The number of prevalent HIV infections in the UK continues to grow, with an estimated 77 550 (73 000–83 300) people aged 15–59 years living with HIV (PLWH), both diagnosed and undiagnosed, in 2008 . Estimates of the temporal trends in prevalence of undiagnosed infection are essential for understanding the possible impacts of disease on healthcare services, of policies and interventions aimed at increasing diagnosis rates, and of the underlying infection incidence.
Historically, a ‘direct method’ has been employed to estimate the number of PLWH in the UK [1–3]. The method has several limitations [4,5], the most important of which are the absence of a formal quantification of uncertainty in an estimate that is inherently uncertain and the inability to include all relevant evidence available and hence to formally ‘triangulate’ different data sources.
To address these problems, since 2005, the UK's Health Protection Agency has produced annual estimates of HIV prevalence using a multiparameter evidence synthesis (MPES) of surveillance and other survey data [4–10]. In contrast to the ‘direct method’, key aspects of MPES [5,6,11,12] are the ability to incorporate all available evidence on prevalence into one model, the correct and coherent propagation of uncertainty in the data and estimation process through to final estimates, and the ability to check that different data sources are providing consistent evidence, with a framework in which to resolve inconsistencies. MPES synthesizes multiple diverse data sources, performing a formal statistical ‘triangulation’, ensuring, through an iterative process of model appraisal and development, that estimates are consistent with each other and all data employed. The most important such example is the use of information on diagnosed infections to help constrain estimates of total HIV prevalence, as opposed to direct [3,13] and other methods for estimating prevalence [14,15] (see van Veen et al., submitted manuscript, for a comparison of these with MPES). Estimation is carried out in a Bayesian setting, for ease of model formulation and incorporation of prior knowledge.
Since 2005, the MPES model for prevalence [6,12,16] has been further developed in response to critical appraisal of the interpretation of evidence. Inconsistent data have been reconciled through modelling of recognized biases and extra information has been incorporated to reduce uncertainty [5,12]. Here, we provide comparable yearly estimates of HIV prevalence, diagnosed and undiagnosed, by applying a consistent MPES model [1,10] to datasets from 2001 to 2008.
Several surveillance systems, population-based or community-based surveys and studies are available to inform prevalence.
Population and exposure category sizes
We synthesize evidence on population and exposure category sizes from three sources. The Office for National Statistics provides estimates of the total population size . These are not available by country of birth except in census years, hence the sub-Saharan Africa (SSA)-born population size is informed by combining data from the 2001 census  with data on the birth rate  and the number of birth registrations to SSA-born mothers .
The National survey of Sexual Attitudes and Lifestyles (NATSAL ) provides information on exposure category sizes for men who have sex with men (MSM) and individuals attending sexually transmitted infection (STI) clinics.
Indirect estimates of the recent injecting drug user (IDU) population size are provided by the Home Office , based on capture–recapture techniques, and by Sweeting et al., based on an evidence synthesis of household surveys. Estimates of the past-to-recent ratio of the IDU population size are also provided by Sweeting et al..
Data on the number of diagnosed PLWH and their exposure group distribution are provided by the Survey of Prevalent HIV Infections Diagnosed (SOPHID [24,25]). SOPHID is an annual, cross-sectional survey of all diagnosed PLWH who attend a National Health Service facility for care. Information is available on exposure, age, sex, ethnicity, and region of residence. Note that SOPHID measures ethnicity, whereas other surveillance systems measure only region of birth, so to combine data from SOPHID with data from other sources, we make the assumption that black African diagnosed individuals make up the large majority of diagnosed individuals who are SSA born.
Yearly data on new diagnoses are available from the HIV/AIDS Patient  register. Although these are not used directly in our estimation of prevalence, they are used to validate the above assumption of a correspondence between diagnosed black African and SSA-born individuals. The register includes information on both region of birth and ethnicity. Among new diagnoses in SSA-born heterosexual PLWH aged 15–44 years, over 95% each year are black African individuals. Of new diagnoses in black African heterosexual PLWH aged 15–44 years, over 70% each year are African-born individuals.
HIV prevalence and proportion diagnosed
Data on total prevalence, prevalence of undiagnosed infection, and proportions of infections diagnosed are obtained from several sources. The Unlinked Anonymous Prevalence Monitoring Programme  is a series of anonymous, annual seroprevalence surveys, measuring HIV prevalence (total or undiagnosed) and/or the proportion of infections that are diagnosed, in three groups: pregnant women (UAPW), IDUs in contact with specialist services (UAIDU), and STI clinic attendees (UASTI). Blood or oral fluid samples are anonymously tested for HIV. Information is available on age, sex, and regions of birth and residence.
By comparing the number of PLWH in the UAPW survey to the number of diagnosed women registered with the National Survey of HIV in Pregnancy and Childhood [28,29], information on the proportion of pregnant PLWH either previously diagnosed or diagnosed during the current pregnancy is obtained, by regions of birth and residence. Estimates of the proportion of diagnosed HIV-positive pregnant women who subsequently change their future fertility decisions  are also available. These are used to relate observed HIV prevalence in pregnant women to prevalence in all women, based on known differences in birth rates among diagnosed HIV-positive women compared with other women .
Ratios of prevalence of undiagnosed infection in MSM in London who have not recently attended a STI clinic compared with those who have are available from a community survey, the Gay Men's Sexual Health Survey (GMSHS) [31–33]. Outside London, such data are not directly available, so we instead use estimates from NATSAL  on the ratio of proportions who have ever had an STI in non-STI-clinic-attending MSM compared with STI-clinic-attending MSM, as a proxy for the ratio of prevalence of undiagnosed infection in the two groups.
Finally, the Sigma BASS Line survey  among individuals identifying as African provides information on the ratio of proportions of African men compared with women who have ever tested for HIV, used as a proxy for the ratio of proportions of PLWH diagnosed in SSA-born men compared with women.
The MPES model for HIV prevalence has been described more fully elsewhere [5,6,12,16], but briefly, the population aged 15–44 years is divided into exposure categories (defined to be mutually exclusive, such that individuals with multiple exposures are classified into the group with highest risk) and regions of residence: London and the rest of England and Wales (‘outside London’). Five exposures – stratified by sex – are considered, as in Fig. 1, with the hierarchy of risk from highest to lowest as follows: MSM; non-MSM IDUs; non-MSM, non-IDUs, SSA-born heterosexuals; non-MSM, non-IDUs, non-SSA-born heterosexuals who have attended a STI clinic in the last five years; and the remaining lower-risk population. MSM are further stratified by time of last sexual contact and of last STI clinic attendance (less than 5 versus ≥5 years ago or never).
Data on the sizes of some key exposure categories are available only for the age range 15–44 years, so we concentrate on individuals aged 15–44 years in England and Wales, although estimates may be scaled to the range 15–59 years and extended to the UK . As we are interested in prevalence of undiagnosed infection, we also exclude individuals infected via blood products and mother-to-child transmission, assumed all diagnosed.
The aim is to estimate simultaneously three basic parameters for each exposure category g and region r: the proportion of the total male and female populations, respectively, of region r in group g,
and the proportion of prevalent cases that are diagnosed,
From these, functions of parameters are also estimated, such as prevalence of undiagnosed infection,
The total number of HIV infections by region and exposure is equal to
total diagnosed and undiagnosed infections are equal to
the total male or female population of region r, respectively.
The data sources provide evidence either directly on one of
or indirectly on multiple parameters, through (possibly complex) functions. For example, SOPHID [24,25] provides information on the number of diagnosed infections, expressed as
indirectly informing all parameters. Figure 2 gives a schematic illustration of how the data sources are influenced by the parameters, and hence how – given the data – we infer the distribution of the parameters.
Some assumptions are made to mitigate a lack of data over time on some group sizes.
In particular, we assume the NATSAL survey, carried out in 2001, provides information on
that is unbiased throughout 2001 to 2008, that is that the proportionate MSM size has not changed in that period, although the absolute number has increased. In addition, the size of the SSA-born population is clearly affected by migration patterns, but as yearly and easily interpretable migration data are not available by region of birth (as opposed to ethnicity [35,36]), we model the population using information on birth rates. The increase in
is assumed to be a function of the increase in birth rate in all women and of the absolute number of births to SSA-born mothers . We hence rely on assuming the birth rate in SSA-born women has increased proportionately to the increase in the birth rate among all women.
The model is fitted simultaneously to each of k datasets
one for each year. Hence, we index each parameter also by year, t. Although no parameters are shared over time (i.e. no temporal smoothing), changes in
over time may be measured by estimating the year-to-year odds ratios (ORs) of both parameters. Inference is carried out in a Bayesian framework: prior information on
is updated through the observed data
to obtain the joint posterior distribution of these parameters and hence the functional parameters of interest, such as prevalence of undiagnosed infection. Where possible, minimally informative Beta(1,1) prior distributions were used, with informative prior distributions employed only to represent expert opinion or external information on biases [5,6,12]. The model is written and fitted in WinBUGS , using a Markov chain Monte Carlo algorithm to sample from the posterior distribution. This distribution fully describes the uncertainty inherent in the data and estimation process, summarized by its quantiles: the median and 95% credible interval. The goodness-of-fit of the model to the data has been assessed through standard methods [5,6,12] and found, after the iterative process of model development, to be satisfactory.
Table 1 displays summaries of the posterior distributions of the yearly number of PLWH, both undiagnosed and total, by exposure. Figures 3 and 4 display summaries of the posterior distributions of, respectively, the prevalence of HIV (%) and the proportion of PLWH aware of their infection (%). Throughout, we report the median (95% credible interval). When reporting ORs, these compare 2008 to 2001.
Overall prevalence and proportion diagnosed
The estimated total number of PLWH in England and Wales aged 15–44 years (Table 1) has increased from 32 400 (29 600–35 900) in 2001 to 54 500 (50 500–59 100) in 2008. The number of diagnosed infections has also increased from 18 800 (18 100–19 500) to 38 500 (37 100–39 900). Estimated prevalence in 2008 [0.24% (0.23–0.26%)] is significantly greater than in 2001 [0.15% (0.14–0.17%)] with ORs 1.26 (1.09–1.46) in London and 2.18 (1.75–2.65) outside. In contrast, the number of undiagnosed infections has remained relatively stable, although the credible intervals are large and do not preclude either an increasing or decreasing trend, at least since the slight peak of 19 100 (14 700–25 000) undiagnosed in 2003 (Table 1).
The estimated proportion of PLWH diagnosed increases over time, from 58% (52–64%) in 2001 to 71% (65–76%) in 2008, although the uncertainty is large. This increase is significant in both regions [ORs 1.56 (1.01–2.33) in London and 2.05 (1.21–3.63) outside].
Men who have sex with men
Estimated HIV prevalence among MSM (Fig. 3) is stable at approximately 5% (4–6%) each year since 2002. This is due to an increase in prevalence of diagnosed infection, from 2.69% (2.33–3.14%) to 3.87% (3.35–4.51%) in 2008, balanced by a decrease in prevalence of undiagnosed infection, from 2.22% (1.66–3.05%) in 2002 to 1.74% (1.28–2.47%).
There is variation by region, however, with an estimated OR of prevalence outside London of 1.53 (1.13–2.04), in contrast to the nonsignificant OR in London of 1.26 (0.92–1.74). Similarly, although overall there is an increase in the proportion diagnosed (Fig. 4), this increase is more prominent outside London, with an estimated significant OR of 2.14 (1.03–4.41) compared with the nonsignificant OR in London of 1.14 (0.62–2.06).
Injecting drug users
The number of PLWH among IDUs appears stable since 2001 (Table 1), although the credible intervals are very wide and hence do not preclude increasing or decreasing trends. There is a slight peak in prevalence of undiagnosed infection in 2005, at 0.11% (0.05–0.21%) in men and 0.12% (0.05–0.24%) in women.
Although the credible intervals for the ORs of prevalence are wide and hence any trend is nonsignificant, the medians suggest that prevalence may have decreased in London and increased outside: 0.81 (0.41–1.67) and 1.34 (0.73–2.49), respectively. Likewise, the median ORs of proportion diagnosed suggest a slight (but nonsignificant) decrease over time, in contrast to all other exposure categories: 0.61 (0.18–2.06) in London and 0.43 (0.11–1.60) outside.
Sub-Saharan Africa-born heterosexuals
Estimated HIV prevalence (Fig. 3) in both men and women peaks in 2003, at 2.21% (1.56–3.55%) and 3.28% (2.82–3.79%), respectively, with a slight decrease for men and a stable prevalence for women thereafter. For men, prevalence of diagnosed infection remains stable at just over 1% from 2003 onwards, with a slight, although very uncertain, decrease in prevalence of undiagnosed infection from 1.18% (0.52–2.51%) in 2003 to 0.44% (0.19–0.88%) in 2008. In contrast, for women, prevalence of diagnosed infection is steadily increasing, from 1.57% (1.49–1.64%) in 2001 to 2.62% (2.50–2.75%) in 2008. As with men, however, there is a slight, but uncertain, decrease in prevalence of undiagnosed infection from 1.10% (0.66–1.55%) in 2004 to 0.77% (0.40–1.18%) in 2008.
These results hide variation by region, with the ORs of prevalence in both men and women significantly greater than one outside London, but not inside: 0.82 (0.62–1.13) inside versus 1.79 (1.11–2.88) outside for men; and 1.00 (0.82–1.24) in London versus 2.21 (1.50–3.08) outside for women. The OR of proportion diagnosed is significantly greater than the one in London [3.24 (1.14–8.18)], but not outside [1.90 (0.71–5.79)]. In both regions, the OR is slightly greater for men [3.41 (0.99–10.04) in London, 2.10 (0.69–7.18) outside] than for women [3.14 (1.17–7.67) in London, 1.79 (0.68 – 5.33) outside], although the credible intervals overlap too much to see a significant difference by sex.
There is an increase in overall prevalence (Fig. 3) in both men and women, although the increase is only significant in women [OR 1.85 (1.47–2.23) and 1.84 (1.14–2.91) inside and outside London respectively]. For both men and women, an increase in prevalence of diagnosed infection contributes to this increase, whereas prevalence of undiagnosed infection remains relatively stable. Prevalence of diagnosed infection among men has increased from 0.013% (0.012–0.014%) in 2001 to 0.026% (0.024–0.027%) in 2008. For women, the increase is from 0.013% (0.013–0.014%) to 0.037% (0.036–0.039%).
The increase in proportion of PLWH diagnosed is more prominent for heterosexual men and women (regardless of region of birth) than for MSM and IDUs (Fig. 4). The OR of proportion diagnosed among all heterosexuals is 2.51 (1.42–4.03) in London and 2.50 (1.25–5.52) outside.
We have presented estimates of the prevalence of HIV, from a statistically rigorous evidence synthesis, fully accounting for uncertainty. We have shown that since 2001, HIV prevalence among 15–44-year-olds in England and Wales has increased (Fig. 3). The increase consists of an increase in the prevalence of diagnosed infection in most exposure groups, coupled with an increase in the proportion diagnosed (Fig. 4). However, prevalence of undiagnosed infection remains stable, with no evidence of a significant decreasing trend (Fig. 3): indeed, the credible intervals for some exposure groups are so wide that an increasing trend is possible (Table 1).
Although the increase in proportion diagnosed is a positive sign, the lack of evidence of a decrease in prevalence of undiagnosed infection strongly suggests not enough is being done to reduce both incidence and the pool of those unaware of their infection. A stable prevalence of undiagnosed infection together with increased prevalence of diagnosed infection suggests sustained numbers of new infections entering the pool of undiagnosed infections and diagnosis rates that are too low to reduce the pool of undiagnosed infection, despite increasing over time. Trends in prevalence alone cannot tell us what proportion of prevalent infections are long-standing and undiagnosed due to low testing propensity and what proportion are new infections. To distinguish the two requires estimates of HIV incidence in recent years .
Our estimates suggest significant differences in trends in prevalence inside and outside London, with the 2008–2001 ORs of prevalence greater outside London than in, for all groups except UK/elsewhere-born heterosexuals. This suggests prevalence is increasing at a greater rate outside London than inside, although absolute prevalence remains around four times higher than outside, reflecting the fact that region has long been an important indicator of differential risk of HIV.
Although an MPES approach makes efficient use of all available data, a lack of data in some exposure categories and regions entails some assumptions. The results presented here rely on assumptions about proportionate group sizes over time (Section 3). We also assume we have correctly interpreted the data and that they provide unbiased evidence on the populations of interest. Where the data are known to be unrepresentative of these and we have independent information about their biases, we have introduced extra parameters and data to model the biases [5,6,16]. Where we have no clear idea of whether a potential bias actually exists, we assume the data are representative. For example, the UASTI survey observation of prevalence of undiagnosed infection in MSM may overestimate this quantity if diagnosed individuals participating in the survey do not disclose their diagnosis, hence overestimating the number of undiagnosed infections in STI-clinic-attending MSM. However, in the absence of further evidence, we assume this is not so. Likewise, we assume the use of the ratio (observed at 0.4) of proportions ever diagnosed with an STI in non-STI-clinic-attending compared to STI-clinic-attending MSM as a proxy for the ratio of prevalence of undiagnosed infection in the two groups outside London is reasonable. A sensitivity analysis, assuming instead the ratio lies between 0.8 and 1.2 (based on work synthesising evidence from the GMSHS and NATSAL surveys; Walker et al., submitted), results in between 1000 and 2000 more estimated undiagnosed infections in MSM per year. This difference is smaller than the width of the corresponding credible intervals (Table 1), suggesting the results are reasonably robust to the assumption.
The results presented average over all individuals aged 15–44 years. Heterogeneity by age is likely, so development of an age-stratified model is important. We have not introduced any shared parameters over time: random-walk models for both prevalence and proportion diagnosed have been explored , resulting in slightly more precise estimates and vaguely smoothed trends, for group and region combinations where there is a paucity of data. However, the substantive conclusions are not changed.
Sensitivity to the assumption of an increasing birth rate among SSA-born women proportionate to the overall increase in all women has also been explored : an assumption of constant birth rate since 2001 gives a larger estimated population size, as the number of births has increased substantially in that time . So for a given prevalence, we estimate a larger number of infections and hence a smaller proportion diagnosed [e.g. in SSA-born women in 2006, with increasing birth rate the estimated proportion is 86% (75–98%) compared to 75% (63–91%) assuming constant birth rate ]. Recent estimates  of the total fertility rate in UK-born and non-UK-born women suggest that further assessment of the plausibility of this assumption is needed, which will be possible when the 2011 census has taken place.
Where informative prior distributions were assumed, analyses were carried out to assess sensitivity to these . When prior distributions were less informative, there was little effect on those group/region combinations with substantial evidence to inform parameters. For less well identified parameters (lower-risk men in particular), less informative prior distributions resulted in greater uncertainty, as well as higher posterior median estimates for the number undiagnosed.
Despite these caveats, the estimates presented here are derived robustly, on the basis of all available data, fully reflecting our uncertainty about the HIV epidemic in England and Wales. The implication that not enough is being done to increase testing and diagnosis rates and to reduce transmission is clear from the estimated sustained prevalence of undiagnosed infection.
A.M.P. is supported by Medical Research Council grant G0600675. A.E.A. was supported by funding from the Medical Research Council, London. D.D.A. is supported by the Health Protection Agency and by Medical Research Council grant U.1052.00.007.
A.M.P. contributed to the design of the study, carried out the implementation, development and critical appraisal of the statistical model and wrote the manuscript. O.N.G. contributed to the design of the study and reviewed and edited the manuscript. T.R.C., C.H., V.H., L.L. and B.R. provided data, contributed to the development and critical appraisal of the model and reviewed the manuscript. V.D. contributed to the critical appraisal of the model and reviewed the manuscript. A.E.A. and D.D.A. initiated and designed the study, contributed to the development and critical appraisal of the model and reviewed and edited the manuscript.
The authors thank Aicha Goubar for the initial implementation of the model and helpful discussion, Susie Huntington and Alison Brown for providing UA and SOPHID data and helpful discussion, Fortune Ncube and Barry Evans for helpful discussion, Cath Mercer for providing NATSAL data and helpful discussion, Pat Tookey for providing NSHPC data and helpful discussion, Sue Cliffe and Mario Cortina-Borja for providing survey data and helpful discussion, Julie Dodds, Danielle Mercey and Andrew Copas for providing GMSHS data and helpful discussion, Ford Hickson for providing Sigma BASS Line survey data and Mike Sweeting for providing estimates of the IDU population size and helpful discussion.
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