Abrams, K. R., & Crowther, M. J. (2018). Impact of model misspecification in shared frailty survival models. arXiv preprint arXiv: 1810.08140.
[6]	Emura, T., Matsui, S., & Rondeau, V. (2019). Survival Analysis with Correlated Endpoints: Joint Frailty-Copula Models. Springer Singapore.
[7]	Colchero, F., & Kiyakoglu, B. Y. (2019). Beyond the proportional frailty model: Bayesian estimation of individual heterogeneity on mortality parameters. Biometrical Journal.
[8]	Zarulli, V. (2016). Unobserved heterogeneity of frailty in the analysis of socioeconomic differences in health and mortality. European Journal of Population, 32 (1), 55-72.
[9]	Pitacco, E. (2019). Heterogeneity in mortality: a survey with an actuarial focus. European Actuarial Journal, 1-28.
[10]	Wang, A., Chandra, K., & Jia, X. (2018). The analysis of left truncated bivariate data using frailty models. Scandinavian Journal of Statistics, 45 (4), 847-860.
[11]	Martins, A., Aerts, M., Hens, N., Wienke, A., & Abrams, S. (2018). Correlated gamma frailty models for bivariate survival time data. Statistical methods in medical research, 0962280218803127.
[12]	Klein, J. P., van Houwelingen, H. C., Ibrahim, J. G., & Scheike, T. H. (2016). Frailty Models. In Handbook of Survival Analysis (pp. 461-477). Chapman and Hall/CRC.
[13]	Van den Berg, G. J., & Drepper, B. (2016). Inference for shared-frailty survival models with left-truncated data. Econometric Reviews, 35 (6), 1075-1098.
[14]	Rondeau, V., Gonzalez, J. R., Mazroui, Y., Mauguen, A., Diakite, A., Laurent, A.,... & Sofeu, C. L. (2019). frailtypack-package: General Frailty models: shared, joint and nested frailty.
[15]	Gupta, R. C. (2018). Association measures in the bivariate correlated frailty model. REVSTAT–Statistical Journal, 16 (2), 257-278.

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APA Style

Bernadette Ikandi, Samuel Musili Mwalili, Anthony Wanjoya. (2019). Joint Survival Model of CD4 Outcome for HIV/TB Coinfected: Data from Kenya AIDS Indicator Survey. International Journal of Data Science and Analysis, 5(5), 86-91. https://doi.org/10.11648/j.ijdsa.20190505.12

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ACS Style

Bernadette Ikandi; Samuel Musili Mwalili; Anthony Wanjoya. Joint Survival Model of CD4 Outcome for HIV/TB Coinfected: Data from Kenya AIDS Indicator Survey. Int. J. Data Sci. Anal. 2019, 5(5), 86-91. doi: 10.11648/j.ijdsa.20190505.12

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AMA Style

Bernadette Ikandi, Samuel Musili Mwalili, Anthony Wanjoya. Joint Survival Model of CD4 Outcome for HIV/TB Coinfected: Data from Kenya AIDS Indicator Survey. Int J Data Sci Anal. 2019;5(5):86-91. doi: 10.11648/j.ijdsa.20190505.12

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@article{10.11648/j.ijdsa.20190505.12,
  author = {Bernadette Ikandi and Samuel Musili Mwalili and Anthony Wanjoya},
  title = {Joint Survival Model of CD4 Outcome for HIV/TB Coinfected: Data from Kenya AIDS Indicator Survey},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {5},
  pages = {86-91},
  doi = {10.11648/j.ijdsa.20190505.12},
  url = {https://doi.org/10.11648/j.ijdsa.20190505.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190505.12},
  abstract = {HIV infection leads to immune deficiency, increasing the risk of TB in people with HIV. HIV/TB co-infection increases the risk of death from TB or other opportunist infections. CD4 cell counts (cells/mm3) along with viral load are measures of treatment failure. This study purposed to apply shared frailty model in analyzing the survival and hazard rates of the TB/HIV co-infected persons. This work is very important because co-morbidity with TB and HIV is a rambling cause of death in Africa. The research employed a bivariate Gamma Frailty model to get the correlation amongst the HIV/TB outcomes to necessitate valid and reliable statistical inferencing. A survival frailty model on the CD4 counts is developed and fitted to factor in the unobserved heterogeneity that might occur in some observations. Ignoring some unobserved or unmeasured effects gives misguided estimates of survival. Thus, correcting these overdispersion or under-dispersion helps adjust these frailties. Frailty model provided a solid statistical analysis to CD4 data accounting for TB/HIV co-infection. The study also carried out some simulations along with the standard errors to compare the true values of the parameters. From the simulation findings, it is evident that precision and coverage improves with increase in sample size. Data used in this paper is from Kenya AIDS Indicator Survey (2012) which comprised of 648 HIV-positive patients, 10978 HIV-negative, and 2094 whose status was unknown. From the results, it is evident that the survival rate for the HIV positive individuals who are TB negative, with CD4 ≤ 310 is higher, at 0.9963 than that of the TB positive persons, at 0.975. The research finding points TB/HIV co-infection as a key factor for predicting immunological failure as measured by CD4 counts. The Kenyan government, and in particular the ministry of health should develop policies that mandate TB diagnosis among the PLHIV and linkage to TB treatment for the positive cases.},
 year = {2019}
}

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TY - JOUR
T1 - Joint Survival Model of CD4 Outcome for HIV/TB Coinfected: Data from Kenya AIDS Indicator Survey
AU - Bernadette Ikandi
AU - Samuel Musili Mwalili
AU - Anthony Wanjoya
Y1 - 2019/10/28
PY - 2019
N1 - https://doi.org/10.11648/j.ijdsa.20190505.12
DO - 10.11648/j.ijdsa.20190505.12
T2 - International Journal of Data Science and Analysis
JF - International Journal of Data Science and Analysis
JO - International Journal of Data Science and Analysis
SP - 86
EP - 91
PB - Science Publishing Group
SN - 2575-1891
UR - https://doi.org/10.11648/j.ijdsa.20190505.12
AB - HIV infection leads to immune deficiency, increasing the risk of TB in people with HIV. HIV/TB co-infection increases the risk of death from TB or other opportunist infections. CD4 cell counts (cells/mm3) along with viral load are measures of treatment failure. This study purposed to apply shared frailty model in analyzing the survival and hazard rates of the TB/HIV co-infected persons. This work is very important because co-morbidity with TB and HIV is a rambling cause of death in Africa. The research employed a bivariate Gamma Frailty model to get the correlation amongst the HIV/TB outcomes to necessitate valid and reliable statistical inferencing. A survival frailty model on the CD4 counts is developed and fitted to factor in the unobserved heterogeneity that might occur in some observations. Ignoring some unobserved or unmeasured effects gives misguided estimates of survival. Thus, correcting these overdispersion or under-dispersion helps adjust these frailties. Frailty model provided a solid statistical analysis to CD4 data accounting for TB/HIV co-infection. The study also carried out some simulations along with the standard errors to compare the true values of the parameters. From the simulation findings, it is evident that precision and coverage improves with increase in sample size. Data used in this paper is from Kenya AIDS Indicator Survey (2012) which comprised of 648 HIV-positive patients, 10978 HIV-negative, and 2094 whose status was unknown. From the results, it is evident that the survival rate for the HIV positive individuals who are TB negative, with CD4 ≤ 310 is higher, at 0.9963 than that of the TB positive persons, at 0.975. The research finding points TB/HIV co-infection as a key factor for predicting immunological failure as measured by CD4 counts. The Kenyan government, and in particular the ministry of health should develop policies that mandate TB diagnosis among the PLHIV and linkage to TB treatment for the positive cases.
VL - 5
IS - 5
ER -

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Author Information

Bernadette Ikandi

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Samuel Musili Mwalili

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Wanjoya

Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya

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APA Style

Bernadette Ikandi, Samuel Musili Mwalili, Anthony Wanjoya. (2019). Joint Survival Model of CD4 Outcome for HIV/TB Coinfected: Data from Kenya AIDS Indicator Survey. International Journal of Data Science and Analysis, 5(5), 86-91. https://doi.org/10.11648/j.ijdsa.20190505.12

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ACS Style

Bernadette Ikandi; Samuel Musili Mwalili; Anthony Wanjoya. Joint Survival Model of CD4 Outcome for HIV/TB Coinfected: Data from Kenya AIDS Indicator Survey. Int. J. Data Sci. Anal. 2019, 5(5), 86-91. doi: 10.11648/j.ijdsa.20190505.12

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AMA Style

Bernadette Ikandi, Samuel Musili Mwalili, Anthony Wanjoya. Joint Survival Model of CD4 Outcome for HIV/TB Coinfected: Data from Kenya AIDS Indicator Survey. Int J Data Sci Anal. 2019;5(5):86-91. doi: 10.11648/j.ijdsa.20190505.12

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@article{10.11648/j.ijdsa.20190505.12,
  author = {Bernadette Ikandi and Samuel Musili Mwalili and Anthony Wanjoya},
  title = {Joint Survival Model of CD4 Outcome for HIV/TB Coinfected: Data from Kenya AIDS Indicator Survey},
  journal = {International Journal of Data Science and Analysis},
  volume = {5},
  number = {5},
  pages = {86-91},
  doi = {10.11648/j.ijdsa.20190505.12},
  url = {https://doi.org/10.11648/j.ijdsa.20190505.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdsa.20190505.12},
  abstract = {HIV infection leads to immune deficiency, increasing the risk of TB in people with HIV. HIV/TB co-infection increases the risk of death from TB or other opportunist infections. CD4 cell counts (cells/mm3) along with viral load are measures of treatment failure. This study purposed to apply shared frailty model in analyzing the survival and hazard rates of the TB/HIV co-infected persons. This work is very important because co-morbidity with TB and HIV is a rambling cause of death in Africa. The research employed a bivariate Gamma Frailty model to get the correlation amongst the HIV/TB outcomes to necessitate valid and reliable statistical inferencing. A survival frailty model on the CD4 counts is developed and fitted to factor in the unobserved heterogeneity that might occur in some observations. Ignoring some unobserved or unmeasured effects gives misguided estimates of survival. Thus, correcting these overdispersion or under-dispersion helps adjust these frailties. Frailty model provided a solid statistical analysis to CD4 data accounting for TB/HIV co-infection. The study also carried out some simulations along with the standard errors to compare the true values of the parameters. From the simulation findings, it is evident that precision and coverage improves with increase in sample size. Data used in this paper is from Kenya AIDS Indicator Survey (2012) which comprised of 648 HIV-positive patients, 10978 HIV-negative, and 2094 whose status was unknown. From the results, it is evident that the survival rate for the HIV positive individuals who are TB negative, with CD4 ≤ 310 is higher, at 0.9963 than that of the TB positive persons, at 0.975. The research finding points TB/HIV co-infection as a key factor for predicting immunological failure as measured by CD4 counts. The Kenyan government, and in particular the ministry of health should develop policies that mandate TB diagnosis among the PLHIV and linkage to TB treatment for the positive cases.},
 year = {2019}
}

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