IJE Advance Access originally published online on April 17, 2007
International Journal of Epidemiology 2007 36(3):679-687; doi:10.1093/ije/dym019
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Estimating the number of vertically HIV-infected children eligible for antiretroviral treatment in resource-limited settings
1Centre for Paediatric Epidemiology and Biostatistics, Institute of Child Health UCL, London, UK.
2Health Section, UNICEF, New York, NY, USA.
3HIV Section, UNICEF, New York, NY, USA.
* Corresponding author. Centre for Paediatric Epidemiology and Biostatistics, Institute of Child Health UCL, 30 Guilford Street, London WC1N 1EH, UK. E-mail: m.newell{at}ich.ucl.ac.uk
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Abstract |
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 Top Abstract IntroductionMaterials and methodsResultsDiscussionModel availabilityAcknowledgementReferences |
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Background With the gradual roll-out of antiretroviral therapy (ART) to delay progression of HIV disease in children in programmes across sub-Saharan Africa and resource-limited settings elsewhere, reliable information on the number of vertically infected children eligible for such treatment is urgently required.
Methods We present a model to estimate the number of vertically HIV-infected children by age who have progressed to moderate to severe disease (MSD) and as such are eligible for ART on the basis of clinical disease, allowing for: antenatal HIV prevalence, use of interventions to prevent mother-to-child transmission (PMTCT), infant feeding policies and availability of co-trimoxazole to prevent opportunistic infections that may hasten the onset of serious disease. The model assumptions were informed by published evidence and expert opinion; rates of progression to serious disease were inferred from mortality of infected and uninfected children of HIV-infected mothers; and mortality among children treated with ART was based on a study of treated children in Abidjan. To allow widespread use the model has been developed using the Excel spreadsheet software.
Results With South Africa as a hypothetical example, published antenatal prevalence and demographic data, and assuming PMTCT coverage with single dose nevirapine of 11%, all exposed and infected children receive co-trimoxazole, and various infant feeding policy scenarios, estimated numbers of children eligible for ART are presented.
Conclusions This model is easy to implement and flexible and can be used in ART programmes at national and local level.
Keywords HIV, paediatric, vertical transmission, antiretroviral, estimations
Accepted 29 January 2007
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Introduction |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionModel availabilityAcknowledgementReferences |
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Globally
2.3 million children under 15 years of age are living with HIV and 700,000 children were estimated to have acquired HIV in 2005,1 mostly through mother-to-child transmission (MTCT).2,3 Close to 90% of paediatric infections occur in sub-Saharan Africa, with HIV prevalence among women of childbearing ages reaching 40% or more in some parts of southern Africa.1,4
Without specific interventions, 20–40% of children born to HIV-infected women will also be infected;5,6 which can be reduced to 15–25% with short course peripartum antiretroviral drug prophylaxis.7–9 Breastfeeding is an important additional mode of acquisition.5,6,10–12 Without antiretroviral therapy (ART) and other supportive prophylaxis, a substantial proportion of infected children rapidly progress to serious disease and death, and by age 1 year only 60% of infected children will still be alive.13–15
In the WHO 3 x 5 initiative,16 the focus so far has been mainly on adults, but while children only constitute 6% of all HIV infections, they account for 16% of all HIV-related deaths.17 Recently the focus has shifted towards children.18 Although infected children, like adults, become eligible for ART on the basis of clinical symptoms or signs, or immunological status,19 their disease progression is more complex, early diagnosis for infants is hindered by passively acquired maternal antibodies and specific paediatric formulations are limited.19–22
To inform the optimum delivery of treatment to children in programmes, particularly in resource-limited settings, we developed a model to estimate the number of HIV-infected children by age eligible for ART on the basis of clinical disease progression, allowing for: antenatal HIV prevalence, use of interventions to prevent mother-to-child transmission (PMTCT), infant feeding policies and availability of co-trimoxazole and ART.
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Materials and methods |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionModel availabilityAcknowledgementReferences |
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For the initial model development we assumed a stable population, with no changes in birth rates, population size, antenatal prevalence, coverage of PMTCT or treatments over the previous 10 years (Figure 1) (Box 1).
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Box 1 Definitions
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t,i|
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and 
are the probabilities of perinatal/in utero and breastfeeding transmissions, allowing for the extent of PMTCT and duration of breastfeeding; 
t is the proportion of women attending antenatal clinic infected with HIV, ßt is the crude live birth rate per head of population per year and Pt is the population size at time t. The first part of the sum therefore refers to children infected at or before birth and the second provides the number of children, negative at birth that became infected through postnatal transmission. Note that the number of live deliveries per year at time t can be expressed as Dt = ßt Pt.
The number of infected children alive by age i at time t, At,i can be written as
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| (2) |
is the cumulative mortality rate at time t for infected children aged i.
The cumulative HIV-attributable mortality rate at time t for children of age i is 
, where 
is the cumulative mortality rate at time t for uninfected children aged i and is assumed to be the background mortality rate for infected children. Mortality rates from birth to 5 years, for infected and uninfected children, were taken from published and unpublished data,14 and we assumed a constant yearly mortality risk between 5 and 10 years of 0.3 and 9% in uninfected and infected children, respectively; survival of infected children is independent of feeding method and PMTCT-exposure.14
The values of t, ß t , Pt , , and are obtained from the literature and are displayed in Table 1.
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The paediatric treatment need equates to the number of surviving infected children with HIV-related disease severe enough to warrant treatment; here this level of disease is classified as moderate to severe disease (MSD) in accordance with the WHO treatment guidelines.24 Let the proportion of the cumulative MSD development rate attributable to age i be:
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| (3) |
t,i is the age-specific mortality rate for children aged i with MSD at time t. In Equation (3) the cumulative proportion of children developing MSD is equal to the annual increase in cumulative HIV-attributable mortality divided by the age-specific mortality rate among children with MSD.
We used age-specific mortality rates for symptomatic children available from the literature25 as starting values for an iterative procedure which increases them to take into account that HIV-attributable mortality will occur in children with MSD and not in those with mildly symptomatic disease. Assuming 95% will develop MSD by age 10 years, we used the Excel solver function26,
to find the updated values of t,i, which satisfy
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For infants under 1 year of age, who suffer more acute illness than older children, mortality in the month of developing MSD was assumed to be 95% with no further mortality for the rest of year 1 if they survived this month. All children who survive the year in which MSD developed suffer the MSD mortality rate of the following period (Table 2).
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In the first year of life the total number of MSD cases in need of treatment (Tt,i) simply equates to the number of surviving MSD cases that developed during the first year, but in later years the total number of MSD cases in need of treatment was calculated by adding the surviving MSD cases from the previous period to the new MSD cases for the current period and applying the period-specific mortality rate. For the children aged 1 year we have: Tt,1 =
t,1 It(1 – t,1), and in general:
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| (4) |
We assume that mortality in uninfected children represents the background mortality of all exposed children, any additional mortality in the infected children is HIV associated, all HIV-attributable mortality occurs in children with moderate/severe HIV-related disease so that HIV-attributable mortality is a proportion of total MSD cases, and all children who survive until the end of the period in which they progressed to MSD are eligible for treatment. With a stable antenatal HIV prevalence, birth rate and population size the number of surviving MSD cases in their ith year can thus be assumed to be the number of i-year olds needing treatment.
Treatment options
Co-trimoxazole only
Pneumocystis carinii pneumonia (PCP) remains the most common opportunistic AIDS defining disease in infants,27,28 affecting in particular infants <6 months old.14,27,29,30–33 Co-trimoxazole is a highly effective PCP prophylactic with a reduced, but still important, efficacy against the bacterial infections of older children.25,28 Based on Chinto et al.,25 which excluded children under 1 year of age, and expert opinion we assume co-trimoxazole reduces mortality during the first 6 months of life to 40% of its original value and after the first year to 57%. For months 7–11 a gradual increment simulates the gradual decrease in effectiveness of co-trimoxazole. Mortality of uninfected children is unaffected by co-trimoxazole. HIV-related mortality and cumulative MSD progression rate use reduced mortality rates with co-trimoxazole. Through preventing common opportunistic infections co-trimoxazole will significantly reduce the rate of developing MSD and the likelihood of mortality in MSD, by 20% (Table 3).
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ART only, for children 1 year of age or older
Without ART, disease progression is particularly rapid in the first 6–12 months of life and many infants who develop MSD during this period will not be diagnosed with HIV and treated unless they survive until the end of the year. We assume that where ART is available it is supplied to MSD cases >1 year of age19,34 and has no impact on the rate of progression to MSD; mortality rate for MSD cases once on treatment is reduced to 9% per year 35 and all children stay on treatment once started.
Co-trimoxazole to all children and ART to children over 1 year of age
We assume no interaction between co-trimoxazole and ART, a rate of progression to MSD as with co-trimoxazole only, once MSD has developed the reduced mortality of the co-trimoxazole model applies for the period in which the MSD develops and at the end of the relevant age period, children with MSD are placed on ART and a constant mortality rate of 9% per year applies.
Co-trimoxazole and ART to all children
Assumptions here are the same as above, with additional ART available for children <1 year of age given early diagnosis of infection. With the rapid progression of disease in young infants and limited time between symptom and death ART is assumed to have a lesser effect than in older children, reducing the mortality in MSD cases by 50%. Due to the availability of rapid diagnostics once a child develops MSD they are put on ART at the end of the month in which the MSD develops (Figure 2).
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Allowing for trends in antenatal HIV prevalence
To reflect a more realistic, non-static, population and changes in treatment and PMTCT practices over time, the following additional steps apply: for each of the past 10 years the number of expected deliveries to infected women, infected and uninfected children born under different types and coverage of PMTCT can be calculated using the appropriate demographic information and antenatal prevalence, and the number of surviving infected children in each age group is derived by applying the appropriate treatment survival rate for that period to the cohort born in the corresponding year (t – i). In general, the numbers of children needing treatment at age i, at time t can be recursively written as:
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Results |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionModel availabilityAcknowledgementReferences |
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To illustrate the model, we use South Africa as an example with published data on antenatal prevalence over the past 10 years36 and demographic information.23 All input data used are in the public domain. PMTCT, as single dose nevirapine (sdNVP), has been available since 2000 and we assume a PMTCT programme coverage of 11% in 2003;37 and different infant feeding approaches. Co-trimoxazole has been recommended for all HIV-exposed children since approximately 2000, and we assume in this example that 100% coverage is reached at the end of 2003; coverage of ART is assumed to be 0%.
Antenatal prevalence information is available from 2003 backwards, when the estimated population size was 47.432 million, and the birth rate 23.8 per thousand, giving 47,432,000*(23.8/1000) = 1,128,881 live births in 2003, which for an antenatal prevalence of 27.9% gives 314,958 children born to HIV-infected mothers (Table 4).
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The overall transmission probability depends on PMTCT coverage and breastfeeding practices. With sdNVP PMTCT the in utero/perinatal transmission probability is assumed to be 0.1 and 0.2 without. With 11% coverage of sdNVP this would give (11*0.1) + (89*0.2) = 18.9% of all exposed children being infected at or before birth, in this case equalling 0.189*314,958 = 59,527 children infected by birth. We assumed that in total 5% of women refrain from breastfeeding with a postnatal transmission probability of zero, 50% to breastfeed for <6 months with a postnatal transmission probability of 0.04 and the remaining 45% breastfeed for longer with a transmission probability of 0.20. Therefore, an additional ((5*0) + (50*0.04) + (45*0.20)) = 11% of exposed children who were uninfected at birth are infected postnatally, 0.11*(314,958 – 59,527) = 28,097, giving a total of 59,527 + 28,097 = 87,624 exposed children who acquire infection.
To calculate the number of children surviving to certain ages we applied the cumulative mortality rate to the number of infected infants born in each of the past 10 years, with mortality rates depending on available treatment in a given year.
To calculate the number of children with MSD at each age, the annual MSD rate is applied to the corresponding birth cohort, allowing for the availability of co-trimoxazole (Table 5) and an MSD mortality rate.
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In addition to children who develop MSD in a given age interval and survive, there are also surviving children who developed MSD at an earlier age. To calculate the number of children with MSD surviving into the next year, the mortality rates of the periods through which they have survived are applied, using the correct birth cohort to allow for changes in antenatal prevalence. This gives the total number of children in each age band eligible treatment (Table 5).
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Discussion |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionModel availabilityAcknowledgementReferences |
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Using South Africa as an illustration, we present a model for programmatic purposes to estimate the number of HIV-infected children at different ages that would become eligible for ART. Without ART and co-trimoxazole prophylaxis, with the rapid disease progression and high mortality rate early in life and the difficulty of diagnosing vertically acquired infection in young infants, the number of infected infants surviving the first year who become eligible for treatment is comparatively small. After the first year the number becoming eligible for treatment remains fairly constant,
50% higher than at the end of the first year. When co-trimoxazole is available for all children under 18 months, and for all symptomatic children, the substantially reduced mortality results in an increased proportion of infants who develop MSD surviving long enough to be diagnosed and become eligible for treatment. On the other hand, ART when available only to children of 1 year or older (because of the difficulty of diagnosing infection in young infants and the rapid disease progression and high mortality in the first year), only impacts on numbers of surviving children known to be infected. As children who become eligible for treatment remain on treatment for the rest of their lives and the mortality rate when on treatment is dramatically reduced, there is an accumulation of children in the treatment category. When rapid diagnosis of vertically acquired HIV or pre-emptive ART for children with indeterminate infection status is available, infants <12–18 months old can receive ART, and co-trimoxazole can be given to all exposed children born to HIV-infected mothers. With both ART and co-trimoxazole for all infants there is a rise in the number of children eligible for ART and the number of children alive and not on treatment. By the end of the first year approximately double the numbers of children would be eligible than without early treatment. This then substantially increases the numbers on treatment across all age ranges.
This easy to use, flexible model has been designed for programmatic use at national and local level, but has some limitations. First, we assume that children who develop MSD are put on antiretroviral treatment either the year or month following their disease progression, depending on the availability of rapid diagnostics; once services are functioning well treatment could be initiated immediately, increasing the demand for ART to a limited extent. Secondly, the model relies on population data with a margin of error and assumptions regarding mortality and progression rates. However, these estimates may be based on only a few studies, and could either over- or under-estimate mortality and thus lead to an over- or under-estimate of the number of infected children in the model. The use of locally derived data would be more appropriate but these are not normally available. In order to provide the user with an idea of the uncertainty surrounding the estimates, the programmatic model also calculates upper and lower certainty boundaries, created using the maximum and minimum plausible estimate for each parameter (transmission, mortality, MSD mortality and MSD progression rates). Furthermore, as parameters and rates used in the model can be changed manually, the user can experiment further with the sensitivity of the model and, where local parameter estimates are available, produce a more locally applicable and accurate estimate. Additionally, the very lack of accurate estimates of the numbers of children requiring treatment in resource-limited regions that necessitated the creation of this model limits our ability for validation.
We aim to adapt the model to explore the effect of the provision of other therapies to treat or prevent opportunistic infections and differences in background mortality which would mainly affect the rates for uninfected children.14 Should these investigations produce significant results then the use of locally derived mortality data would have to be further encouraged. We also aim to adapt the model as a tool to evaluate the success of an intervention program, either at PMTCT level or at disease treatment level; by predicting the number of infected children born or eligible for treatment that would be expected under the new regimen and comparing these to the actual number observed the performance of the intervention can be assessed.
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Model availability |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionModel availabilityAcknowledgementReferences |
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Please contact the corresponding author for a programmatic version of the model.
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Acknowledgement |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionModel availabilityAcknowledgementReferences |
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The authors gratefully acknowledge Colin Newell for developing the Excel spreadsheet front of the model and UNICEF for their support.
Conflict of interest: None declared.
KEY MESSAGES
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Notes |
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A function that optimizes (maximizes or minimizes) the value of a target cell, within preset boundaries, by altering values in other cells, that are related via a set formula to the target cell. The optimizer employs the simplex, generalized-reduced-gradient, and branch-and-bound methods to find the optimal solution. 
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References |
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TopAbstractIntroductionMaterials and methodsResultsDiscussionModel availabilityAcknowledgementReferences |
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