Bayesian back-calculation using a multi-state model with application to HIV

HIV disease progression among heterosexually-infected individuals before the introduction of universal ART in China: A linear mixed-effects model

In 2016, China introduced universal antiretroviral therapy (ART) for all HIV-infected individuals regardless of CD4 cell count. However, the natural history and rate of CD4 count decline among heterosexually-infected individuals remain uncharacterized. Analyzing national surveillance data can address this gap and shed light on the pathogenesis of HIV in this population. We used a linear mixed-effects model to assess CD4 trajectory over time before ART initiation and estimated the median time from HIV seroconversion to reaching CD4 thresholds of < 500, < 350, and < 200 cell/mm3. From the Chinese HIV/AIDS Comprehensive Response Information Management System, 59,085 eligible individuals were identified, with 113 having data to estimate the date of HIV seroconversion. The linear mixed-effects models estimated an intercept of 23.64 (95% confidence interval [CI]: 22.41 to 24.87) and a slope of -1.32 (95% CI: -1.34 to -1.30) for males, and an intercept of 22.70 (95% CI: 21.00 to 24.40) and a slope of -1.29 (95% CI: -1.31 to -1.27) for females. The estimated median times from HIV seroconversion to reaching CD4 count thresholds of < 500, < 350, < 200 cells/mm3 were 0.97, 3.74, and 7.20 years for males, and 0.26, 3.09, and 6.48 years for females, respectively. Males consistently took longer to reach these CD4 count thresholds compared to females of the same age group. Older individuals (≥ 40 years) reached CD4 thresholds faster than younger individuals (15-29 years), indicating more rapid disease progression in older people living with HIV.

A Tale of Three Recent Pandemics: Influenza, HIV and SARS-CoV-2

Emerging infectious diseases are one of the main threats to public health, with the potential to cause a pandemic when the infectious agent manages to spread globally. The first major pandemic to appear in the 20th century was the influenza pandemic of 1918, caused by the influenza A H1N1 strain that is characterized by a high fatality rate. Another major pandemic was caused by the human immunodeficiency virus (HIV), that started early in the 20th century and remained undetected until 1981. The ongoing HIV pandemic demonstrated a high mortality and morbidity rate, with discrepant impacts in different regions around the globe. The most recent major pandemic event, is the ongoing pandemic of COVID-19, caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which has caused over 5.7 million deaths since its emergence, 2 years ago. The aim of this work is to highlight the main determinants of the emergence, epidemic response and available countermeasures of these three pandemics, as we argue that such knowledge is paramount to prepare for the next pandemic. We analyse these pandemics’ historical and epidemiological contexts and the determinants of their emergence. Furthermore, we compare pharmaceutical and non-pharmaceutical interventions that have been used to slow down these three pandemics and zoom in on the technological advances that were made in the progress. Finally, we discuss the evolution of epidemiological modelling, that has become an essential tool to support public health policy making and discuss it in the context of these three pandemics. While these pandemics are caused by distinct viruses, that ignited in different time periods and in different regions of the globe, our work shows that many of the determinants of their emergence and countermeasures used to halt transmission were common. Therefore, it is important to further improve and optimize such approaches and adapt it to future threatening emerging infectious diseases.

A Markov based model to estimate the number of syphilis cases among floating population

Syphilis is a sexually transmitted disease that spreads widely around the world, infecting tens of millions of people every year. In China, syphilis not only causes more than 1 million infections every year, but also has its own characteristics in spreading pattern: this disease always spreads with the migration of floating population. There have been many related investigations and studies on the transmission of syphilis with the floating population in China, but the study of quantitative modeling in this field is very limited. In this paper, based on the Markov process model and datasets collected in Zhejiang Province, China, we construct a new model to analyze the transmission and immigration process of syphilis. The results show that immigrant patients are one of the sources of infection of syphilis in Zhejiang province, and the infection rate is remarkable which should not be ignored. By using the PRCC method to analyze the relationship between parameters and infected cases, we also find two main effective measures that can control the spread of syphilis and reduce the infection rate: the self-attention of infected persons, and the use of sexual protection measures. With the increasing frequent exchanges of people among different countries and regions, studying the transmission of diseases with the floating populations has become more and more important. The method we use in this paper gives a new insight studying this issue, providing a quantitative research method using the data of diagnosed cases. All the methods and models in this paper can be extendly used in the studies of other diseases where immigrant patients should be considered.

A multi-state Markov model using notification data to estimate HIV incidence, number of undiagnosed individuals living with HIV, and delay between infection and diagnosis: Illustration in France, 2008-2018

Thirty-five years since the discovery of the human immunodeficiency virus (HIV), the epidemic is still ongoing in France. To guide HIV prevention strategies and monitor their impact, it is essential to understand the dynamics of the HIV epidemic. The indicator for reporting the progress of new infections is the HIV incidence. Given that HIV is mainly transmitted by undiagnosed individuals and that earlier treatment leads to less HIV transmission, it is essential to know the number of infected people unaware of their HIV-positive status as well as the time between infection and diagnosis. Our approach is based on a non-homogeneous multi-state Markov model describing the progression of the HIV disease. We propose a penalized likelihood approach to estimate the HIV incidence curve as well as the diagnosis rates. The HIV incidence curve was approximated using cubic M-splines, while an approximation of the cross-validation criterion was used to estimate the smoothing parameter. In a simulation study, we evaluate the performance of the model for reconstructing the HIV incidence curve and diagnosis rates. The method is illustrated in the population of men who have sex with men using HIV surveillance data collected by the French Institute for Public Health Surveillance since 2004.

Tracking elimination of HIV transmission in men who have sex with men in England: a modelling study

BACKGROUND

To manage the HIV epidemic among men who have sex with men (MSM) in England, treatment as prevention strategies based on test and treat were strengthened between 2011 and 2015, and supplemented from 2015 by scale-up of pre-exposure prophylaxis (PrEP). We examined the effect of these interventions on HIV incidence and investigated whether internationally agreed targets for HIV control and elimination of HIV transmission by 2030 might be within reach among MSM in England.

METHODS

We used a novel, age-stratified, CD4-staged Bayesian back-calculation model to estimate HIV incidence and undiagnosed infections among adult MSM (age ≥15 years) during the 10-year period between 2009 and 2018. The model used data on HIV and AIDS diagnoses routinely collected via the national HIV and AIDS Reporting System in England, and knowledge on the progression of HIV through CD4-defined disease stages. Estimated incidence trends were extrapolated, assuming a constant MSM population from 2018 onwards, to quantify the likelihood of achieving elimination of HIV transmission, defined as less than one newly aquired infection per 10 000 MSM per year, by 2030.

FINDINGS

The peak in HIV incidence in MSM in England was estimated with 80% certainty to have occurred in 2012 or 2013, at least 1 year before the observed peak in new diagnoses in 2014. Results indicated a steep decrease in the annual number of new infections among MSM, from 2770 (95% credible interval 2490-3040) in 2013 to 1740 (1500-2010) in 2015, followed by a steadier decrease from 2016, down to 854 (441-1540) infections in 2018. A decline in new infections was consistently estimated in all age groups, and was particularly marked in MSM aged 25-34 years, and slowest in those aged 45 years or older. Similar trends were estimated in the number of undiagnosed infections, with the greatest decrease after 2013 in the 25-34 years age group. Under extrapolation assumptions, we calculated a 40% probability of achieving the defined target elimination threshold by 2030.

INTERPRETATION

The sharp decrease in HIV incidence, estimated to have begun before the scale up of PrEP, indicates the success of strengthening treatment as prevention measures among MSM in England. To achieve the 2030 elimination threshold, targeted policies might be required to reach those aged 45 years or older, in whom incidence is decreasing at the slowest rate.

FUNDING

UK Medical Research Council, UK National Institute of Health Research Health Protection Unit in Behavioural Science and Evaluation, and Public Health England.

Spatial modeling of individual-level infectious disease transmission: Tuberculosis data in Manitoba, Canada

Geographically dependent individual level models (GD-ILMs) are a class of statistical models that can be used to study the spread of infectious disease through a population in discrete-time in which covariates can be measured both at individual and area levels. The typical ILMs to illustrate spatial data are based on the distance between susceptible and infectious individuals. A key feature of GD-ILMs is that they take into account the spatial location of the individuals in addition to the distance between susceptible and infectious individuals. As a motivation of this article, we consider tuberculosis (TB) data which is an infectious disease which can be transmitted through individuals. It is also known that certain areas/demographics/communities have higher prevalent of TB (see Section 4 for more details). It is also of interest of policy makers to identify those areas with higher infectivity rate of TB for possible preventions. Therefore, we need to analyze this data properly to address those concerns. In this article, the expectation conditional maximization algorithm is proposed for estimating the parameters of GD-ILMs to be able to predict the areas with the highest average infectivity rates of TB. We also evaluate the performance of our proposed approach through some simulations. Our simulation results indicate that the proposed method provides reliable estimates of parameters which confirms accuracy of the infectivity rates.

Estimating the First 90 of the UNAIDS 90-90-90 Goal: A Review

Estimating the population with undiagnosed HIV (PUHIV) is the most methodologically challenging aspect of evaluating 90-90-90 goals. The objective of this review is to discuss assumptions, strengths, and shortcomings of currently available methods of this estimation. Articles from 2000 to 2018 on methods to estimate PUHIV were reviewed. Back-calculation methods including CD4 depletion and test-retest use diagnosis CD4 count, or previous testing history to determine likely infection time thus, providing an estimate of PUHIV for previous years. Biomarker methods use immunoassays to differentiate recent from older infections. Statistical techniques treat HIV status as missing data and impute data for models of infection. Lastly, population surveys using HIV rapid testing most accurately calculates the current HIV prevalence. Although multiple methods exist to estimate the number of PUHIV, the appropriate method for future applications depends on multiple factors, namely data availability and population of interest.

Extending Bayesian back-calculation to estimate age and time specific HIV incidence

CD4-based multi-state back-calculation methods are key for monitoring the HIV epidemic, providing estimates of HIV incidence and diagnosis rates by disentangling their inter-related contribution to the observed surveillance data. This paper, extends existing approaches to age-specific settings, permitting the joint estimation of age- and time-specific incidence and diagnosis rates and the derivation of other epidemiological quantities of interest. This allows the identification of specific age-groups at higher risk of infection, which is crucial in directing public health interventions. We investigate, through simulation studies, the suitability of various bivariate splines for the non-parametric modelling of the latent age- and time-specific incidence and illustrate our method on routinely collected data from the HIV epidemic among gay and bisexual men in England and Wales.

Estimating the number of people living with HIV and the undiagnosed fraction in Spain in 2013

OBJECTIVE

We aim to estimate the number of people living with HIV and the undiagnosed fraction in Spain, where coverage of the HIV surveillance system has only recently become complete.

METHODS

The reconstruction of all HIV diagnoses and infections was obtained by combining HIV and AIDS surveillance data. The imputation of the diagnoses and back-calculation of the infection incidence are integrated in a Bayesian framework to take into account the uncertainty associated with unavailable data.

RESULTS

An estimated 141 000 [95% credible interval (CI) 128 000-155 000] persons were living with HIV by the end of 2013, in Spain and 18% (95% CI 14.3-22.1%) were unaware of it. A similar fraction of undiagnosed infections was obtained in men who have sex with men and heterosexuals (18.8 and 20.1%, respectively), but for injection drug users, this fraction was 3.5%.

CONCLUSION

This study provides the first estimates of the number of people living with HIV and the undiagnosed fraction in Spain, using routine surveillance data. The proposed method could be useful for countries where the geographical coverage of the HIV surveillance system is partial or was completed only recently.

Estimation of delay to diagnosis and incidence in HIV using indirect evidence of infection dates

BACKGROUND

Minimisation of the delay to diagnosis is critical to achieving optimal outcomes for HIV patients and to limiting the potential for further onward infections. However, investigation of diagnosis delay is hampered by the fact that in most newly diagnosed patients the exact timing of infection cannot be determined and so inferences must be drawn from biomarker data.

METHODS

We develop a Bayesian statistical model to evaluate delay-to-diagnosis distributions in HIV patients without known infection date, based on viral sequence genetic diversity and longitudinal viral load and CD4 count data. The delay to diagnosis is treated as a random variable for each patient and their biomarker data are modelled relative to the true time elapsed since infection, with this dependence used to obtain a posterior distribution for the delay to diagnosis. Data from a national seroconverter cohort with infection date known to within ± 6 months, linked to a database of viral sequences, are used to calibrate the model parameters. An exponential survival model is implemented that allows general inferences regarding diagnosis delay and pooling of information across groups of patients. If diagnoses are only observed within a given window period, then it is necessary to also model incidence as a function of time; we suggest a pragmatic approach to this problem when dealing with data from an established epidemic. The model developed is used to investigate delay-to-diagnosis distributions in men who have sex with men diagnosed with HIV in London in the period 2009-2013 with unknown date of infection.

RESULTS

Cross-validation and simulation analyses indicate that the models developed provide more accurate information regarding the timing of infection than does CD4 count-based estimation. Delay-to-diagnosis distributions were estimated in the London cohort, and substantial differences were observed according to ethnicity.

CONCLUSION

The combination of all available biomarker data with pooled estimation of the distribution of diagnosis-delays allows for more precise prediction of the true timing of infection in individual patients, and the models developed also provide useful population-level information.

Determining the likely place of HIV acquisition for migrants in Europe combining subject-specific information and biomarkers data

In most HIV-positive individuals, infection time is only known to lie between the time an individual started being at risk for HIV and diagnosis time. However, a more accurate estimate of infection time is very important in certain cases. For example, one of the objectives of the Advancing Migrant Access to Health Services in Europe (aMASE) study was to determine if HIV-positive migrants, diagnosed in Europe, were infected pre- or post-migration. We propose a method to derive subject-specific estimates of unknown infection times using information from HIV biomarkers' measurements, demographic, clinical, and behavioral data. We assume that CD4 cell count (CD4) and HIV-RNA viral load trends after HIV infection follow a bivariate linear mixed model. Using post-diagnosis CD4 and viral load measurements and applying the Bayes' rule, we derived the posterior distribution of the HIV infection time, whereas the prior distribution was informed by AIDS status at diagnosis and behavioral data. Parameters of the CD4-viral load and time-to-AIDS models were estimated using data from a large study of individuals with known HIV infection times (CASCADE). Simulations showed substantial predictive ability (e.g. 84% of the infections were correctly classified as pre- or post-migration). Application to the aMASE study (n = 2009) showed that 47% of African migrants and 67% to 72% of migrants from other regions were most likely infected post-migration. Applying a Bayesian method based on bivariate modeling of CD4 and viral load, and subject-specific information, we found that the majority of HIV-positive migrants in aMASE were most likely infected after their migration to Europe.

High percentage of undiagnosed HIV cases within a hyperendemic South African community: a population-based study

BACKGROUND

Undiagnosed HIV infections could undermine efforts to reverse the global AIDS epidemic by 2030. In this study, we estimated the percentage of HIV-positive persons who remain undiagnosed within a hyperendemic South African community.

METHODS

The data come from a population-based surveillance system located in the Umkhanyakude district of the northern KwaZulu-Natal province, South Africa. We annually tested 38 661 adults for HIV between 2005 and 2016. Using the HIV-positive test results of 12 039 (31%) participants, we then back-calculated the incidence of infection and derived the number of undiagnosed cases from this result.

RESULTS

The percentage of undiagnosed HIV cases decreased from 29.3% in 2005 to 15.8% in 2011. During this period, however, approximately 50% of the participants refused to test for HIV, which lengthened the average time from infection to diagnosis. Consequently, the percentage of undiagnosed HIV cases reversed direction and steadily increased from 16.1% to 18.9% over the 2012-2016 period.

CONCLUSIONS

Results from this hyperendemic South African setting show that the HIV testing rate is low, with long infection times, and an unsatisfactorily high percentage of undiagnosed cases. A high level of repeat HIV testing is needed to minimise the time from infection to diagnosis if the global AIDS epidemic is to be reversed within the next two decades.

Using CD4 Data to Estimate HIV Incidence, Prevalence, and Percent of Undiagnosed Infections in the United States

INTRODUCTION

The incidence and prevalence of HIV infection are important measures of HIV trends; however, they are difficult to estimate because of the long incubation period between infection and symptom development and the relative infrequency of HIV screening. A new method is introduced to estimate HIV incidence, prevalence, and the number of undiagnosed infections in the United States using data from the HIV case surveillance system and CD4 test results.

METHODS

Persons with HIV diagnosed during 2006-2013 and their CD4 test results were used to estimate the distribution of diagnosis delay from HIV infection to diagnosis based on a well-characterized CD4 depletion model. This distribution was then used to estimate HIV incidence, prevalence, and the number of undiagnosed infections.

RESULTS

Applying this method, we estimated that the annual number of new HIV infections decreased after 2007, from 48,300 (95% confidence interval [CI]: 47,300 to 49,400) to 39,000 (95% CI: 36,600 to 41,400) in 2013. Prevalence increased from 923,200 (95% CI: 914,500 to 931,800) in 2006 to 1,104,600 (95% CI: 1,084,300 to 1,124,900) in 2013, whereas the proportion of undiagnosed infections decreased from 21.0% in 2006 (95% CI: 20.2% to 21.7%) to 16.4% (95% CI: 15.7% to 17.2%) in 2013.

CONCLUSIONS

HIV incidence, prevalence, and undiagnosed infections can be estimated using HIV case surveillance data and information on first CD4 test result after diagnosis. Similar to earlier findings, the decreases in incidence and undiagnosed infections are encouraging but intensified efforts for HIV testing and treatment are needed to meet the goals of the National HIV/AIDS Strategy.

Immunological function of Langerhans cells in HIV infection

BACKGROUND

Langerhans cells (LCs) are one of the initial target cells for HIV following sexual exposure and they are productively infected by HIV. HIV-infected LCs migrate to the draining lymph nodes (dLNs) and transmit the virus to CD4⁺ T cells, leading to the dissemination of HIV. In contrast with the role of LCs in initial HIV acquisition, little is known about the modulation of immune responses by HIV-infected LCs.

OBJECTIVE

We aimed to elucidate the induction of HIV-specific CD8⁺ T cells and regulatory T cells (Tregs), both of which play important roles in regulating the progression of HIV infection.

METHODS

We examined the inducibility of HLA-A*0201 restricted HIV-specific CD8⁺ T cells and Tregs by HIV-primed LCs or HIV-primed dendritic cells (DCs) as a control.

RESULTS

The number of HIV-specific CD8⁺ T cells induced by HIV-primed monocyte-derived LCs (mLCs) was significantly higher than that by HIV-primed monocyte-derived DCs (mDCs). Additionally, HIV-specific CD8⁺ T cells induced by HIV-primed mLCs produced more IFN-γ than HIV-nonspecific CD8⁺ T cells. HIV-primed human epidermal LCs also induced IFN-γ-producing HIV-specific CD8⁺ T cells. As for the induction of Tregs, HIV-primed mLCs and human epidermal LCs significantly impaired the induction of FoxP3^hiCD45RA^- effector Tregs than HIV-unprimed mLCs and human epidermal LCs.

CONCLUSIONS

HIV-primed LCs trigger beneficial immune responses against HIV infection through the increased induction of HIV-specific CD8⁺ T cells and the decreased induction of effector Tregs in the initial phase of HIV infection, thereby contributing to the prolonged onset of AIDS.

Testing the hypothesis that treatment can eliminate HIV: a nationwide, population-based study of the Danish HIV epidemic in men who have sex with men

BACKGROUND

Worldwide, approximately 35 million individuals are infected with HIV; about 25 million of these live in sub-Saharan Africa. WHO proposes using treatment as prevention (TasP) to eliminate HIV. Treatment suppresses viral load, decreasing the probability an individual transmits HIV. The elimination threshold is one new HIV infection per 1000 individuals. Here, we test the hypothesis that TasP can substantially reduce epidemics and eliminate HIV. We estimate the impact of TasP, between 1996 and 2013, on the Danish HIV epidemic in men who have sex with men (MSM), an epidemic UNAIDS has identified as a priority for elimination.

METHODS

We use a CD4-staged Bayesian back-calculation approach to estimate incidence, and the hidden epidemic (the number of HIV-infected undiagnosed MSM). To develop the back-calculation model, we use data from an ongoing nationwide population-based study: the Danish HIV Cohort Study.

FINDINGS

Incidence, and the hidden epidemic, decreased substantially after treatment was introduced in 1996. By 2013, incidence was close to the elimination threshold: 1·4 (median, 95% Bayesian credible interval [BCI] 0·4-2·1) new HIV infections per 1000 MSM and there were only 617 (264-858) undiagnosed MSM. Decreasing incidence and increasing treatment coverage were highly correlated; a treatment threshold effect was apparent.

INTERPRETATION

Our study is the first to show that TasP can substantially reduce a country's HIV epidemic, and bring it close to elimination. However, we have shown the effectiveness of TasP under optimal conditions: very high treatment coverage, and exceptionally high (98%) viral suppression rate. Unless these extremely challenging conditions can be met in sub-Saharan Africa, the WHO's global elimination strategy is unlikely to succeed.

FUNDING

National Institute of Allergy and Infectious Diseases.

Estimating HIV Incidence, Time to Diagnosis, and the Undiagnosed HIV Epidemic Using Routine Surveillance Data

BACKGROUND

Estimates of the size of the undiagnosed HIV-infected population are important to understand the HIV epidemic and to plan interventions, including "test-and-treat" strategies.

METHODS

We developed a multi-state back-calculation model to estimate HIV incidence, time between infection and diagnosis, and the undiagnosed population by CD4 count strata, using surveillance data on new HIV and AIDS diagnoses. The HIV incidence curve was modelled using cubic splines. The model was tested on simulated data and applied to surveillance data on men who have sex with men in The Netherlands.

RESULTS

The number of HIV infections could be estimated accurately using simulated data, with most values within the 95% confidence intervals of model predictions. When applying the model to Dutch surveillance data, 15,400 (95% confidence interval [CI] = 15,000, 16,000) men who have sex with men were estimated to have been infected between 1980 and 2011. HIV incidence showed a bimodal distribution, with peaks around 1985 and 2005 and a decline in recent years. Mean time to diagnosis was 6.1 (95% CI = 5.8, 6.4) years between 1984 and 1995 and decreased to 2.6 (2.3, 3.0) years in 2011. By the end of 2011, 11,500 (11,000, 12,000) men who have sex with men in The Netherlands were estimated to be living with HIV, of whom 1,750 (1,450, 2,200) were still undiagnosed. Of the undiagnosed men who have sex with men, 29% (22, 37) were infected for less than 1 year, and 16% (13, 20) for more than 5 years.

CONCLUSIONS

This multi-state back-calculation model will be useful to estimate HIV incidence, time to diagnosis, and the undiagnosed HIV epidemic based on routine surveillance data.

A Bayesian hierarchical model with novel prior specifications for estimating HIV testing rates

Human immunodeficiency virus (HIV) infection is a severe infectious disease actively spreading globally, and acquired immunodeficiency syndrome (AIDS) is an advanced stage of HIV infection. The HIV testing rate, that is, the probability that an AIDS-free HIV infected person seeks a test for HIV during a particular time interval, given no previous positive test has been obtained prior to the start of the time, is an important parameter for public health. In this paper, we propose a Bayesian hierarchical model with two levels of hierarchy to estimate the HIV testing rate using annual AIDS and AIDS-free HIV diagnoses data. At level one, we model the latent number of HIV infections for each year using a Poisson distribution with the intensity parameter representing the HIV incidence rate. At level two, the annual numbers of AIDS and AIDS-free HIV diagnosed cases and all undiagnosed cases stratified by the HIV infections at different years are modeled using a multinomial distribution with parameters including the HIV testing rate. We propose a new class of priors for the HIV incidence rate and HIV testing rate taking into account the temporal dependence of these parameters to improve the estimation accuracy. We develop an efficient posterior computation algorithm based on the adaptive rejection metropolis sampling technique. We demonstrate our model using simulation studies and the analysis of the national HIV surveillance data in the USA.

Inferring HIV incidence from case surveillance with CD4+ cell counts

BACKGROUND

In some countries, HIV surveillance is based on case-reporting of newly diagnosed infections. We present a new back-projection method for estimating HIV-incidence trends using individuals' CD4 cell counts at diagnosis.

METHODS

On the basis of a review of CD4 cell count distributions among HIV-uninfected people, CD4 cell count following primary infection, and rates of CD4 cell count decline over time among people with HIV, we simulate the expected distribution in time between infection and diagnosis. Applying this to all diagnosed individuals provides a distribution of likely infection times and estimates for population incidence, level of undiagnosed HIV, and the average time from infection to diagnosis each year. We applied this method to the national HIV case surveillance data of Australia for 1983-2013.

RESULTS

The estimated number of new HIV infections in Australia in 2013 was 912 (95% uncertainty bound 835-1002). We estimate that 2280 (95% uncertainty bound 1900-2830) people were living with undiagnosed HIV at the end of 2013, corresponding to approximately 9.4% (95% uncertainty bound 7.8-10.1%) of all people living with HIV. With increases in the average CD4 count at diagnosis, the inferred HIV testing rate has been increasing over time and the estimated mean and median times between infection and diagnosis have decreased substantially. However, the estimated mean time between infection and diagnosis is considerably greater than the median, indicating that some people remain undiagnosed for long periods. Differences were found between cases attributable to male homosexual exposure versus other cases.

CONCLUSION

This methodology provides a novel way of estimating population incidence by combining diagnosis dates and CD4 cell counts at diagnosis.

Use of surveillance data on HIV diagnoses with HIV-related symptoms to estimate the number of people living with undiagnosed HIV in need of antiretroviral therapy

Background

It is important to have methods available to estimate the number of people who have undiagnosed HIV and are in need of antiretroviral therapy (ART).

Methods

The method uses the concept that a predictable level of occurrence of AIDS or other HIV-related clinical symptoms which lead to presentation for care, and hence diagnosis of HIV, arises in undiagnosed people with a given CD4 count. The method requires surveillance data on numbers of new HIV diagnoses with HIV-related symptoms, and the CD4 count at diagnosis. The CD4 count-specific rate at which HIV-related symptoms develop are estimated from cohort data. 95% confidence intervals can be constructed using a simple simulation method.

Results

For example, if there were 13 HIV diagnoses with HIV-related symptoms made in one year with CD4 count at diagnosis between 150–199 cells/mm³, then since the CD4 count-specific rate of HIV-related symptoms is estimated as 0.216 per person-year, the estimated number of person years lived in people with undiagnosed HIV with CD4 count 150–199 cells/mm3 is 13/0.216 = 60 (95% confidence interval: 29–100), which is considered an estimate of the number of people living with undiagnosed HIV in this CD4 count stratum.

Conclusions

The method is straightforward to implement within a short period once a surveillance system of all new HIV diagnoses, collecting data on HIV-related symptoms at diagnosis, is in place and is most suitable for estimating the number of undiagnosed people with CD4 count <200 cells/mm3 due to the low rate of developing HIV-related symptoms at higher CD4 counts. A potential source of bias is under-diagnosis and under-reporting of diagnoses with HIV-related symptoms. Although this method has limitations as with all approaches, it is important for prompting increased efforts to identify undiagnosed people, particularly those with low CD4 count, and for informing levels of unmet need for ART.

Estimating HIV incidence from case-report data: method and an application in Colombia

Objective:

Quantifying HIV incidence is essential for tracking epidemics but doing this in concentrated epidemic can be a particular challenge because of limited consistent high-quality data about the size, behaviour and prevalence of HIV among key populations. Here, we examine a method for estimating HIV incidence from routinely collected case-reporting data.

Methods:

A flexible model of HIV infection, diagnosis and survival is constructed and fit to time-series data on the number of reported cases in a Bayesian framework. The time trend in the hazard of infection is specified by a penalized B-spline. We examine the performance of the model by applying it to synthetic data and determining whether the method is capable of recovering the input incidence trend. We then apply the method to real data from Colombia and compare our estimates of incidence with those that have been derived using alternative methods.

Results:

The method can feasibly be applied and it successfully recovered a range of incidence trajectories in synthetic data experiments. However, estimates for incidence in the recent past are highly uncertain. When applied to data from Colombia, a credible trajectory of incidence is generated which indicates a much lower historic level of HIV incidence than has previously been estimated using other methods.

Conclusion:

It is feasible, though not satisfactory, to estimate incidence using case-report data in settings with good data availability. Future work should examine the impact on missing or biased data, the utility of alternative formulations of flexible functions specifying incidence trends, and the benefit of also including data on deaths and programme indicators such as the numbers receiving antiretroviral therapy.

Frailties in multi-state models: Are they identifiable? Do we need them?

The inclusion of latent frailties in survival models can serve two purposes: (1) the modelling of dependence in clustered data, (2) explaining lack of fit of univariate survival models, like deviation from the proportional hazards assumption. Multi-state models are somewhere between univariate data and clustered data. Frailty models can help in understanding the dependence in sequential transitions (like in clustered data) and can be useful in explaining some strange phenomena in the effect of covariates in competing risks models (like in univariate data). The (im)possibilities of frailty models will be exemplified on a data set of breast cancer patients with death as absorbing state and local recurrence and distant metastasis as intermediate events.

New method for estimating HIV incidence and time from infection to diagnosis using HIV surveillance data: results for France

OBJECTIVE

To estimate HIV incidence and time between HIV infection and diagnosis of infection.

DESIGN

We devised a new model for estimating the incidence of HIV infection and the time between infection and diagnosis from HIV surveillance data. Our approach takes into account temporal changes in HIV test-seeking behaviors and requires few data on individuals newly diagnosed with HIV (i.e. date of diagnosis and clinical status at diagnosis). Using our new approach, we analyzed data for patients newly diagnosed with HIV in France between April 2003 and December 2008.

RESULTS

The estimated mean time between infection and diagnosis ranged from 37.0 months among men who have sex with men to approximately 53.0 months among heterosexual men. Intermediate values were obtained for injecting drug users and heterosexual women. We estimated that mean times changed very slightly (≤1.2 months) during the period 2004-2007: it shortened among MSM, remained stable among non-French-national heterosexual men, and lengthened in all the other exposure categories. We estimated that the total number of new infections increased, but not significantly, between 2004 and 2007, reaching 7851 [95% confidence interval 5400-9919] in 2007. MSM accounted for the largest number of new infections (38%).

CONCLUSION

HIV continues to spread in France, and the average time between infection and HIV diagnosis remains excessively long. New policies to expand the offer and acceptance of voluntary HIV testing are thus urgently needed. Our method will also be very useful to monitor and evaluate the impact of future HIV testing policies.

HIV in hiding: methods and data requirements for the estimation of the number of people living with undiagnosed HIV

Many people who are HIV positive are unaware of their infection status. Estimation of the number of people with undiagnosed HIV within a country or region is vital for understanding future need for treatment and for motivating testing programs. We review the available estimation approaches which are in current use. They can be broadly classified into those based on prevalence surveys and those based on reported HIV and AIDS cases. Estimation based on prevalence data requires data from regular prevalence surveys in different population groups together with estimates of the size of these groups. The recommended minimal case reporting data needed to estimate the number of patients with undiagnosed HIV are HIV diagnoses, including CD4 count at diagnosis and whether there has been an AIDS diagnosis in the 3 months before or after HIV diagnosis, and data on deaths in people with HIV. We would encourage all countries to implement several methods that will help develop our understanding of strengths and weaknesses of the various methods.

Bayesian evidence synthesis for a transmission dynamic model for HIV among men who have sex with men

Understanding infectious disease dynamics and the effect on prevalence and incidence is crucial for public health policies. Disease incidence and prevalence are typically not observed directly and increasingly are estimated through the synthesis of indirect information from multiple data sources. We demonstrate how an evidence synthesis approach to the estimation of human immunodeficiency virus (HIV) prevalence in England and Wales can be extended to infer the underlying HIV incidence. Diverse time series of data can be used to obtain yearly “snapshots” (with associated uncertainty) of the proportion of the population in 4 compartments: not at risk, susceptible, HIV positive but undiagnosed, and diagnosed HIV positive. A multistate model for the infection and diagnosis processes is then formulated by expressing the changes in these proportions by a system of differential equations. By parameterizing incidence in terms of prevalence and contact rates, HIV transmission is further modeled. Use of additional data or prior information on demographics, risk behavior change and contact parameters allows simultaneous estimation of the transition rates, compartment prevalences, contact rates, and transmission probabilities.

Growth rates in epidemic models: application to a model for HIV/AIDS progression

The most common quantity used to describe the growth of an epidemic when modelling infectious diseases is the basic reproduction number R0. While R0 is most appropriate for epidemics with short-lasting infections, long-lasting infections such as HIV/AIDS may call for the use of growth rates with other properties. For a group of multi-state compartment models we define both R0, the actual reproduction number Ra(t), and the intrinsic growth rate r. We study the relationship between these different reproduction numbers and growth rates and take a brief look at how they could be estimated from actual observed data. The work is illustrated by a model for HIV/AIDS progression among homosexual men in England and Wales. We conclude that other measures of growth, in addition to R0, give important supplementary information.

Cost-utility analysis of screening high-risk groups for anal cancer

OBJECTIVES

Cost-utility analysis of screening for anal cancer in high-risk groups from a UK perspective.

METHODS

Criteria for the assessment of screening programmes were combined in a Markov model representing the natural history of anal cancer and HIV infection in the UK population of men who have sex with men (MSM). Alternative screening programmes were overlaid on the natural history model to evaluate their impact. The model was populated using data derived from a systematic review of the literature, and calibrated probabilistically to represent joint uncertainty in the input parameters.

RESULTS

Reference case results showed screening is unlikely to be cost-effective. Sensitivity analyses identified two important parameters: regression from low-grade anal intra-epithelial neoplasia (AIN) and utility effects. Increased AIN regression rates resulted in a minimum incremental cost per QALY gained of 39,405 pounds, whereas a best case scenario reduced the ratio to 20,996 pounds.

CONCLUSIONS

There are major areas of uncertainty. New analyses of existing primary data, undertaken specifically to inform regression rates may usefully update key parameters at little additional cost. If these analyses increase the likelihood that screening is cost-effective, further studies of the utility effects of treatment for high-grade AIN, and potential screening attendance rates may be justified.

The burden of hepatitis C in England

In England, a large number of individuals are infected with the hepatitis C virus (HCV) and may develop future liver complications, such as decompensated cirrhosis and hepatocellular carcinoma (HCC). Estimates of the magnitude of this future burden are required to plan healthcare resources. We have estimated past incidence of HCV infection in England and predict future burden of end-stage liver disease in the HCV-infected population. A model of the natural history of HCV as a series of disease stages was constructed. A back-calculation approach was performed, using the natural history model and data on annual HCC deaths in England from 1996 to 2004 with mention of HCV and hospital episode statistics for end-stage liver disease with HCV. The number of HCV-infected people living with compensated cirrhosis is predicted to rise from 3705 [95% credible interval (CrI): 2820-4975] in 2005 to 7550 (95% CrI: 5120-11,640) in 2015. The number of decompensated cirrhosis and/or HCC cases is also predicted to rise, to 2540 (95% CrI: 2035-3310) by 2015. HCV incidence increased during the 1980s, with an annual incidence of 12 650 (95% CrI: 6150-26,450) by 1989. HCV-related cirrhosis and deaths from HCC in England are likely to increase dramatically within the next decade. If patients are left undiagnosed and untreated, the future burden of the disease on healthcare resources will be substantial.

Bayesian statistics in medicine: a 25 year review

This review examines the state of Bayesian thinking as Statistics in Medicine was launched in 1982, reflecting particularly on its applicability and uses in medical research. It then looks at each subsequent five-year epoch, with a focus on papers appearing in Statistics in Medicine, putting these in the context of major developments in Bayesian thinking and computation with reference to important books, landmark meetings and seminal papers. It charts the growth of Bayesian statistics as it is applied to medicine and makes predictions for the future. From sparse beginnings, where Bayesian statistics was barely mentioned, Bayesian statistics has now permeated all the major areas of medical statistics, including clinical trials, epidemiology, meta-analyses and evidence synthesis, spatial modelling, longitudinal modelling, survival modelling, molecular genetics and decision-making in respect of new technologies.

Twenty-five years of the AIDS epidemic in Brazil: principal epidemiological findings, 1980-2005

The Brazilian AIDS epidemic is undergoing important changes in its third decade. The present article reviews some central findings: the proportional reduction in cases related to injection drug use; the stability, in recent years, of new cases in the male homosexual/bisexual population; and the relative and absolute increment in heterosexual transmission, even though the estimates of incident rates still point to the first two categories mentioned as those most affected by the epidemic. Still should be detached the persistent increase in incidence rates among women and its stability in the younger age groups, probably the result of behavior changes (such as the consistent use among youth of condoms in sexual relations with casual partners and a reduction in cases related to injection drug use). It is well-know that HIV prevalence in the general population has stabilized at less than 1%, which characterizes Brazil as one of the countries with a concentrated epidemic. The article also emphasizes the growth of AIDS morbidity-mortality in the less favored socioeconomic strata and in women, and the stability of the mortality rate among men.