Updates to the Spectrum/AIM model for estimating key HIV indicators at national and subnational levels

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Introduction
The Spectrum software (Avenir Health, Glastonbury, Connecticut, USA) is used to prepare estimates of key HIV indicators by national programs, UNAIDS and other international organizations. The model uses estimated incidence trends developed by fitting to HIV prevalence data [1,2] and then tracks the newly infected population by age, sex, CD4 þ count category and antiretroviral therapy (ART) status. The model relies on countryspecific service statistics, survey and surveillance data, and uses epidemiological parameters derived from scientific studies to inform patterns of incidence, progression, mortality, and fertility. Updates to some of these parameters are described in this article, others have been described previously. Table 1 provides a list of the key parameters used.

AIDS mortality for people not receiving antiretroviral therapy
Spectrum tracks adults living with HIV by CD4 þ count category (>500, 350-500, 250-349, 200-249, 100-199, 50-99, and <50 cells/ml). For those not on ART, the rates of mortality by CD4 þ count and progression to lower CD4 þ categories were determined by fitting a progression model to survival curves from the ALPHA Network cohort data from the pre-ART period [2,12,13] The estimated annual mortality rates are shown in Table  2. Note that these rates imply that even at high CD4 þ counts, some people still die from HIV-related causes. Today, with a large portion of the HIV population on ART, the mortality rates for those not on treatment could be different if the chance of starting treatment is related to the likelihood of death (i.e. those most likely to die are also most likely to start treatment). Data from Western Europe and North America indicate that in 2017 there were 13 000 (9900-18 000) AIDS-related deaths out of an estimated population of people living with HIV (PLHIV) of 2.2 (1.9-2.4) million [14], an annual mortality rate of just 0.6%. ART coverage in these settings is high, at 78% (60%-90%), but about 20% of PLHIV are still without treatment. Even if all mortality occurred in those not on ART, the mortality rate would be only 2.7%/year. A likely explanation is that people who would have died without treatment, regardless of CD4 þ count, are more likely to start treatment than those who are less likely to die. As a result, the people who are not on ART are the least likely to die. In that case, mortality rates from the pre-ART era will overestimate mortality rates today. We have accounted for this relationship in Spectrum by reducing the mortality rate for adults not on ART in each CD4 þ category as the ART coverage rate in that CD4 þ category increases.
where m is the annual pre-ART mortality rate of PLHIV not on ART in CD4 þ category 'c' and m 0 is the adjusted mortality rate.
The effect of this adjustment on mortality rates is small when ART coverage is low and large when ART coverage is high. The Kenya AIDS Indicator Survey of 2012 [15] reported ART coverage among all HIVinfected adults of about 35%, and that 31% of HIVinfected adults not on ART had CD4 þ counts below 350 cells/ml, 15% had CD4 þ counts 350-500 cells/ml, and 55% CD4 þ counts above 500 cells/ml. With no adjustment, the overall annual mortality rate would be about 13% among those not on ART and about 2.3% for those on ART, yielding a combined annual mortality rate of 9%. With the mortality adjustment described here, the average annual mortality rate for those not on ARTwould

Incidence by age
In 2016, 10% of Spectrum files estimated antiretroviral coverage for prevention of mother-to-child HIV transmission (PMTCT) at over 100%, which may indicate that Spectrum calculations underestimated PMTCT need. PMTCT need depends directly on HIV prevalence among reproductive-age women, and so on HIV incidence patterns by age. Spectrum uses incidence rate ratios (IRRs) to disaggregate adult (ages 15-49 or 15þ) HIV incidence by age and sex [16]. Analysis of files with high PMTCT coverage revealed that Spectrum's default IRRs for generalized epidemics often underestimated HIV prevalence among young women relative to HIV prevalence in national surveys. For the 2017 HIV estimates, we developed a tool in Spectrum that adjusts IRRs to better fit HIV prevalence patterns in these surveys.
Spectrum utilizes age-specific and sex-specific IRR patterns. Sex-specific IRRs (sIRRs) quantify the femaleto-male incidence ratio over time. Users may choose a default sIRR trend for generalized or concentrated epidemics or estimate it externally and input it manually [17]. The IRR fitting tool multiplies this input trend by a fitted scale factor w.
Fitted aIRRs may be either fixed or varying over time. Fixed aIRRs use the same age pattern of incidence over time. Time-varying aIRRs use one age pattern at the time of each survey; we linearly interpolate these patterns between surveys, and extrapolate by keeping the age pattern constant before the earliest survey and after the latest survey.
We fit IRRs within a Bayesian framework. We used the Nelder-Mead simplex method [19] to maximize the product of (a) a likelihood based on HIV prevalence survey data and (b) a prior distribution informed by incidence patterns from cohort studies. HIV prevalence survey data used for fitting consists of the number of respondents who tested HIV positive out of the total number tested by sex and 5-year age group. We derived the likelihood by assuming the number who tested positive was binomially distributed given the number tested and the model's HIV prevalence estimate in that age/sex group. We fitted IRR patterns to all surveys simultaneously. We accounted for complex survey design by dividing numbers of respondents by the survey design effect.
Bayesian parameter estimation requires placing prior probability distributions on model parameters based on external data or domain knowledge, so that parameter estimates incorporate this information alongside survey data. Our prior distribution only requires that w is positive. We developed a data-driven prior probability distribution on aIRRs. We first used Incremental Mixture Importance Sampling [20] to sample aIRRs consistent with HIV incidence patterns at six ALPHA network sites in Malawi, Tanzania, South Africa, Uganda, and Zimbabwe [21]. The IRR fitting tool uses a mixture model of these site-specific incidence patterns as its prior distribution on incidence by age. We specify this prior as a mixture of multivariate lognormal distributions on a, m, and s for each sex, with one component of the mixture model corresponding to each ALPHA network site. This prior ensures that Spectrum produces realistic incidence patterns for settings similar to those observed at ALPHA network sites, whenever survey data are weak.
We fitted IRRs separately for men and women for 27 countries with national HIV prevalence surveys. We fitted both fixed and time-varying IRRs in countries with multiple surveys, and selected the IRR model with lower Akaike information criterion (AIC). Figure 1 shows the resulting fitted aIRRs. Time-varying IRRs had lower AIC in four countries, whereas fixed IRRs had lower AIC in 23 countries. Whereas Spectrum's default generalized epidemic pattern suggests HIV incidence peaks at ages 25-34 for men and 25-29 for women, newly fitted incidence patterns usually peaked at younger ages. The better fits to the survey age pattern of prevalence improves the estimates of the number of women needing PMTCT services as fertility is concentrated in the younger ages.
The resulting IRRs are applied on the incidence trends estimated by EPP (which can be for adults 15-49 or 15þ) to distribute incidence by age and sex while leaving incidence 15-49 (or 15þ) unchanged.

Mother-to-child transmission rates
In 2015, a review of existing literature identified 48 new studies (in addition to 32 from the original 2012 review) to determine the probability of mother-to-child transmission for women receiving no antiretroviral (ARV) drugs and those receiving different ARV regimens to update transmission probabilities for the 2016 Spectrum model [9,22]. In 2018, an additional 24 publications and 3 abstracts were added to the 2016 analysis (see Annex for full listing of studies used for this analysis and a further explanation of regimen categories). The largest number of new studies were related to peripartum transmission rates from women starting ART during pregnancy (11 studies in formula-feeding, 7 in breastfeeding populations) and from women starting ART before pregnancy  The review did not identify major changes from prior estimates, with differences between 2015 and 2018 in the decimal-point range. The greatest difference was for the estimate of postpartum transmission with ART started before pregnancy (0.013%/month in 2015 based on a small number ofstudies, withadditional dataincreasedto 0.023%/month in 2018). Additionally, estimated peripartum transmission rates in women on ART (started during pregnancy or preconception) were slightly higher in breastfeeding than formulafeeding populations, likely secondary to the contribution of early postpartum transmission to peripartum transmission in breastfeeding populations.  pregnancy and the postpartum period among women on lifelong ART. Of women registering for antenatal HIV care, we derived the proportion retained in care at delivery. Of women in care at delivery, we derived the proportion retained in care at 6-10 weeks, and 6, 12, 18, and 24 months postpartum, irrespective of breastfeeding practices. From 24-month retention data, we derived a constant rate of postpartum loss to follow-up (LTFU) and translated this rate to a monthly risk.

Maternal retention in care
We identified 39 unique references (supplementary appendix, http://links.lww.com/QAD/B528) describing 62 351 women from 13 low-income and middle-income countries. One study lacked data from any timepoints of interest [23]. Prior Spectrum values for maternal retention at delivery were stratified by timing of ART initiation (preconception: 75%; during pregnancy: 80%). In the updated literature review, we found limited evidence to support different retention for these two groups (supplementary appendix, http://links.lww.com/QAD/B528). The pooled proportion of women retained in care at delivery was 80%. Pooled postpartum retention among women in care at delivery was 67, 77, 74, 66, and 68% at 6-10 weeks, and 6, 12, 18, and 24 months, yielding a postpartum LTFU probability of 1.6% per month.
Definitions of retention in care varied substantially between studies, potentially influencing these pooled estimates [24]. Silent clinic transfers are frequent among pregnant and postpartum women [25,26]. Most studies did not report on clinic transfers, or classified transferred patients as nonretained, potentially underestimating retention in care. Consistent definitions of retention and more complete ascertainment of silent transfers and postpartum maternal mortality are needed to better refine estimates of retention in care throughout the PMTCT continuum.

Age at antiretroviral therapy initiation among pediatric patients
As in previous Spectrum AIM model estimates, the age distribution of children initiating ART was adjusted to match the age distributions among children living with HIV (CLHIV) at ART start in the International Epidemiological Databases to Evaluate AIDS (IeDEA) Consortium (www.iedea.org). We included data from 85 924 ART-naïve children aged less than 15 years at ART initiation, with a recorded birth date and sex, who  Table 3.
Likely explanations for these patterns include: overall reduced numbers of new infant infections in recent calendar years because of increased coverage of effective PMTCT interventions; scale-up of early infant diagnosis and WHO guidelines recommending universal ART for all children aged less than 2 years in 2010 and 5 years in 2013; and backlog of undiagnosed HIV in long-term slow progressors aged at least 10 years who make up a relatively larger proportion of CLHIV in the context of fewer new infant infections, as well as adolescents with nonperinatally acquired HIV.
As previously described, the IeDEA data were transformed into age-specific probabilities of initiating ART among HIV-positive children not on ART [27].

District estimates
Most countries apply the Spectrum model at the national level, but in 2018, 12  This tool provides detailed district-level estimates of key HIV indicators for HIV planning. It is designed to be useful for PEPFAR planning by providing key inputs into the develop of country operational plans. The main advantages of the tool are that it uses the official Spectrum estimates, ensures that all district estimates add up to the official provincial and national estimates, and provides a range of key indicators and sex/age groups. The main limitation is that it applies the same proportion distribution by district to each indicator. The distribution probably is different by indicator, but little information is available on which to base estimates.

Conclusion
The updates to the Spectrum/AIM model use newly available data from surveys and epidemiological studies and are intended to improve the estimation of HIV epidemics. The updates described in this article, along with those described in other articles in this supplement, make better use of available research and survey information to improve the estimation of HIV-related mortality, incidence, and mother-to-child transmission and provide for national and subnational estimates. The most important effects are expected to be improved estimates of the coverage of PMTCT services (through more precise estimates of the number of HIV-infected pregnant women) and the burden of pediatric HIV and adult mortality.
Updates to the Spectrum/AIM model Stover et al. S233