The Spectrum software (Avenir Health, Glastonbury, CT, USA) is used by national programs and the Joint United Nations Programme on HIV/AIDS (UNAIDS) to prepare estimates of trends and current values of key HIV indicators for 161 countries. The model uses country-specific HIV surveillance, national surveys, case reports, and vital registration data to determine trends in HIV prevalence and incidence. These are combined with country-specific data on program outputs [number on ART, number receiving prevent mother-to-child transmission (PMTCT), number of children receiving co-trimoxazole] and global/regional epidemiological patterns (rates of disease progression, mortality, and mother-to-child transmission) to produce estimates of key indicators, including the number of people living with HIV, new HIV infections, HIV-related deaths, and coverage of ART and PMTCT programs and their associated uncertainty. An increasing number of countries are producing estimates at both the national and subnational levels. A detailed description of the methods and assumptions is available in the Spectrum/AIM manual (http://www.avenirhealth.org/software-spectrum.php) and in previous publications [1–5]. Spectrum files for the latest UNAIDS estimates are available for most countries from UNAIDS (http://apps.unaids.org/spectrum/).
The Spectrum/Estimations and Projections Package (EPP) software is updated annually in response to new information and needs. Several of the updates for the 2016 round of estimates are described in detail in other articles in this supplement: improved pediatric model (Mahy et al.), new data on mortality on ART (Angregg et al.), and incidence fitting to program data (Mahiane et al.). This study describes the remaining updates, including new demographic data, estimating uncertainty at the regional level, options for estimating incidence trends, and improvements to the age dynamics in the EPP model.
Spectrum projections require demographic data on the population by age and sex in the base year (usually 1970) and annual estimates of fertility, non-AIDS mortality, and migration. Most applications use demographic data from the World Population Prospects 2015 Revision produced by the United Nations Population Division . These estimates and projections are for 5-year age groups and 5-year time periods. The Population Division applies demographic interpolation procedures to produce estimates by single age and single year for use in Spectrum. For most countries, life tables represent all-cause mortality but for 21 high HIV burden countries, the Population Division provided non-AIDS life tables so that the HIV mortality can be added by Spectrum . The high burden countries are Angola, Botswana, Burundi, Cameroon, Central African Republic, Congo, Equatorial Guinea, Ethiopia, Gabon, Kenya, Lesotho, Malawi, Mozambique, Namibia, Rwanda, South Africa, Swaziland, Uganda, the United Republic of Tanzania, Zambia, and Zimbabwe.
Compared with the 2012 revision, the 2015 revision adjusts the global population in 2015 upward by 0.3% and the population of low and middle-income countries downward by 0.5%. The largest absolute changes occur in India (29 million higher) and China (26 million lower) but the largest percentage changes occur in Eritrea (−22%), Republic of Moldova (+18%), Syria (−17%), and Lebanon (+17%).
In total, 27 countries in sub-Saharan Africa use EPP to fit prevalence curves to surveillance and survey data separately for urban and rural areas. For the current round estimates of the proportion of the population 15–49 living in urban areas was updated using the percentage urban in the total population in 2014 from the United Nations Population Division's World Urbanization Prospects: the 2014 Revision .
A few countries adjust the demographic data from the United Nations with their own estimates, especially in cases where there is a recent census. For nine countries (Benin, Côte d’Ivoire, Haiti, India, Kenya, Mozambique, Nigeria, the Republic of Moldova, and Zimbabwe), Spectrum is applied to subnational regions (states, provinces, or regions) and the results are aggregated to the national total. In these cases, the subnational demographics need to be prepared. The International Programs staff of the US Census Bureau has produced a toolkit to support the preparation of subnational demographic data (http://www.census.gov/population/international/software/sptoolkit/).
Implementing test and treat and option B+
Eligibility for treatment among adults can be specified by CD4+ cell count threshold. Most national programs currently use 350 cells/μl or 500 cells/μl. Special populations can also be identified that are eligible for treatment regardless of CD4+ cell count. These populations include pregnant women, people coinfected with HIV and TB, serodiscordant couples, sex workers, MSM, and people who inject drugs. As a result of new WHO guidelines released last year , a number of programs are moving to ‘treat all,’ meaning that all people living with HIV are eligible for treatment. Spectrum allocates new ART patients by CD4+ cell count on the basis of the proportion of eligible people not on treatment and expected mortality if treatment is not initiated. As a result, a change in eligibility guidelines can alter the distribution by CD4+ cell count of new patients. Unless the number of people on ART increases appropriately, it is possible that a change in guidelines could result in fewer people with low CD4+ cell counts starting ART if some treatment slots are taken up by those with higher CD4+ cell counts (the number of people on ART is input to Spectrum rather than the rate of initiation as numbers on treatment are regularly reported to UNAIDS and WHO). The distribution of new patients by CD4+ cell count is estimated as the average of the distribution based on probability of death (which provides preference to those with low CD4+ cell counts) and the distribution of those eligible for treatment but not on treatment. To avoid an unlikely shift in the distribution of new patients when eligibility criteria change, Spectrum can adjust the distribution based on the median CD4+ cell count of new patients, if these data are available, by adjusting the distributions above and below the specified median CD4+ cell count to match that median. For years without data on the median CD4+ cell count at initiation no adjustment is done. This adjustment is an important feature because the distribution of new patients by CD4+ cell count can have a significant effect on estimates of HIV-related mortality.
Option B+ is now recommended for all HIV-positive pregnant women. This means that all HIV-positive pregnant women should be started on lifelong ART regardless of CD4+ cell count. Many national programs have already adopted option B+ as their standard. In Spectrum, option B+ is separated into three components: those women already on ART at the time of the first antenatal visit, those women starting on ART during the current pregnancy more than 4 weeks before delivery, and those starting on ART less than 4 weeks before delivery. Each category has a different probability of perinatal transmission (0.21, 1.9, and 7.6%, respectively; Mahy et al., in this supplement). Women receiving option B+ are also included in the total number of adults on ART. To avoid double counting data on women receiving option B+ are only used to calculate the mother-to-child transmission rate. Adult HIV-related mortality rates are based on program data on the number of men and women on ART, which should include women who started ART though option B+.
Spectrum produces 95% plausibility bounds for indicators by processing a large number of projections (usually 1000) with random variation around key input parameters. For each projection: a different incidence curve is randomly selected from the 3000 curves generated by EPP, different progression, and non-ART mortality rates are randomly selected from the 1000 values generated by fitting to the range of survival patterns from the Analyzing Longitudinal Population-based HIV/AIDS data on Africa network, different mortality patterns for those on ART are selected from the 100 draws produced by the International Epidemiological Databases to Evaluate AIDS Consortium by fitting to individual patient data, and mother-to-child transmission rates are selected from a normal distribution with a SD of 5% around the median values. The incidence curves are country specific, whereas the other inputs the uncertainty analysis are based on regional or international data. Global and regional estimates are prepared by aggregating national results. Indicators expressed as numbers of people (e.g., new infections) are simply added and those expressed as rates (e.g., prevalence) are calculated from the aggregate numerators and denominators.
To create plausibility bounds for these aggregate estimates we first ensure that the same random number sequence is used to produce the uncertainty draws for each country. Then 1000 draws for the aggregated indicators are produced by summing the draws for each country in the same order. Using the same random number sequence for each country analysis means that the parameters based on global values are perfectly correlated (reflecting the fact that we use the same values for all countries), whereas those based on country-specific values, such as incidence trends, are uncorrelated. Thus, the resulting plausibility bounds for regional or global estimates assume perfect correlation for key epidemiological parameters (which leads to more uncertainty than if they were uncorrelated) while allowing country-specific values to be uncorrelated (which leads to some offsetting of variation).
Generating incidence trends
Spectrum uses the trend in incidence among all adults 15–49 to calculate new infections, then disaggregates new infections by age and sex, then tracks the consequences of those new infections as people progress through the various CD4+ categories, initiate ART, die from HIV or other causes, and so on. These calculations are the same regardless of the source of the incidence trends. Currently there are five different options for producing the incidence trend.
- EPP. The most widely used option is EPP. It estimates incidence from prevalence trends fit to surveillance and survey data. Detailed information on EPP is available elsewhere  and recent updates are described later in this article. It is most useful in situations where good surveillance data are available and when national prevalence surveys are available.
- Fitting to program data. The ‘Fit to program data’ tool estimates an incidence trend as a single or double logistics curve fitted to data from new HIV case reports, estimates of People Living with HIV, and vital registration of AIDS deaths (Mahiane et al., in this supplement). It is most useful in countries where good surveillance data are not available but case reporting and registration of AIDS deaths is relatively complete. The ‘Fit to mortality’ tool can be used to fit with just AIDS mortality data.
- AIDS Epidemic Model (AEM). This is a simulation model that calculates incidence trends by key populations based on behavioral trends . For the latest round of estimates, AEM was used in nine countries (Bangladesh, Cambodia, Indonesia, Lao PDR, Malaysia, Myanmar, Nepal, Thailand, and Vietnam) and is also used for strategic planning and investment case analyses.
- Goals. Like AEM, Goals is a simulation model that calculates incidence trends by risk group on the basis of behaviors. It has not been used for the 2016 round of HIV estimates but was used to estimate incidence trends for the UNAIDS Fast-Track strategy  and by many countries for their investment case analyses.
- Direct input. Incidence trends generated through some other approach can be entered directly into Spectrum.
Estimations and Projections Package
Adjusting the 15–49 population for entrants and exits
Although Spectrum is a completely age and sex-structured model, in the interests of fitting speed, EPP is not. EPP treats the 15 to 49-year-old population as a single compartment, using average values of mortality, both on and off of ART, for the 15 to 49-year-old population and including no age-specific incidence variations. This results in slightly different incidence and prevalence trends being produced by EPP and Spectrum. This has been dealt with by using an automatically calculated incidence adjustment in Spectrum to align the results.
In the past, the assumption was made that all entrants at age 15 were HIV negative and that HIV positive exits at age 50 were proportional to the rate of demographic age outs. However, in a number of African settings, significant numbers of children born with HIV are surviving to ages 15 and older. Furthermore, because the age structure of people living with HIV changes over time, the number of 50-year olds living with HIV exiting the 15–49 population in Spectrum is different from that expected based on demographic structure. This effect was found to be even more pronounced after ART scale-up when substantially more people living with HIV survive well beyond age 50. These variations were found to be contributing to divergence between Spectrum and EPP trends.
In the current version of Spectrum, these variations in the 15 and 50-year-old entrants and exits have been corrected by having Spectrum pass EPP, a series of annual values for the proportion of the 15 and 50-year-old population of people living with HIV. EPP then uses these values to calculate a number of entrants and exits that is better aligned with the number being produced by Spectrum. Work is underway to allow for full age-structured models in EPP in the near future, which should bring the two into close alignment and eliminate the need for the Spectrum incidence adjustment.
Prevalence among pregnant women: trend adjustment in fitting
Theoretically, EPP is intended to fit national epidemics in the population at large. However, in generalized epidemics, the data available has primarily been drawn from antenatal clinics and, more recently, from PMTCT sites. The current version of EPP thus makes two sets of adjustments during the fitting procedure to better reflect national prevalence: a fitted offset in probit space between data and survey data correcting for ante-natal clinic (ANC) biases in the ANC data; and an adjustment to the calculated model prevalence trend before comparison with the ANC data during fitting to correct for expected time-varying differences between antenatal and general population prevalence trends.
It has long been recognized that national prevalence among the overall population was generally lower than prevalence at antenatal clinic sites , which was strongly confirmed when population-based prevalence surveys in generalized settings became commonplace . Earlier versions of EPP applied separate fixed downward calibrations to urban and rural ANC data to adjust for this , whereas more recent versions have allowed for a variable, but still constant, calibration factor between antenatal and general population prevalence. This calibration factor, which describes an offset between the antenatal clinic and survey data being fit, is set during the fitting procedure [10,16]. These calibrations have been largely attributed to preferential location of ANC surveillance sites in higher prevalence parts of the country and lower prevalence of HIV among men , but other factors such as ANC uptake, age pattern differences, and HIV-related fertility reductions also play a role .
However, on closer examination of data from surveys in sub-Saharan Africa, it was recognized that the evolving age pattern of HIV prevalence among women was also creating different prevalence trends between all HIV-positive women and pregnant women . In particular, it was found that trends among pregnant women were generally overestimating prevalence declines relative to the female population as a whole because of the shift of HIV to older women, who were generally less fertile and thus less likely to be captured in ANC settings. The rapid scale-up of ART is also likely to be altering the patterns of subfertility over time. Recognizing that this could be influencing the national trends, the Reference Group decided EPP should adjust for the evolution of national prevalence over time relative to ANC prevalence in its fitting procedures. Using the previous year's national Spectrum file for each country, the ratio of national prevalence to prevalence in pregnant women was calculated and then added in EPP as a database. This ratio can evolve quite dynamically over time depending upon past prevalence patterns, population age structure, male–female ratios, changes in fertility patterns, ART uptake, and other factors, all of which are taken into account in the Spectrum calculations. As a result, the pattern varies substantially from country to country, as seen in Fig. 1 for three typical countries and the median of all 52 countries and subnational areas.
In EPP's current fitting procedures, this adult to pregnant women ratio is used to adjust the prevalence calculated by the model, which represents the national prevalence among adults 15–49, to get an estimate of the prevalence among pregnant women. This adjusted prevalence is then used in the likelihood terms for ANC data, whereas the unadjusted prevalence is used to calculate the likelihood terms for survey data. The ANC calibration term is still maintained in the fitting to account for other systematic biases in ANC data relative to national survey prevalence. This adjustment of prevalence for pregnant women allows EPP to take into account many of the age and fertility-related changes in ANC data over time and produce a more realistic estimate of the national trend in HIV prevalence.
Estimating prevalence for all adults 15+
A handful of countries collect surveillance data in populations that cover a larger age range than the 15–49, which is the default for fitting in EPP. To meet the needs of these countries, both Spectrum and EPP have been modified to allow the use of 15 and older (15+) populations as well as 15–49. The setting for this is available within Spectrum, as shown in Fig. 2, and if chosen, will result in Spectrum passing EPP populations for ages 15 and above and interpreting all incidence and prevalence values from EPP as for 15+ populations.
Incorporating incidence measures into the fitting
In the past, EPP has primarily relied on fitting surveillance data for HIV prevalence. One of the challenges inherent in this approach is that often very different incidence patterns can produce similar prevalence patterns over the time frame of an epidemic, making it difficult to determine which of the incidence patterns is more likely. However, incidence assays are being incorporated into some surveys, including the Population-based HIV Impact Assessment being conducted in a number of countries now. In addition, cohort-based measurements of incidence are available for some higher incidence countries and key populations. Both of these incidence measures can help to reduce the ambiguity in choosing the most realistic incidence pattern. Bao et al. developed approaches for adding incidence assays to the EPP likelihood calculations and more recently, cohort-based incidence has been added by assuming a simple binomial likelihood for the number of recent infections detected in the test given the number of samples taken. For assays, formula (9) from Bao et al. is used for the likelihood, although if the assay is from one of the surveys being used in the fitting, a simpler binomial likelihood term is assumed.
For assays, the essential inputs are the numbers of recent and nonrecent infections, the number testing HIV negative, and assay characteristics, including the false recent rate, the mean duration of recent infection, and the cutoff time for what is considered a recent infection (T). For cohorts, the only inputs required are the numbers of recent and nonrecent infections and the number of negative samples. The EPP interface for entering these data is shown in Fig. 3 and an example of the influence of entering a roughly 1% incidence measure in 2011 on a fit is shown in Fig. 4.
Future additions anticipated in Estimations and Projections Package
Under the guidance of the Reference Group, development of Spectrum and EPP continues to address new issues and concerns as they arise. A number of items are currently being explored for possible incorporation into future versions of EPP. It has been noted that EPP may be underestimating the amount of uncertainty associated with ANC data, thus a variance inflation term is being incorporated into the likelihood calculations (Eaton and Marston, in this supplement). This will take into account additional sources of uncertainty which are inherent in the collection of ANC and PMTCT data, for example, variations in testing quality, changes in sample composition over time, shifts in catchment areas, and so on. Work is also underway to incorporate the hierarchical model of Bao et al. (in this supplement) that will allow areas with more data and longer trends to inform the fitting in those areas with less data and shorter time trends. Research is currently underway to determine the best way of using PMTCT data in EPP and matching it appropriately with previous years of ANC data (Sheng and Bao, in this supplement). Once those methods become clear, modifications will be made to incorporate them. Finally, work is underway to develop a full sex and age-structured model for EPP fitting that will eliminate most of the variation between Spectrum and EPP as well as eliminating the need for the ANC general population adjustments described earlier.
AIDS Epidemic model
As described earlier, the AEM has been added as a potential source of incidence trends for Spectrum. The AEM is a mathematical process model that includes the major routes of HIV transmission in low level and concentrated epidemic settings : heterosexual behaviors (sex work, casual sex, and husband–wife sex), male same-sex behavior, and needle sharing. The key populations currently included in the model are: female sex workers and clients, MSM and male sex workers, male and female people who inject drugs, female sex workers who inject drugs, transgendered individuals, and the lower risk male and female population. Projection inputs and results are stored in a number of AEM Excel-based workbooks, which can also be used for program and policy analysis. A number of Asian countries are using AEM for their national models, so rather than have them prepare independent EPP estimates, AEM and Spectrum have been modified to work together. AEM generates the necessary files for communicating incidence and prevalence trends to Spectrum from a menu within one of its workbooks, and Spectrum then interprets these values as applying to a 15 and older population and uses them just as it would the results from EPP.
In conclusion, the Spectrum/EPP software is updated annually to incorporate the latest information and to respond to new programing needs. For the 2015 round of estimates, the model includes new options for determining incidence trends using program data, adjustments to the prevalence fitting procedures to account for changing age patterns, and options to implement new guidelines for treatment (treat all) and preventing mother-to-child transmission (option B+).
J.S. leads the development of the Spectrum model and software. T.B. and R.P. develop the EPP model and software. T.B. and W.P. develop the AEM model and software. J.S. and T.B. prepared the initial draft of the study. All authors reviewed and approved the final draft.
Conflicts of Interest
There are no conflicts of interest.
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