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Giddings R, Indravudh P, Medley GF, Bozzani F, Gafos M, Malhotra S, Terris-Prestholt F, Torres-Rueda S, Quaife M. Infectious Disease Modelling of HIV Prevention Interventions: A Systematic Review and Narrative Synthesis of Compartmental Models. PHARMACOECONOMICS 2023; 41:693-707. [PMID: 36988896 PMCID: PMC10163138 DOI: 10.1007/s40273-023-01260-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 02/26/2023] [Indexed: 05/06/2023]
Abstract
BACKGROUND The HIV epidemic remains a major public health problem. Critical to transmission control are HIV prevention strategies with new interventions continuing to be developed. Mathematical models are important for understanding the potential impact of these interventions and supporting policy decisions. This systematic review aims to answer the following question: when a new HIV prevention intervention is being considered or designed, what information regarding it is necessary to include in a compartmental model to provide useful insights to policy makers? The primary objective of this review is therefore to assess suitability of current compartmental HIV prevention models for informing policy development. METHODS Articles published in EMBASE, Medline, Econlit, and Global Health were screened. Included studies were identified using permutations of (i) HIV, (ii) pre-exposure prophylaxis (PrEP), circumcision (both voluntary male circumcision [VMMC] and early-infant male circumcision [EIMC]), and vaccination, and (iii) modelling. Data extraction focused on study design, model structure, and intervention incorporation into models. Article quality was assessed using the TRACE (TRAnsparent and Comprehensive Ecological modelling documentation) criteria for mathematical models. RESULTS Of 837 articles screened, 48 articles were included in the review, with 32 unique mathematical models identified. The substantial majority of studies included PrEP (83%), whilst fewer modelled circumcision (54%), and only a few focussed on vaccination (10%). Data evaluation, implementation verification, and model output corroboration were identified as areas of poorer model quality. Parameters commonly included in the mathematical models were intervention uptake and effectiveness, with additional intervention-specific common parameters identified. We identified key modelling gaps; critically, models insufficiently incorporate multiple interventions acting simultaneously. Additionally, population subgroups were generally poorly represented-with future models requiring improved incorporation of ethnicity and sexual risk group stratification-and many models contained inappropriate data in parameterisation which will affect output accuracy. CONCLUSIONS This review identified gaps in compartmental models to date and suggests areas of improvement for models focusing on new prevention interventions. Resolution of such gaps within future models will ensure greater robustness and transparency, and enable more accurate assessment of the impact that new interventions may have, thereby providing more meaningful guidance to policy makers.
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Affiliation(s)
| | | | | | | | - Mitzy Gafos
- London School of Hygiene & Tropical Medicine, London, UK
| | | | | | | | - Matthew Quaife
- London School of Hygiene & Tropical Medicine, London, UK
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Chen Y, He J, Wang M. A hybrid of long short-term memory neural network and autoregressive integrated moving average model in forecasting HIV incidence and morality of post-neonatal population in East Asia: global burden of diseases 2000-2019. BMC Public Health 2022; 22:1938. [PMID: 36261815 PMCID: PMC9580197 DOI: 10.1186/s12889-022-14321-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2022] [Accepted: 09/26/2022] [Indexed: 11/10/2022] Open
Abstract
Background To forecast the human immunodeficiency virus (HIV) incidence and mortality of post-neonatal population in East Asia including North Korea, South Korea, Mongolia, Japan and China Mainland and Taiwan province. Methods The data on the incidence and mortality of HIV in post-neonatal population from East Asia were obtained from the Global Burden of Diseases (GBD). The morbidity and mortality of post-neonatal HIV population from GBD 2000 to GBD 2013 were applied as the training set and the morbidity and mortality from GBD 2014 to GBD 2019 were used as the testing set. The hybrid of ARIMA and LSTM model was used to construct the model for assessing the morbidity and mortality in the countries and territories of East Asia, and predicting the morbidity and mortality in the next 5 years. Results In North Korea, the incidence and mortality of HIV showed a rapid increase during 2000–2010 and a gradual decrease during 2010–2019. The incidence of HIV was predicted to be increased and the mortality was decreased. In South Korea, the incidence was increased during 2000–2010 and decreased during 2010–2019, while the mortality showed fluctuant trend. As predicted, the incidence of HIV in South Korea might be increased and the mortality might be decreased during 2020–2025. In Mongolia, the incidence and mortality were slowly decreased during 2000–2005, increased during 2005–2015, and rapidly decreased till 2019. The predicted incidence and mortality of HIV showed a decreased trend. As for Japan, the incidence of HIV was rapidly increased till 2010 and then decreased till 2015. The predicted incidence of HIV in Japan was gradually increased. The mortality of HIV in Japan was fluctuant during 2000–2019 and was slowly decreased as predicted. The incidence and mortality of HIV in Taiwan during 2000–2019 was increased on the whole. The predicted incidence of HIV during was stationary and the mortality was decreased. In terms of China Mainland, the incidence and mortality of HIV was fluctuant during 2000–2019. The predicted incidence of HIV in China Mainland was stationary while the mortality was rapidly decreased. Conclusion On the whole, the incidence of HIV combined with other diseases in post-neonatal population was increased before 2010 and then decreased during 2010–2019 while the mortality of those patients was decreased in East Asia.
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Affiliation(s)
- Ying Chen
- Respiratory Medicine Department, XiXi Hospital of HangZhou (Affiliated HangZhou XiXi Hospital, Zhe Jiang University School of Medicine), No.2 Hengbu Road, Liuxia Street, Xihu District, Hangzhou, 310000, Zhejiang Province, China
| | - Jiawen He
- Respiratory Medicine Department, XiXi Hospital of HangZhou (Affiliated HangZhou XiXi Hospital, Zhe Jiang University School of Medicine), No.2 Hengbu Road, Liuxia Street, Xihu District, Hangzhou, 310000, Zhejiang Province, China
| | - Meihua Wang
- Respiratory Medicine Department, XiXi Hospital of HangZhou (Affiliated HangZhou XiXi Hospital, Zhe Jiang University School of Medicine), No.2 Hengbu Road, Liuxia Street, Xihu District, Hangzhou, 310000, Zhejiang Province, China.
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Elsensohn MH, Dantony E, Iwaz J, Villar E, Couchoud C, Ecochard R. Improving survival in end-stage renal disease: A case study. Stat Methods Med Res 2018; 28:3579-3590. [DOI: 10.1177/0962280218811357] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Background: With the increase of life expectancy, *On behalf of the REIN registry. end-stage renal disease (ESRD) is affecting a growing number of people. Simultaneously, renal replacement therapies (RRTs) have considerably improved patient survival. We investigated the way current RRT practices would affect patients' survival. Methods: We used a multi-state model to represent the transitions between RRTs and the transition to death. The concept of “crude probability of death” combined with this model allowed estimating the proportions of ESRD-related and ESRD-unrelated deaths. Estimating the ESRD-related death rate requires comparing the mortality rate between ESRD patients and the general population. Predicting patients' courses through RRTs and Death states could be obtained by solving a system of Kolmogorov differential equations. The impact of practice on patient survival was quantified using the restricted mean survival time (RMST) which was compared with that of healthy subjects with same characteristics. Results: The crude probability of ESRD-unrelated death was nearly zero in the youngest patients (18–45 years) but was a sizeable part of deaths in the oldest (≥70 years). Moreover, in the oldest patients, the proportion of expected death was higher in patient without vs. with diabetes because the former live older. In men aged 75 years at first RRT, the predicted RMSTs in patients with and without diabetes were, respectively, 61% and 69% those of comparable healthy men. Conclusion: Using the concept of “crude probability of death” with multi-state models is feasible and useful to assess the relative benefits of various treatments in ESRD and help patient long-term management.
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Affiliation(s)
- MH Elsensohn
- Hospices Civils de Lyon, Pôle Santé Publique, Service de Biostatistique-Bioinformatique, Lyon, France
- Université de Lyon, Lyon, France
- CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Évolutive, Équipe Biostatistique Santé, Villeurbanne, France
| | - E Dantony
- Hospices Civils de Lyon, Pôle Santé Publique, Service de Biostatistique-Bioinformatique, Lyon, France
- Université de Lyon, Lyon, France
- CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Évolutive, Équipe Biostatistique Santé, Villeurbanne, France
| | - J Iwaz
- Hospices Civils de Lyon, Pôle Santé Publique, Service de Biostatistique-Bioinformatique, Lyon, France
- Université de Lyon, Lyon, France
- CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Évolutive, Équipe Biostatistique Santé, Villeurbanne, France
| | - E Villar
- Hospices Civils de Lyon, Pôle Santé Publique, Service de Biostatistique-Bioinformatique, Lyon, France
- Université de Lyon, Lyon, France
- CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Évolutive, Équipe Biostatistique Santé, Villeurbanne, France
- Centre Hospitalier Saint Joseph-Saint Luc, Service de Néphrologie, Lyon, France
| | - C Couchoud
- CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Évolutive, Équipe Biostatistique Santé, Villeurbanne, France
- REIN Registry, Agence de la Biomédecine, Saint Denis La Plaine, France
| | - R Ecochard
- Hospices Civils de Lyon, Pôle Santé Publique, Service de Biostatistique-Bioinformatique, Lyon, France
- Université de Lyon, Lyon, France
- CNRS, UMR 5558, Laboratoire de Biométrie et Biologie Évolutive, Équipe Biostatistique Santé, Villeurbanne, France
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Grebe E, Welte A, Johnson LF, van Cutsem G, Puren A, Ellman T, Etard JF, Huerga H. Population-level HIV incidence estimates using a combination of synthetic cohort and recency biomarker approaches in KwaZulu-Natal, South Africa. PLoS One 2018; 13:e0203638. [PMID: 30212513 PMCID: PMC6136757 DOI: 10.1371/journal.pone.0203638] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2018] [Accepted: 08/26/2018] [Indexed: 11/30/2022] Open
Abstract
Introduction There is a notable absence of consensus on how to generate estimates of population-level incidence. Incidence is a considerably more sensitive indicator of epidemiological trends than prevalence, but is harder to estimate. We used a novel hybrid method to estimate HIV incidence by age and sex in a rural district of KwaZulu-Natal, South Africa. Methods Our novel method uses an ‘optimal weighting’ of estimates based on an implementation of a particular ‘synthetic cohort’ approach (interpreting the age/time structure of prevalence, in conjunction with estimates of excess mortality) and biomarkers of ‘recent infection’ (combining Lag-Avidity, Bio-Rad Avidity and viral load results to define recent infection, and adapting the method for age-specific incidence estimation). Data were obtained from a population-based cross-sectional HIV survey conducted in Mbongolwane and Eshowe health service areas in 2013. Results Using the combined method, we find that age-specific HIV incidence in females rose rapidly during adolescence, from 1.33 cases/100 person-years (95% CI: 0.98,1.67) at age 15 to a peak of 5.01/100PY (4.14,5.87) at age 23. In males, incidence was lower, 0.34/100PY (0.00-0.74) at age 15, and rose later, peaking at 3.86/100PY (2.52-5.20) at age 30. Susceptible population-weighted average incidence in females aged 15-29 was estimated at 3.84/100PY (3.36-4.40), in males aged 15-29 at 1.28/100PY (0.68-1.50) and in all individuals aged 15-29 at 2.55/100PY (2.09-2.76). Using the conventional recency biomarker approach, we estimated HIV incidence among females aged 15-29 at 2.99/100PY (1.79-4.36), among males aged 15-29 at 0.87/100PY (0.22-1.60) and among all individuals aged 15-59 at 1.66/100PY (1.13-2.27). Discussion HIV incidence was very high in women aged 15-30, peaking in the early 20s. Men had lower incidence, which peaked at age 30. The estimates obtained from the hybrid method are more informative than those produced by conventional analysis of biomarker data, and represents a more optimal use of available data than either the age-continuous biomarker or synthetic cohort methods alone. The method is mainly useful at younger ages, where excess mortality is low and uncertainty in the synthetic cohort estimates is reasonably small. Conclusion Application of this method to large-scale population-based HIV prevalence surveys is likely to result in improved incidence surveillance over methods currently in wide use. Reasonably accurate and precise age-specific estimates of incidence are important to target better prevention, diagnosis and care strategies.
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Affiliation(s)
- Eduard Grebe
- DST-NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA), Stellenbosch University, Stellenbosch, South Africa
- * E-mail:
| | - Alex Welte
- DST-NRF Centre of Excellence in Epidemiological Modelling and Analysis (SACEMA), Stellenbosch University, Stellenbosch, South Africa
| | - Leigh F. Johnson
- Centre for Infectious Diseases Epidemiology and Research (CIDER), University of Cape Town, Cape Town, South Africa
| | - Gilles van Cutsem
- Centre for Infectious Diseases Epidemiology and Research (CIDER), University of Cape Town, Cape Town, South Africa
- Médecins Sans Frontières, Cape Town, South Africa
| | - Adrian Puren
- National Institute for Communicable Diseases (NICD), National Health Laboratory Service, Johannesburg, South Africa
| | - Tom Ellman
- Médecins Sans Frontières, Cape Town, South Africa
| | - Jean-François Etard
- TransVIHMI, Institut de Recherche pour le Développement (IRD), Institut National de la Santé et de la Recherche Médicale (INSERM), Montpellier University, Montpellier, France
- Epicentre, Paris, France
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Blaizot S, Huerga H, Riche B, Ellman T, Shroufi A, Etard JF, Ecochard R. Combined interventions to reduce HIV incidence in KwaZulu-Natal: a modelling study. BMC Infect Dis 2017; 17:522. [PMID: 28747167 PMCID: PMC5530541 DOI: 10.1186/s12879-017-2612-5] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2017] [Accepted: 07/18/2017] [Indexed: 11/10/2022] Open
Abstract
BACKGROUND Combined prevention interventions, including early antiretroviral therapy initiation, may substantially reduce HIV incidence in hyperendemic settings. Our aim was to assess the potential short-term impact of combined interventions on HIV spreading in the adult population of Mbongolwane and Eshowe (KwaZulu-Natal, South Africa) using sex- and age-specific scenarios, and age-targeted interventions. METHODS A mathematical model was used with data on adults (15-59 years) from the Mbongolwane and Eshowe HIV Impact in Population Survey to compare the effects of various interventions on the HIV incidence rate. These interventions included increase in antiretroviral therapy (ART) coverage with extended eligibility criteria, increase in voluntary medical male circumcision (VMMC), and implementation of pre-exposure prophylaxis (PrEP) among women. RESULTS With no additional interventions to the ones in place at the time of the survey (ART at CD4 < 350 and VMMC), incidence will decrease by 24% compared to the baseline rate. The implementation of "ART at CD4<500" or "ART for all" would reduce further the incidence rate by additional 8% and 15% respectively by 4 years and 20% and 34% by 10 years. Impacts would be higher with age-targeted scenarios than without. CONCLUSIONS In Mbongolwane and Eshowe, implementation of the new South African guidelines, recommending ART initiation regardless of CD4 count, would accelerate incidence reduction. In this setting, combining these guidelines, VMMC, and PrEP among young women could be an effective strategy in reducing the incidence to low levels.
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Affiliation(s)
- Stéphanie Blaizot
- Service de Biostatistique, Hospices Civils de Lyon, F-69003 Lyon, France
- Université de Lyon, F-69000 Lyon, France
- Université Lyon 1, F-69100 Villeurbanne, France
- CNRS UMR 5558, Equipe Biostatistique-Santé, Laboratoire de Biométrie et Biologie Evolutive, F-69100 Villeurbanne, France
| | | | - Benjamin Riche
- Service de Biostatistique, Hospices Civils de Lyon, F-69003 Lyon, France
- Université de Lyon, F-69000 Lyon, France
- Université Lyon 1, F-69100 Villeurbanne, France
- CNRS UMR 5558, Equipe Biostatistique-Santé, Laboratoire de Biométrie et Biologie Evolutive, F-69100 Villeurbanne, France
| | - Tom Ellman
- Médecins Sans Frontières, Cape Town, South Africa
| | - Amir Shroufi
- Médecins Sans Frontières, Cape Town, South Africa
| | - Jean-François Etard
- Epicentre, F-75011 Paris, France
- IRD UMI 233, INSERM U1175, Université de Montpellier, Unité TransVIHMI, F-34000 Montpellier, France
| | - René Ecochard
- Service de Biostatistique, Hospices Civils de Lyon, F-69003 Lyon, France
- Université de Lyon, F-69000 Lyon, France
- Université Lyon 1, F-69100 Villeurbanne, France
- CNRS UMR 5558, Equipe Biostatistique-Santé, Laboratoire de Biométrie et Biologie Evolutive, F-69100 Villeurbanne, France
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Blaizot S, Kim AA, Zeh C, Riche B, Maman D, De Cock KM, Etard JF, Ecochard R. Estimating HIV Incidence Using a Cross-Sectional Survey: Comparison of Three Approaches in a Hyperendemic Setting, Ndhiwa Subcounty, Kenya, 2012. AIDS Res Hum Retroviruses 2017; 33:472-481. [PMID: 27824254 DOI: 10.1089/aid.2016.0123] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
Abstract
OBJECTIVES Estimating HIV incidence is critical for identifying groups at risk for HIV infection, planning and targeting interventions, and evaluating these interventions over time. The use of reliable estimation methods for HIV incidence is thus of high importance. The aim of this study was to compare methods for estimating HIV incidence in a population-based cross-sectional survey. DESIGN/METHODS The incidence estimation methods evaluated included assay-derived methods, a testing history-derived method, and a probability-based method applied to data from the Ndhiwa HIV Impact in Population Survey (NHIPS). Incidence rates by sex and age and cumulative incidence as a function of age were presented. RESULTS HIV incidence ranged from 1.38 [95% confidence interval (CI) 0.67-2.09] to 3.30 [95% CI 2.78-3.82] per 100 person-years overall; 0.59 [95% CI 0.00-1.34] to 2.89 [95% CI 0.86-6.45] in men; and 1.62 [95% CI 0.16-6.04] to 4.03 [95% CI 3.30-4.77] per 100 person-years in women. Women had higher incidence rates than men for all methods. Incidence rates were highest among women aged 15-24 and 25-34 years and highest among men aged 25-34 years. CONCLUSION Comparison of different methods showed variations in incidence estimates, but they were in agreement to identify most-at-risk groups. The use and comparison of several distinct approaches for estimating incidence are important to provide the best-supported estimate of HIV incidence in the population.
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Affiliation(s)
- Stéphanie Blaizot
- Hospices Civils de Lyon, Service de Biostatistique, Lyon, France
- Université de Lyon, Lyon, France
- Université Lyon 1, Villeurbanne, France
- CNRS UMR 5558, Laboratoire de Biométrie et Biologie Evolutive, Equipe Biostatistique-Santé, Villeurbanne, France
| | - Andrea A. Kim
- Division of Global HIV/AIDS, U.S. Centers for Disease Control and Prevention, Nairobi, Kenya
| | - Clement Zeh
- Division of HIV/AIDS Prevention, U.S. Centers for Disease Control and Prevention, Kisumu, Kenya
| | - Benjamin Riche
- Hospices Civils de Lyon, Service de Biostatistique, Lyon, France
- Université de Lyon, Lyon, France
- Université Lyon 1, Villeurbanne, France
- CNRS UMR 5558, Laboratoire de Biométrie et Biologie Evolutive, Equipe Biostatistique-Santé, Villeurbanne, France
| | | | - Kevin M. De Cock
- Division of Global HIV/AIDS, U.S. Centers for Disease Control and Prevention, Nairobi, Kenya
| | - Jean-François Etard
- Epicentre, Paris, France
- UMI 233 TransVIHMI, Institut de Recherche pour le Développement, INSERM U1175, Université de Montpellier, Montpellier, France
| | - René Ecochard
- Hospices Civils de Lyon, Service de Biostatistique, Lyon, France
- Université de Lyon, Lyon, France
- Université Lyon 1, Villeurbanne, France
- CNRS UMR 5558, Laboratoire de Biométrie et Biologie Evolutive, Equipe Biostatistique-Santé, Villeurbanne, France
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Blaizot S, Maman D, Riche B, Mukui I, Kirubi B, Ecochard R, Etard JF. Potential impact of multiple interventions on HIV incidence in a hyperendemic region in Western Kenya: a modelling study. BMC Infect Dis 2016; 16:189. [PMID: 27129591 PMCID: PMC4851795 DOI: 10.1186/s12879-016-1520-4] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2015] [Accepted: 04/18/2016] [Indexed: 01/25/2023] Open
Abstract
BACKGROUND Multiple prevention interventions, including early antiretroviral therapy initiation, may reduce HIV incidence in hyperendemic settings. Our aim was to predict the short-term impact of various single and combined interventions on HIV spreading in the adult population of Ndhiwa subcounty (Nyanza Province, Kenya). METHODS A mathematical model was used with data on adults (15-59 years) from the Ndhiwa HIV Impact in Population Survey to compare the impacts on HIV prevalence, HIV incidence rate, and population viral load suppression of various interventions. These interventions included: improving the cascade of care (use of three guidelines), increasing voluntary medical male circumcision (VMMC), and implementing pre-exposure prophylaxis (PrEP) use among HIV-uninfected women. RESULTS After four years, improving separately the cascade of care under the WHO 2013 guidelines and under the treat-all strategy would reduce the overall HIV incidence rate by 46 and 58 %, respectively, vs. the baseline rate, and by 35 and 49 %, respectively, vs. the implementation of the current Kenyan guidelines. With conservative and optimistic scenarios, VMMC and PrEP would reduce the HIV incidence rate by 15-25 % and 22-28 % vs. the baseline, respectively. Combining the WHO 2013 guidelines with VMMC would reduce the HIV incidence rate by 35-56 % and combining the treat-all strategy with VMMC would reduce it by 49-65 %. Combining the WHO 2013 guidelines, VMMC, and PrEP would reduce the HIV incidence rate by 46-67 %. CONCLUSIONS The impacts of the WHO 2013 guidelines and the treat-all strategy were relatively close; their implementation is desirable to reduce HIV spread. Combining several strategies is promising in adult populations of hyperendemic areas but requires regular, reliable, and costly monitoring.
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Affiliation(s)
- Stéphanie Blaizot
- Service de Biostatistique, Hospices Civils de Lyon, F-69003, Lyon, France. .,Université de Lyon, F-69000, Lyon, France. .,Université Lyon 1, F-69100, Villeurbanne, France. .,CNRS UMR 5558, Equipe Biostatistique-Santé, Laboratoire de Biométrie et Biologie Evolutive, F-69100, Villeurbanne, France.
| | | | - Benjamin Riche
- Service de Biostatistique, Hospices Civils de Lyon, F-69003, Lyon, France.,Université de Lyon, F-69000, Lyon, France.,Université Lyon 1, F-69100, Villeurbanne, France.,CNRS UMR 5558, Equipe Biostatistique-Santé, Laboratoire de Biométrie et Biologie Evolutive, F-69100, Villeurbanne, France
| | - Irene Mukui
- National AIDS and STDs Control Program, Nairobi, Kenya
| | | | - René Ecochard
- Service de Biostatistique, Hospices Civils de Lyon, F-69003, Lyon, France.,Université de Lyon, F-69000, Lyon, France.,Université Lyon 1, F-69100, Villeurbanne, France.,CNRS UMR 5558, Equipe Biostatistique-Santé, Laboratoire de Biométrie et Biologie Evolutive, F-69100, Villeurbanne, France
| | - Jean-François Etard
- Epicentre, F-75011, Paris, France.,UMI 233 TransVIHMI, Institut de Recherche pour le Développement, Université Montpellier 1, F-34000, Montpellier, France
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Dantony E, Elsensohn MH, Dany A, Villar E, Couchoud C, Ecochard R. Estimating the parameters of multi-state models with time-dependent covariates through likelihood decomposition. Comput Biol Med 2016; 69:37-43. [DOI: 10.1016/j.compbiomed.2015.11.016] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2015] [Revised: 11/25/2015] [Accepted: 11/26/2015] [Indexed: 11/25/2022]
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