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Chakraborty H, Hossain A, Latif MA. A three-state continuous time Markov chain model for HIV disease burden. J Appl Stat 2018. [DOI: 10.1080/02664763.2018.1555573] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
| | - Akhtar Hossain
- Department of Epidemiology and Biostatistics, University of South Carolina, Columbia, SC, USA
| | - Mahbub A.H.M. Latif
- Institute of Statistical Research and Training, University of Dhaka, Dhaka, Bangladesh
- Present address: Graduate School of Public Health, St. Luke's International University, Tokyo, Japan
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Mangal TD. Joint estimation of CD4+ cell progression and survival in untreated individuals with HIV-1 infection. AIDS 2017; 31:1073-1082. [PMID: 28301424 PMCID: PMC5414573 DOI: 10.1097/qad.0000000000001437] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/22/2016] [Revised: 01/26/2017] [Accepted: 02/03/2016] [Indexed: 12/29/2022]
Abstract
OBJECTIVE We compiled the largest dataset of seroconverter cohorts to date from 25 countries across Africa, North America, Europe, and Southeast/East (SE/E) Asia to simultaneously estimate transition rates between CD4 cell stages and death, in antiretroviral therapy (ART)-naive HIV-1-infected individuals. DESIGN A hidden Markov model incorporating a misclassification matrix was used to represent natural short-term fluctuations and measurement errors in CD4 cell counts. Covariates were included to estimate the transition rates and survival probabilities for each subgroup. RESULTS The median follow-up time for 16 373 eligible individuals was 4.1 years (interquartile range 1.7-7.1), and the mean age at seroconversion was 31.1 years (SD 8.8). A total of 14 525 individuals had recorded CD4 cell counts pre-ART, 1885 died, and 6947 initiated ART. Median (interquartile range) survival for men aged 20 years at seroconversion was 13.0 (12.4-13.4), 11.6 (10.9-12.3), and 8.3 years (7.9-8.9) in Europe/North America, Africa, and SE/E Asia, respectively. Mortality rates increase with age (hazard ratio 2.22, 95% confidence interval 1.84-2.67 for >45 years compared with <25 years) and vary by region (hazard ratio 2.68, 1.75-4.12 for Africa and 1.88, 1.50-2.35 for Asia compared with Europe/North America). CD4 cell decline was significantly faster in Asian cohorts compared with Europe/North America (hazard ratio 1.45, 1.36-1.54). CONCLUSION Mortality and CD4 cell progression rates exhibited regional and age-specific differences, with decreased survival in African and SE/E Asian cohorts compared with Europe/North America and in older age groups. This extensive dataset reveals heterogeneities between regions and ages, which should be incorporated into future HIV models.
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Affiliation(s)
- Tara D Mangal
- Medical Research Council Centre for Outbreak Analysis and Modelling, Department of Infectious Disease Epidemiology, Imperial College London, London, UK
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Hellinger FJ. Assessing the cost effectiveness of pre-exposure prophylaxis for HIV prevention in the US. PHARMACOECONOMICS 2013; 31:1091-1104. [PMID: 24271858 DOI: 10.1007/s40273-013-0111-0] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
About 50,000 people are infected with HIV in the US each year and this number has remained virtually the same for the past decade. Yet, in the last few years, evidence from several multinational randomized clinical trials has shown that the provision of antiretroviral drug to uninfected persons (i.e. pre-exposure prophylaxis) reduces the incidence of HIV by about 50 %. However, evidence from cost-effectiveness studies conducted in the US yield widely varying estimates of the cost per quality-adjusted life-year (QALY) gained, and this variation reflects the substantial uncertainty surrounding the determinants of HIV transmission (e.g. adherence rates to prophylactic medications, the average number of sexual partners, the number and types of sexual acts, the viral load of infected partners, and the proportion of contacts where condoms are used), as well as different approaches to translating a reduction in HIV cases into an estimate of the increase in the number of QALYs.
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Affiliation(s)
- Fred J Hellinger
- Center for Delivery, Organization, and Markets, Agency for Healthcare Research and Quality (AHRQ), 540 Gaither Road, Rockville, MD, 20850, USA,
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4
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Yeghiazarian L, Cumberland WG, Yang OO. A stochastic multi-scale model of HIV-1 transmission for decision-making: application to a MSM population. PLoS One 2013; 8:e70578. [PMID: 24302983 PMCID: PMC3841178 DOI: 10.1371/journal.pone.0070578] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2013] [Accepted: 06/20/2013] [Indexed: 11/18/2022] Open
Abstract
BACKGROUND In the absence of an effective vaccine against HIV-1, the scientific community is presented with the challenge of developing alternative methods to curb its spread. Due to the complexity of the disease, however, our ability to predict the impact of various prevention and treatment strategies is limited. While ART has been widely accepted as the gold standard of modern care, its timing is debated. OBJECTIVES To evaluate the impact of medical interventions at the level of individuals on the spread of infection across the whole population. Specifically, we investigate the impact of ART initiation timing on HIV-1 spread in an MSM (Men who have Sex with Men) population. DESIGN AND METHODS A stochastic multi-scale model of HIV-1 transmission that integrates within a single framework the in-host cellular dynamics and their outcomes, patient health states, and sexual contact networks. The model captures disease state and progression within individuals, and allows for simulation of therapeutic strategies. RESULTS Early ART initiation may substantially affect disease spread through a population. CONCLUSIONS Our model provides a multi-scale, systems-based approach to evaluate the broader implications of therapeutic strategies.
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Affiliation(s)
- Lilit Yeghiazarian
- Department of Biomedical, Chemical & Environmental Engineering, University of Cincinnati, Cincinnati, Ohio, United States of America
| | - William G. Cumberland
- Department of Biostatistics, School of Public Health, University of California Los Angeles, Los Angeles, California, United States of America
| | - Otto O. Yang
- Departments of Medicine and Microbiology, Immunology, and Molecular Genetics, Geffen School of Medicine, University of California Los Angeles, Los Angeles, California, United States of America
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Johnson LF, Boulle A. How should access to antiretroviral treatment be measured? Bull World Health Organ 2011; 89:157-60. [PMID: 21346928 DOI: 10.2471/blt.10.080911] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/29/2010] [Revised: 09/29/2010] [Accepted: 10/06/2010] [Indexed: 11/27/2022] Open
Affiliation(s)
- Leigh F Johnson
- Centre for Infectious Disease Epidemiology and Research, University of Cape Town, Anzio Road, Observatory, 7925, Cape Town, South Africa.
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6
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Guo H, Li MY. Global dynamics of a staged-progression model with amelioration for infectious diseases. JOURNAL OF BIOLOGICAL DYNAMICS 2008; 2:154-68. [PMID: 22880698 DOI: 10.1080/17513750802120877] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We analyze the global dynamics of a mathematical model for infectious diseases that progress through distinct stages within infected hosts with possibility of amelioration. An example of such diseases is HIV/AIDS that progresses through several stages with varying degrees of infectivity; amelioration can result from a host's immune action or more commonly from antiretroviral therapies, such as highly active antiretroviral therapy. For a general n-stage model with constant recruitment and bilinear incidence that incorporates amelioration, we prove that the global dynamics are completely determined by the basic reproduction number R(0). If R(0)≤1, then the disease-free equilibrium P(0) is globally asymptotically stable, and the disease always dies out. If R(0)>1, P(0) is unstable, a unique endemic equilibrium P* is globally asymptotically stable, and the disease persists at the endemic equilibrium. Impacts of amelioration on the basic reproduction number are also investigated.
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Affiliation(s)
- Hongbin Guo
- Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1
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Heisterkamp SH, de Vries R, Sprenger HG, Hubben GAA, Postma MJ. Estimation and prediction of the HIV–AIDS-epidemic under conditions of HAART using mixtures of incubation time distributions. Stat Med 2008; 27:781-94. [PMID: 17597471 DOI: 10.1002/sim.2974] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
The estimation of the HIV-AIDS epidemic by means of back-calculation (BC) has been difficult since the introduction of highly active anti-retroviral therapy (HAART) because the incubation time distributions needed for BC were poorly known. Moreover, it has been assumed that if the general public is aware that effective treatments are available then the majority of infected people would be known, and therefore a hidden epidemic was assumed not to exist. Nevertheless, it was suspected that not every infected person would come to the attention of health-care providers, and therefore estimates independent of the patients' registration were necessary. In this paper, the incubation time distributions for HIV treated with the HAART regimen are derived from a cohort study. By using estimates of the proportion treated according to the HAART regimen and the incubation time distributions estimated in the era before the implementation of HAART (pre-HAART), new marginal population incubation time distributions for each of the three risk groups (homosexuals, drug users and others) were constructed. The BC was performed using an empirical Bayesian approach based on the latter incubation time distribution.
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Mathieu E, Foucher Y, Dellamonica P, Daures JP. Parametric and Non Homogeneous Semi-Markov Process for HIV Control. Methodol Comput Appl Probab 2007. [DOI: 10.1007/s11009-007-9033-7] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Glynn MK, Lee LM, McKenna MT. The status of national HIV case surveillance, United States 2006. Public Health Rep 2007; 122 Suppl 1:63-71. [PMID: 17354529 PMCID: PMC1804109 DOI: 10.1177/00333549071220s110] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Since the height of HIV incidence in the mid-1980s, advances in treatment have delayed progression of HIV infection. As a result, surveillance of AIDS cases alone is no longer sufficient to monitor the current status of the HIV epidemic. At the national level, new HIV diagnoses and progression of these cases to AIDS are used to describe the epidemic. The capacity to monitor the national HIV epidemic has consistently improved over the last several years. An increasing number of states report diagnosed HIV cases to the national surveillance system, allowing data from this system to better represent the national picture. Monitoring the national HIV epidemic depends on a nationwide system using standardized methods of data collection, and establishing such a comprehensive system remains one of the highest priorities for national HIV case surveillance.
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Affiliation(s)
- M Kathleen Glynn
- Division of HIV/AIDS Prevention, National Center for HIV, STD, and TB Prevention, Centers for Disease Control and Prevention, Atlanta, GA 30333, USA.
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Mathieu E, Loup P, Dellamonica P, Daures JP. Markov Modelling of Immunological and Virological States in HIV-1 Infected Patients. Biom J 2005; 47:834-46. [PMID: 16450856 DOI: 10.1002/bimj.200410164] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
The purpose of this study was to evaluate the evolution of HIV infected patients and to bring out some significant factors associated with this pathology. The main criteria revealing the State of illness is viral load measurement (VL). However the CD4 lymphocytes also represent an important marker as these reflect the State of the immune reservoir. Many studies have been carried out in this field and different models have been proposed with a view to a better understanding of this disease. Multi State Markov models defined in terms of CD4 counts, or in terms of viral load, have proved to be very useful tools for modelling HIV disease progression. The model we have developed in this study is based on both the CD4 lymphocytes counts and VL. Markov models are characterized by transition intensities. In this paper we explored several structures in succession. First, we used a homogeneous continuous time Markov process with four states defined by crossed values of CD4 and VL in a given patient at a given time. Then, the effect of certain covariates on the infection process was introduced into the model via the transition intensity functions, as with a Cox regression model. Since the hypothesis of homogeneity may be unrealistic in certain cases, we also considered piecewise homogeneous Markov models. Finally, the effects of covariates and time were combined in a piecewise homogeneous model with a covariate. We applied these methods to data from 1313 HIV-infected patients included in the NADIS cohort.
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Affiliation(s)
- E Mathieu
- Clinical Research University Institute, Biostatistics Laboratory, 641 avenue D.G. Giraud, 34093 Montpellier, France.
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Artzrouni M. Back-calculation and projection of the HIV/AIDS epidemic among homosexual/ bisexual men in three European countries: evalution of past projections and updates allowing for treatment effects. Eur J Epidemiol 2004; 19:171-9. [PMID: 15074573 DOI: 10.1023/b:ejep.0000017826.57607.ea] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
This study critically evaluates the quality of 1990 back-calculations and long-term projections of the HIV/AIDS epidemic for homosexual/bisexual men in France, the Federal Republic of Germany, and the UK. The projection captured the general pattern observed in all three countries although the observed AIDS incidence peaked 2-3 years later and declined faster than had been projected. Total AIDS incidences from 1989 to 2000 were overestimated by 38.5% in France, and underestimated by 23.9 and 17.5% in western Germany and the UK. Updated back-calculations and projections to 2020 use AIDS incidence data up to 2000. The procedure incorporates an asymmetric long-tailed cumulative HIV curve as well as the increase in the median incubation period brought about by new therapies introduced during the 1990s. The results suggest that: (i) The rapid decrease in cases during the late 1990s was caused by a median incubation period that increased from 10 years to 21-23 years by the late 1990s. (ii) An imminent bottoming out followed by a protracted increase in AIDS cases from 2000 to at least 2010 could be the consequence of a leveling off of the median incubation period. (iii) A low variant of the projections shows that at least 40,000 homosexual men could develop AIDS in the three countries after 2000.
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Affiliation(s)
- Marc Artzrouni
- Department of Applied Mathematics, University of Pau, BP 1133, Pau, France.
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Posner SJ, Myers L, Hassig SE, Rice JC, Kissinger P, Farley TA. Estimating HIV Incidence and Detection Rates From Surveillance Data. Epidemiology 2004; 15:164-72. [PMID: 15127908 DOI: 10.1097/01.ede.0000112215.19764.2b] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
Abstract
BACKGROUND Markov models that incorporate HIV test information can increase precision in estimates of new infections and permit the estimation of detection rates. The purpose of this study was to assess the functioning of a Markov model for estimating new HIV infections and HIV detection rates in Louisiana using surveillance data. METHODS We expanded a discrete-time Markov model by accounting for the change in AIDS case definition made by the Centers for Disease Control and Prevention in 1993. The model was applied to quarterly HIV/AIDS surveillance data reported in Louisiana from 1981 to 1996 for various exposure and demographic subgroups. When modeling subgroups defined by exposure categories, we adjusted for the high proportion of missing exposure information among recent cases. We ascertained sensitivity to changes in various model assumptions. RESULTS The model was able to produce results consistent with other sources of information in the state. Estimates of new infections indicated a transition of the HIV epidemic in Louisiana from (1) predominantly white men and men who have sex with men to (2) women, blacks, and high-risk heterosexuals. The model estimated that 61% of all HIV/AIDS cases were detected and reported by 1996, yet half of all HIV/non-AIDS cases were yet to be detected. Sensitivity analyses demonstrated that the model was robust to several uncertainties. CONCLUSIONS In general, the methodology provided a useful and flexible alternative for estimating infection and detection trends using data from a U.S. surveillance program. Its use for estimating current infection will need further exploration to address assumptions related to newer treatments.
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Affiliation(s)
- Stephanie J Posner
- HIV/AIDS Program, Louisiana Office of Public Health, Department of Health and Hospitals, New Orleans, Louisiana, USA.
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Kousignian I, Abgrall S, Duval X, Descamps D, Matheron S, Costagliola D. Modeling the time course of CD4 T-lymphocyte counts according to the level of virologic rebound in HIV-1-infected patients on highly active antiretroviral therapy. J Acquir Immune Defic Syndr 2003; 34:50-7. [PMID: 14501793 DOI: 10.1097/00126334-200309010-00007] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
OBJECTIVE To study the influence of the level of virologic rebound during combination antiretroviral therapy on the time course of the CD4 count. METHODS Between January 1997 and December 1999, we enrolled 3736 patients from the French Hospital HIV Database who had an undetectable viral load on a first course of highly active antiretroviral therapy (HAART). Four levels of virologic rebound were defined on the basis of viral load values during the year following initial undetectability on HAART: group 1, all viral loads <500 copies/mL; group 2, all viral loads <5000 copies/mL; group 3, all viral loads <10,000 copies/mL; and group 4, at least 1 viral load >10,000 copies/mL. We developed a continuous time-homogeneous Markov process with 5 reversible stages defined by CD4 count intervals. RESULTS CD4 counts increased continuously over time in each group. The smaller the virologic rebound, the stronger was the increase in the CD4 count (P < 0.0001). The mean CD4 cell count increments between months 2 and 6 were 26, 20, 11, and 2 cells/mm3 in groups 1, 2, 3, and 4, respectively. The rate of gain fell after month 6 and was almost nil in group 4. CONCLUSION After achieving an undetectable viral load on HAART, immunologic reconstitution is possible whatever the subsequent level of viral replication, except among patients with high-level rebound, meaning that in patients with a long history of antiretroviral therapy and a reduced choice of antiretroviral drugs due to acquisition of resistances, delay in antiretroviral therapy switch can be possible in patients with low or intermediate rebound.
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Sypsa V, Touloumi G, Kenward M, Karafoulidou A, Hatzakis A. Comparison of smoothing techniques for CD4 data in a Markov model with states defined by CD4: an example on the estimation of the HIV incubation time distribution. Stat Med 2001; 20:3667-76. [PMID: 11782025 DOI: 10.1002/sim.1080] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Multi-state models defined in terms of CD4 counts are useful for modelling HIV disease progression. A Markov model with six progressive CD4-based states and an absorbing state (AIDS) was used to estimate the cumulative probability of progressing to AIDS in 158 HIV-1 infected haemophiliacs with known seroconversion (SC) dates. A problem arising in such analysis is how to define CD4-based states, since this marker is subject to measurement error and short timescale variability. Four approaches were used: no smoothing, ad hoc smoothing (to move to a later/previous state two consecutive measurements to later/previous states are needed), kernel smoothing and random effects (RE) models. The estimates were compared with the Kaplan-Meier estimate based solely on data concerning time to AIDS. There was an apparent lack of agreement between the Kaplan-Meier and the "no smoothing" estimate. With the exception of the "no smoothing" method, "ad hoc", kernel and RE estimates fell within the range of the 95 per cent CIs of the Kaplan-Meier curve. Simulations demonstrated that the use of raw CD4 counts provides overestimated transition intensities. Compared to the kernel method, ad hoc is easier to implement and overcomes the problem of the choice of bandwidth. The RE approach leads to simple models, since it usually results in very few transitions to previous states, and can handle individuals with sparse data by smoothing their predictions towards the population mean. Ad hoc was the method that performed better, in terms of bias, than the other smoothing approaches.
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Affiliation(s)
- V Sypsa
- Department of Hygiene & Epidemiology, Athens University Medical School, M. Asias 75, 11527 Athens, Greece.
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Geskus RB. Methods for estimating the AIDS incubation time distribution when date of seroconversion is censored. Stat Med 2001; 20:795-812. [PMID: 11241577 DOI: 10.1002/sim.700] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
In most cohort studies on HIV infection and AIDS, data on time from seroconversion to AIDS or death are doubly censored, both at the time origin and at the endpoint of interest. In epidemiological research, the most frequently adopted approach is to restrict the analysis to persons with narrow seroconversion intervals and to impute the midpoint of this interval as date of seroconversion. For many cohort studies, the consequence is that a substantial proportion of the data is not used. We consider four methods that are expected to be less biased when all cohort data are used: two imputation methods, conditional mean and multiple imputation, and two likelihood maximization methods. We derive the likelihood structure of the cohort data and clarify its dependence on study design. All methods are applied to data from the Amsterdam cohort study among injection drug users. In a simulation study the data generation process of this cohort study is imitated. The performance of midpoint, conditional mean and multiple imputation are compared. With midpoint imputation, both an analysis using the full data set, as well as one restricted to the cases with small seroconversion intervals, is performed. Conditional mean imputation comes out as the preferred method. It gives best results with respect to mean squared error. Moreover, when confidence intervals are computed through standard methods that ignore the uncertainty in the imputed date of seroconversion, coverage probabilities are almost correct.
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Affiliation(s)
- R B Geskus
- Municipal Health Service, Division of Public Health and Environment, Nieuwe Achtergracht 100, 1018 WT, Amsterdam, The Netherlands.
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Le Pen C, Rozenbaum W, Downs A, Maurel F, Lilliu H, Brun C. Effect of HAART on health status and hospital costs of severe HIV-infected patients: a modeling approach. HIV CLINICAL TRIALS 2001; 2:136-45. [PMID: 11590522 DOI: 10.1310/c9r1-fy6t-taf0-vqvy] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
PURPOSE The purpose of this study was to assess the impact of highly active antiretroviral therapy (HAART) on health status and hospital costs in severe HIV-infected patients who were followed in a French hospital. METHOD The first 500 patients who received HAART, with CD4 + cell count below 250/mm(3), were considered. Evolution of the distribution of patients among different health states, including death, was modeled through a continuous time Markov model. Hospital financial charges and antiretroviral treatment costs were computed. Health states defined by both CD4 counts and viral load were used to show clinical changes in the patient population over a 14-month period after HAART initiation. The economic impact of HAART initiation was assessed using a simplified model based on CD4 counts only over two 14-month periods, before and after initiation. RESULTS Between day 0 and month 14, the proportion of patients in the least severe state (CD4 + >100/mm(3) and viral load<500 copies/mL) increased from 1% to 50%, and the proportion with more than 100 CD4 + cells/mm(3) increased from 17% to 80%. Antiretroviral treatments amounted to Fr 2,141 per patient-month before HAART initiation and to Fr 3,093 after. Conversely, hospital charges fell from Fr 5,138 per patient-month to Fr 3,136. CONCLUSION Our model gives a representation of the effect of HAART on (1) the improvement of patients' health status, (2) the increase of treatment costs, and (3) the reduction of hospital financial charge. Important savings in hospital charges can compensate for the extra cost associated with the initiation of HAART.
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Affiliation(s)
- C Le Pen
- Laboratoire d'Economie et de Gestion des Organisations de Santé, Dauphine University, Paris, France
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Downs AM, Heisterkamp SH, Ravà L, Houweling H, Jager JC, Hamers FF. Back-calculation by birth cohort, incorporating age- specific disease progression, pre-AIDS mortality and change in European AIDS case definition. European Union Concerted Action on Multinational AIDS Scenarios. AIDS 2000; 14:2179-89. [PMID: 11061660 DOI: 10.1097/00002030-200009290-00015] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
OBJECTIVES To adapt and improve methodology for back-calculation of AIDS in Europe and to examine the feasibility of estimating past HIV incidence by birth cohort. METHODS Empirical Bayesian back-calculation (EBBC) used Markov disease progression models, modified to allow for three diseases added to the AIDS case definition in 1993 and for pre-AIDS mortality, and estimation by penalized maximum likelihood with a neighbour prior. EBBC by 5-year birth cohort assumed a minimum age at infection and age-dependent progression rates; three versions, with varying age effects, were investigated using AIDS cases diagnosed prior to the introduction of highly active antiretroviral therapies (HAART). RESULTS Compared with the no age-effect version, EBBC by birth cohort tended to produce flattened HIV incidence curves in country-exposure groups with < 1000 AIDS cases, reflecting effects of the neighbour prior when data become sparse. Otherwise, birth cohort analysis, with moderate effects of age on progression, gave initially increasing incidence curves and consistent patterns across countries, with the 1960-1964 cohort most affected. In the European Union, incidence is estimated to have peaked in 1983 among homosexual men and in 1988 among injecting drug users; 460000 persons were estimated to be living with HIV/AIDS at the end of 1995. CONCLUSIONS Our improved methodology deals effectively with the change in AIDS case definition and has allowed quantitative assessments of the HIV epidemic by birth cohort using all AIDS cases diagnosed before 1996, thus providing a sound basis for public health policy at a time when estimation of more recent prevalence is compromised by the effects of HAART.
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Affiliation(s)
- A M Downs
- European Centre for the Epidemiological Monitoring of AIDS, Institute de Veille Sanitaire, Saint-Maurice, France
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Guihenneuc-Jouyaux C, Richardson S, Longini IM. Modeling markers of disease progression by a hidden Markov process: application to characterizing CD4 cell decline. Biometrics 2000; 56:733-41. [PMID: 10985209 DOI: 10.1111/j.0006-341x.2000.00733.x] [Citation(s) in RCA: 53] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Multistate models have been increasingly used to model natural history of many diseases as well as to characterize the follow-up of patients under varied clinical protocols. This modeling allows describing disease evolution, estimating the transition rates, and evaluating the therapy effects on progression. In many cases, the staging is defined on the basis of a discretization of the values of continuous markers (CD4 cell count for HIV application) that are subject to great variability due mainly to short time-scale noise (intraindividual variability) and measurement errors. This led us to formulate a Bayesian hierarchical model where, at a first level, a disease process (Markov model on the true states, which are unobserved) is introduced and, at a second level, the measurement process making the link between the true states and the observed marker values is modeled. This hierarchical formulation allows joint estimation of the parameters of both processes. Estimation of the quantities of interest is performed via stochastic algorithms of the family of Markov chain Monte Carlo methods. The flexibility of this approach is illustrated by analyzing the CD4 data on HIV patients of the Concorde clinical trial.
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Geskus RB. On the inclusion of prevalent cases in HIV/AIDS natural history studies through a marker-based estimate of time since seroconversion. Stat Med 2000; 19:1753-69. [PMID: 10861776 DOI: 10.1002/1097-0258(20000715)19:13<1753::aid-sim487>3.0.co;2-f] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
In most cohort studies of HIV infection and AIDS, seroprevalent cases provide a substantial amount of information. Inclusion of these people in natural history studies requires a fairly unbiased method to estimate their seroconversion distribution. When a cohort-based estimate is not feasible, an alternative is to estimate individual seroconversion distributions, based on marker values at entry. In this paper, a non-parametric marker-based estimation method is developed. The method is applied to data from the Amsterdam cohort study on homosexual men. For seroprevalent cases who entered the study between October 1984 and April 1985, individual seroconversion distributions are estimated based on their first measured CD4 count. In subsequent survival analyses, dates of seroconversion are estimated via conditional mean imputation. Inclusion of these seroprevalent cases greatly improves the quality of the data. Age at seroconversion is a significant cofactor for disease progression, a result not found when analysis is restricted to those who seroconvert. To incorporate the uncertainty in the imputed date of seroconversion, a bootstrap procedure is developed for the computation of p-values and confidence intervals. In our analyses, standard procedures, which ignore the uncertainty in the imputed date of seroconversion, perform almost as well.
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Affiliation(s)
- R B Geskus
- Municipal Health Service, Division of Public Health and Environment, Nieuwe Achtergracht 100, 1018 WT Amsterdam, The Netherlands.
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Abstract
An original approach to simulation modeling of the HIV/AIDS epidemic is proposed. This approach uses survivor functions estimated from cohort studies conducted with seropositive and AIDS-diagnosed individuals. The model can be considered an alternative to the usual Markov models and accounts for time-dependent HIV progression to AIDS, and AIDS progression to death. By using various forms of survivor functions, it can also easily be extended to accommodate natural history events, as well as long-term survivors and cofactor effects, when appropriate data are available.
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Affiliation(s)
- G Schinaia
- Dipartimento di Studi Geoeconomici, Statistici, Storici per l'Analisi Regionale, Università di Roma La Sapienza, Rome, Italy.
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Houweling H, Heisterkamp SH, Wiessing LG, Coutinho RA, van Wijngaarden JK, Jager HJ. Methods for estimating HIV prevalence: A comparison of extrapolation from surveys on infection rate and risk behaviour with back-calculation for the Netherlands. Eur J Epidemiol 1998; 14:645-52. [PMID: 9849824 DOI: 10.1023/a:1007495607520] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
OBJECTIVES To compare HIV prevalence estimates (total number infected) by using extrapolation from surveys on infection rate and risk behaviour (EIR) in specific segments of the population and back-calculation (BC) on reported AIDS cases. To discuss potential sources of bias and error, and to identify areas for improvement of the methodology. DESIGN Systematic comparison and epidemiological assessment of data input, underlying assumptions, and output. METHODS Low, possibly unbiased and high estimates of HIV prevalence as of January 1996 for homo/bisexual men, injecting drug users. heterosexual men and women with multiple partners, and blood transfusion recipients and haemophiliacs were derived from surveys and continuous data collections on HIV infection rate and risk behaviour in the Netherlands between 1992 and 1996. These were compared with estimates (point and 95 % CI) by empirical Bayesian BC on AIDS cases 1982-1995. RESULTS AND CONCLUSIONS The estimate of HIV prevalence by EIR was 13,806 with low and high estimates of 9619 and 17,700, respectively. The HIV prevalence estimate by BC was 8812 (95% CI: 7759-9867). The available data from EIR are too limited for accurate estimates of HIV prevalence. EIR estimates could be improved considerably with more precise data on prevalence of risk behaviours and HIV prevalence rate for homosexual men. More confidence can be put in the BC estimates, but these could be underestimates because of the age effect on incubation time, pre-AIDS treatment and relapse of risk behaviour. BC estimates could be improved by a better representation of the incubation time distribution (including the effect of age there-upon), better data on the effectiveness and uptake of pre-AIDS antiretroviral treatment and prophylaxis of opportunistic infections, and on the level of underreporting.
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Affiliation(s)
- H Houweling
- Department of Infectious Diseases Epidemiology, National Institute of Public Health and the Environment (RIVM), Bilthoven, The Netherlands.
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Hendriks JC, Satten GA, van Ameijden EJ, van Druten HA, Coutinho RA, van Griensven GJ. The incubation period to AIDS in injecting drug users estimated from prevalent cohort data, accounting for death prior to an AIDS diagnosis. AIDS 1998; 12:1537-44. [PMID: 9727576 DOI: 10.1097/00002030-199812000-00017] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
OBJECTIVE To estimate the incubation-period distribution (time from seroconversion to AIDS) accounting for death before an AIDS diagnosis (DBAD) in a cohort of injecting drug users (IDU) in Amsterdam, The Netherlands and to compare these estimates with those previously obtained from a contemporaneous study of homosexual and bisexual men in Amsterdam carried out using the same facilities. DESIGN Participants in a cohort study begun in Amsterdam at the end of 1985 have scheduled follow-up visits every 4 months. All participants of Dutch nationality and who had two or more follow-up visits before January 1996 from which CD4 measurements were available were included in this study. Data concerning AIDS diagnosis and death were verified through review of national and municipal registries. METHODS Because time of seroconversion was unknown for study participants and because IDU are at substantial risk for DBAD, we used a Markov model with CD4-based stages that allows for DBAD. The parameters in this model were estimated using the method of maximum likelihood and confidence intervals were calculated using bootstrap methods. RESULTS A total of 173 IDU (134 seroprevalent, 39 seroincident) made 1829 visits. Nearly 10% of the visits were non-consecutive. Forty-five IDU developed AIDS and 25 died without an AIDS diagnosis. We estimated that 24% [95% confidence interval (CI), 17-25%] of IDU die before an AIDS diagnosis. As a result, the median time from seroconversion to AIDS (10.5 years; 95% CI, 9.1-10.7 years) is considerably longer than the median time from seroconversion to death (8.3 years; 95% CI, 7.9-8.5 years). Conditional on survival to an AIDS diagnosis, the median time to AIDS is 8.2 years (95% CI, 7.7-8.7 years). The median survival time after a diagnosis of AIDS is estimated to be 1.0 years. CONCLUSION The high occurrence of DBAD in IDU has a considerable influence on estimates of the incubation-period distribution. Progression from seroconversion to death was faster in the IDU cohort than in a cohort of homosexual men in Amsterdam (median, 8.3 years and 9.6 years, respectively). However, progression to AIDS conditional on survival to an AIDS diagnosis seems to be similar in both the IDU cohort and in the cohort of homosexual men (median, 8.2 years and 8.3 years, respectively).
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Affiliation(s)
- J C Hendriks
- Department of Public Health, Municipal Health Service, Amsterdam, The Netherlands
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Morgan D, Maude GH, Malamba SS, Okongo MJ, Wagner HU, Mulder DW, Whitworth JA. HIV-1 disease progression and AIDS-defining disorders in rural Uganda. Lancet 1997; 350:245-50. [PMID: 9242801 DOI: 10.1016/s0140-6736(97)01474-8] [Citation(s) in RCA: 86] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
BACKGROUND The majority of people infected with HIV-1 live in Africa, yet little is known about the natural history of the disease in that continent. We studied survival times, disease progression, and AIDS-defining disorders, according to the proposed WHO staging system, in a population-based, rural cohort in Uganda. METHODS In 1990 we recruited a random sample of people already infected with HIV-1 (as prevalent cases) detected during the initial survey round of a general-population study to form a natural-history cohort. Individuals from the general-population cohort who seroconverted between 1990 and 1995 (incident cases) were also invited to enroll. Participants were seen routinely every 3 months and when they were III. FINDINGS By the end of 1995, 93 prevalent cases and 86 incident cases had been enrolled. Four patients in the prevalent group were in stage 4 (AIDS) at the initial visit. During the next 5 years, 37 prevalent cases progressed to AIDS. Seven incident cases progressed to AIDS and the cumulative progression to AIDS at 1, 3, and 5 years after seroconversion was 2%, 6%, and 22%, respectively. The cumulative probability of AIDS at 4 years from entering stages 1, 2, and 3 was 11%, 33%, and 58%, respectively. There were 47 deaths among prevalent cases and seven among incident cases during follow-up. The cumulative mortality 4 years after patients entered stages 1, 2, 3, and 4 was 9%, 33%, 56%, and 86%, respectively. The median survival after the onset of AIDS was 9.3 months. INTERPRETATION Our results are important for the setting of priorities and rationalisation of treatment availability in countries with poor resources. We found that progression rates to AIDS are similar to those in developed countries for homosexual cohorts and greater than for cohorts infected by other modes of transmission. However, we have found that the rates of all-cause mortality are much higher and the progression times to death are shorter than in developed countries.
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Affiliation(s)
- D Morgan
- Medical Research Council Programme on AIDS, Uganda Virus Research Institute, Entebbe, Uganda
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