#### Introduction

Globally, most HIV infections in children are acquired through mother-to-child transmission (MTCT), and it is estimated that 1700 infections occur through this route each day [^{1}], most of them in developing countries. In regions with developing economies, the most promising prenatal and intrapartum interventions proven to prevent MTCT of HIV are short-course zidovudine (given to the mother at 36 weeks gestation or earlier and continuing through labor and delivery) [^{2–4}] and short-course nevirapine (one intrapartum dose to the mother and one dose to the neonate) [^{5}]. Promising postnatal intervention choices include avoidance of breastfeeding (replacement feeding) and early weaning (at age 6 months) [^{6,7}]; antiretroviral prophylaxis for the breastfeeding infant is being studied. Short-course antiretroviral prophylaxis, avoidance of breastfeeding and early weaning are the current candidates for widespread implementation through several initiatives to prevent MTCT of HIV underway worldwide.

We developed a decision analysis model to help guide decision-making about intervention policy through the evaluation of the relative effectiveness of interventions under varying conditions. The model was designed to be a simple, locally adaptable tool to allow decision-makers to explore three questions: (1) which currently available, proven intervention or combination of interventions maximizes survival for children less than 5 years of age? (2) How safe would avoidance of breastfeeding have to be to make it a favorable intervention option? (3) What reduction in HIV transmission probability would a postnatal antiretroviral intervention need to achieve for it to surpass the effectiveness of avoidance of breastfeeding, as measured by survival to age 5 years? In this paper, we describe the model and illustrate its use in a setting characterized by high child mortality rates and universal breastfeeding.

#### Methods

We first created a decision tree in which all infants born of HIV-seropositive mothers are divided into mutually exclusive categories; then we added the possible interventions to prevent the MTCT of HIV (Fig. 1). The interventions we evaluated are prenatal short-course antiretroviral prophylaxis with zidovudine [^{2–4}], intrapartum and neonatal short-course antiretroviral prophylaxis with nevirapine [^{5}], avoidance of breastfeeding, early weaning (at age 6 months) [^{6,7}], combinations thereof, and a theoretical postnatal antiretroviral intervention that could be applied in the presence of breastfeeding. The outcome of interest was survival to age 5 years among children born to HIV-seropositive women.

##### Mathematical model

We developed a mathematical model to estimate the probability of survival to 5 years of age among children born to HIV-infected women and exposed to different interventions and combinations of interventions. (The model is available in Excel spreadsheet format at the following website: http://www.cdc.gov/nchstp/od/gap/Spreadsheet.htm). The model relates survival to age 5 years to six key parameters according to the following expression:

where *M*_{H} = among children born to HIV-infected women, proportion who have died by age 5 years (under-5 mortality); *M*_{H+} = among HIV-infected children, proportion who have died by age 5 years*; *M*_{B+} = among uninfected breastfed children born to HIV-infected mothers, proportion who have died by age 5 years; *t*_{P} = probability of HIV transmission at or before birth (HIV-infected mother to her fetus or infant); *t*_{B} = probability of HIV transmission postnatally through breastfeeding (mother's infection preceding conception or birth of child); *B* = among infants born to HIV-infected mothers, proportion breastfed; *R* = relative risk of mortality (uninfected children who were not breastfed compared with uninfected children who were breastfed). All analyses are based on the assumption that under-5 mortality is 100% for HIV-infected children, whether they were born infected, or were infected postnatally, and regardless of feeding method [^{8}], i.e., *M*_{H+} = 1 and drops out of the equation (below).

We defined a base case (no intervention) and estimated base-case *M*_{H} for a setting representative of a developing country where *M*_{B+} = 150 per 1000 live births [^{9}]. We assumed *t*_{P} = 0.20, [^{10,11}]; *t*_{B} = 0.16, [^{6}]; and universal breastfeeding (i.e. *B* = 1) for all interventions except those that included avoidance of breastfeeding. Similarly, to estimate under-5 mortality for children exposed to interventions (*M*_{HI}), we used intervention transmission probabilities at or before birth and postnatally through breastfeeding (*t*_{PI} and *t*_{BI}, respectively) in accord with published literature (Table 1). (The subscript ‘I’ in *t*_{PI} and *t*_{BI} indicates a parameter in the presence of an intervention.)

We computed 95% confidence intervals for each model from the empirical 2.5 and 97.5 percentile points of 20 000 simulations, using S-Plus version 3.3 (Statistical Solutions, Seattle, Washington, USA). For each simulation, we computed the model predictions from parameter values (for *t*_{P}, *t*_{B}, *M*_{B+}) obtained from binomial distributions. For each binomial distribution, we used a point estimate of the relevant parameter and sample size obtained from the literature (Table 1); for *M*_{B+}, we assumed a probability of 0.15 and a sample size of 1000.

We evaluated each intervention or intervention combination by comparing the survival to age 5 years with that which would occur without intervention (number of prevented deaths).

To evaluate the base case, we simplified Eqn (2):

where *M*_{HB+} = among breastfed children born to HIV-infected mothers, proportion who have died by age 5 years.

Substituting the actual values used, for the base case, the equation simplifies to:

(Among breastfed children born to HIV-infected mothers, the probability of survival to age 5 years, without intervention, is 57.1%). The 95% confidence interval is 0.525–0.614.

To estimate 1 − *M*_{HI}, the probability of survival to age 5 years in the presence of prenatal or perinatal antiretroviral interventions, we made the same simplifying assumptions but substituted *t*_{PI} for *t*_{P} as indicated in Table 1. To estimate 1 − *M*_{HI} in the presence of postnatal interventions, we assumed *t*_{P} = 0.20 and *B* = 0 for the avoidance of breastfeeding intervention, and *B* = 1 for postnatal antiretroviral prophylaxis; we also substituted *t*_{BI} for *t*_{B.} We varied *R*, the relative risk of mortality among uninfected children (not breastfed compared with breastfed) to explore its influence on the effectiveness of avoidance of breastfeeding and early weaning. Few studies have estimated *R* for children older than 1 year of age. However, among infants up to 1 year of age, estimates range from 1.3 to 7.9 in different settings (in the absence of specific programs to increase the safety of replacement feeding) [^{12}]. The infant feeding interventions were evaluated at 1.0 < *R* < 4.0. For combinations of avoidance of breastfeeding and antiretroviral interventions, we applied all of the preceding modifications.

To evaluate the effectiveness of the avoidance of breastfeeding intervention, we simplified Eqn (1), by deleting the terms applying to breastfed children.

For combinations of avoidance of breastfeeding and antiretroviral interventions, we applied all of the preceding modifications.

We evaluated survival at age 5 years in the presence of early weaning by modifying Eqn (1) as follows:

which assumes that *M*_{H+} = 1 (under-5 mortality is 100% for HIV-infected children), *B* = 1 (all infants are breastfed for 6 months) and that the relative risk of mortality associated with early weaning is the midpoint between 1 and the *R* at which avoidance of breastfeeding is being evaluated [^{13}].

To compare interventions that include avoidance of breastfeeding with all other interventions and with the base case (which assumes universal breastfeeding), we defined a theoretical critical point for the relative risk of mortality, called *R*_{0}. If *R* > *R*_{0}, then breastfeeding would have a more favorable effect on survival to 5 years of age (as measured by prevented deaths) than would an infant feeding intervention like avoidance of breastfeeding or early weaning. When *R* < *R*_{0}, then avoidance of breastfeeding or early weaning would have a relatively greater effect on survival to age 5 years compared with breastfeeding. Similarly, to compare interventions that include postnatal antiretroviral prophylaxis with other interventions, we defined a critical *t*_{BI}, called *t*_{BI0}. This *t*_{BI0} represents the reduction in the probability of transmission through breastfeeding that would be needed if postnatal antiretroviral prophylaxis is to prevent more deaths by age 5 years than would a currently available antiretroviral or infant feeding intervention (given a particular value of *R*).

#### Results

##### Survival

In the base case (universal breastfeeding and no intervention), 571 per 1000 breastfed children born to HIV-infected mothers would survive to age 5 years (95% confidence interval, 525–614). Table 2 shows the numbers of children surviving to age 5 years per 1000 children born to HIV-infected mothers, for each currently available intervention, and Table 3 shows the effectiveness of currently available interventions, expressed as numbers of deaths prevented by age 5 years per 1000 children born to HIV-infected mothers. All interventions are effective to some degree when *R* ≤ 1.5 (positive numbers represent prevented deaths), with a consistent pattern of combinations of avoidance of breastfeeding with prenatal short-course zidovudine and with intrapartum and neonatal short-course nevirapine preventing the most deaths (see Table 4).

Interventions that include early weaning and avoidance of breastfeeding sequentially cease to be preventive and begin to be associated with deaths that would not have occurred in the absence of the intervention as *R* increases above 1.5 and 1.9, respectively. (Negative numbers in Table 3 represent the numbers of deaths attributable to the interventions.) The critical point, *R*_{0,} comes first for early weaning as a single intervention at *R*_{0} = 1.5, i.e. at *R* > 1.5, early weaning results in more deaths than with no intervention. For avoidance of breastfeeding as a single intervention, *R*_{0} = 1.9. For intrapartum and neonatal short-course nevirapine with avoidance of breastfeeding, *R*_{0} = 2.3, and with early weaning, *R*_{0} = 2.4; for prenatal short-course zidovudine with avoidance of breastfeeding, *R*_{0} = 2.4 and with early weaning, *R*_{0} = 2.7. At *R* > 2.9, only the antiretroviral medications (prenatal short-course zidovudine and intrapartum and neonatal short-course nevirapine) without a feeding intervention are effective as a preventive measure.

##### Critical efficacy of a postnatal antiretroviral intervention

Next we determined values of *t*_{BI0}, the reduction in HIV transmission through breastfeeding needed for a postnatal antiretroviral prophylaxis strategy to prevent more deaths by age 5 years than would currently available interventions. To surpass the effectiveness of prenatal short-course zidovudine and intrapartum and neonatal short-course nevirapine interventions, postnatal antiretroviral prophylaxis must achieve *t*_{BI0} = 69% and 50%, respectively (does not vary by *R*). In contrast, the *t*_{BI0} for postnatal antiretroviral prophylaxis to surpass interventions that include a feeding component varies by *R* (Fig. 2).

As shown in Figure 2, at any *R*, a postnatal antiretroviral intervention must achieve *t*_{BI0} = 25% to be more effective than early weaning as a single intervention; *t*_{BI0} = 75% to be more effective than the combination of intrapartum and neonatal short-course nevirapine and early weaning; and *t*_{BI0} = 94% to be more effective than the combination of prenatal short-course zidovudine and early weaning. If *R* > 1.5, any intervention (including postnatal antiretroviral prophylaxis) that increases survival to age 5 years would be more effective than early weaning as a single intervention, because early weaning causes deaths in this range of *R*.

If *R* < 1.5, even a postnatal antiretroviral intervention that is 100% effective in reducing HIV transmission through breastfeeding cannot increase survival to age 5 years more than prenatal short-course zidovudine combined with avoidance of breastfeeding or intrapartum and neonatal short-course nevirapine together with avoidance of breastfeeding. At *R* = 1.5, *t*_{BI0} = 50% for postnatal antiretroviral prophylaxis to surpass the effectiveness of avoidance of breastfeeding as a single intervention; this *t*_{BI0} declines with *R* > 1.5, and reaches 0% when *R* > 1.9. That is, if *R* > 1.9, any intervention (including postnatal antiretroviral prophylaxis) that increases survival to age 5 years would be more effective than avoidance of breastfeeding as a single intervention, because avoidance of breastfeeding causes deaths in this range of *R*.

For the same reason, any intervention (including postnatal antiretroviral prophylaxis) that increases survival to age 5 years would be more effective than (1) avoidance of breastfeeding in combination with intrapartum and neonatal short-course nevirapine if *R* > 2.2; and (2) avoidance of breastfeeding in combination with prenatal short-course zidovudine if *R* > 2.4.

#### Discussion

Recently developed interventions to prevent MTCT of HIV have led to drastic reductions in perinatal infections in industrialized countries [^{14,15}] and to the hope of similar achievements in countries with intermediate and developing economies. In developed countries, avoidance of breastfeeding has been recommended for HIV-infected mothers since 1985 [^{16}] because replacement feeding is safe and affordable and tends not to be stigmatizing.

However, avoidance of breastfeeding or early weaning as an intervention poses a dilemma in regions with intermediate and developing economies where hygienic replacement feeding is more difficult. Although one-third to one-half of MTCT of HIV in these regions may be through breast milk [^{6}], breastfeeding also provides immunologic protection and ideal nutrition to the infant, and helps new mothers delay subsequent pregnancy. Additionally, although avoidance of breastfeeding or early weaning can eliminate or reduce HIV transmission, replacement feeding, if not hygienic, can dramatically increase morbidity and mortality from diarrheal diseases and respiratory infections [^{17}]. Balancing the positive and negative effects of avoidance of breastfeeding and early weaning is thus a critical consideration.

We present a tool that can help decision-makers explore key questions about the relative effectiveness of antiretroviral and infant feeding interventions for prevention of MTCT of HIV. This model expands on decision models developed before the advent of antiretroviral therapies [^{18,19}], and on one more recent modeling exercise that addressed only infant feeding interventions [^{20}].

The model presented here indicates that for HIV-exposed children in settings where *R* < 1.9, the combination interventions that include avoidance of breastfeeding with prenatal short-course zidovudine or intrapartum and neonatal short-course nevirapine prevent the greatest numbers of deaths. For settings in which replacement feeding is less safe, the interventions that include avoidance of breastfeeding can actually result in more deaths (even after accounting for prevented deaths from HIV infection) than would no intervention. This net negative effect occurs when *R* > 1.9 for avoidance of breastfeeding as a single intervention, when *R* > 2.3 for intrapartum and neonatal short-course nevirapine with avoidance of breastfeeding, and when *R* > 2.4 for prenatal short-course zidovudine with avoidance of breastfeeding.

The advantages of breastfeeding during the first few months of life have been well documented [^{20–24}]. A pooled analysis has shown that these benefits decline steadily as the infant gets older [^{13}]. Early weaning has been proposed as a way to maximize these benefits and minimize the risk of HIV infection. However, new evidence indicates that 75% of HIV transmission through breast milk occurs before 6 months of age [^{6,25}], the currently accepted age for early weaning. As with avoidance of breastfeeding, early weaning exposes children to the risks associated with replacement feeding, but unlike avoidance of breastfeeding, early weaning may result in some postnatal HIV transmission.

Our results show that when *R* < 1.5, avoidance of breastfeeding and combinations of antiretroviral prophylaxis and avoidance of breastfeeding result in better survival to age 5 years than would early weaning and combinations of antiretroviral prophylaxis with early weaning. As is true with avoidance of breastfeeding, the benefits of early weaning are greater when the relative risk of mortality is low (when *R* < 1.5). When *R* > 1.5, early weaning as a single intervention can result in more deaths than would no intervention. This net negative effect on survival was also observed for intrapartum and neonatal short-course nevirapine combined with early weaning at *R* > 2.4 and for prenatal short-course zidovudine combined with early weaning at *R* > 2.7.

It is important to note that avoidance of breastfeeding and early weaning may be made safer (*R* can be reduced) by ensuring access to clean water, training mothers to properly prepare, store and feed breast milk substitutes, and reinforcing what they have learned [^{26}]. If the risks associated with avoidance of breastfeeding and early weaning could be reduced (i.e. to *R* < 1.5) in what are currently considered high-risk settings for these interventions, either might be more worth considering as part of the strategy to prevent MTCT of HIV. However, infant feeding interventions should not be chosen nor implemented before carefully evaluating and developing plans for ongoing monitoring of the degree to which replacement feeding can be safeguarded, and the potential for discrimination against mothers who do not breastfeed.

The HIV risk-reduction benefits associated with replacement feeding might be retained as well as the benefits of breastfeeding if an effective postnatal antiretroviral intervention is developed that is implementable and effective in the presence of breastfeeding. Investigations of such prophylaxis regimens of zidovudine and nevirapine are being conducted among HIV-exposed infants in Ethiopia, South Africa and Zimbabwe. As our results indicate, postnatal antiretroviral prophylaxis may surpass interventions including avoidance of breastfeeding, depending on *R* and on how much prophylaxis reduces the probability of HIV transmission through breastfeeding; postnatal antiretroviral prophylaxis would be more effective than early weaning as a single intervention, at any *R*, if it reduced this probability by 25%.

The model illustrated here is not intended to be used as the sole basis for policy decisions, primarily because the relevant *R* (the mortality ratio among breastfed and non-breastfed HIV-uninfected children whose mothers are participating in a program to prevent MTCT of HIV) is difficult to know until the MTCT prevention program has started. Rather, it can be used, along with other information (such as the baseline *R* and whether the recommended conditions for the safe practice of replacement feeding are present [^{27}]), to explore whether the level of *R* needed to meet prevention program goals, with a specific intervention, might be achievable locally. If it appears unlikely that *R* can be reduced to less than 1.5, early weaning alone and combinations of antiretroviral interventions with early weaning should be avoided. Likewise, if it appears unlikely that *R* can be reduced to less than 1.9, antiretroviral interventions with breastfeeding would be preferred over avoidance of breastfeeding and combinations of antiretroviral interventions with avoidance of breastfeeding.

In countries participating in the initiative to prevent MTCT of HIV sponsored by UNICEF, UNAIDS, and WHO, HIV-infected women are empowered to make an informed choice about whether to breastfeed or use breast milk substitutes, and breast milk substitutes are being made available to women who choose them. At these MTCT prevention initiative sites, there is ongoing monitoring of these women and their infants, compared with a similar cohort who have chosen to breastfeed. This monitoring process should provide real-time estimates of *R*, which can be used in conjunction with our model to evaluate whether the intervention strategy chosen is appropriate to the setting, or whether an alternative intervention strategy might be more effective. The precision of the estimates of *R* will vary according to the number of mother–child pairs observed, and our model is clearly sensitive to small variations in *R*. Therefore, we recommend that interpretation of the results of the model take into account the precision of the estimate of *R* (as measured by the 95% confidence interval).

Several of our simplifying assumptions may not reflect the complexity of HIV transmission from mothers to infants. For the interventions to be applied in the presence of breastfeeding, we assumed that breastfeeding was exclusive. There is suggestive evidence that non-exclusive breastfeeding may increase the risk of HIV transmission.[^{28}] We also assumed full acceptance of and adherence to all interventions. In the interest of brevity, we do not include sensitivity analyses reflecting these variations in acceptance and adherence, but they can be done by modifying either the proportion breastfed (*B*) or the transmission rate affected by the intervention (*T*_{BI} or *T*_{PI} ) according to the degree of acceptance and adherence.

We have illustrated use of the model presented here for a setting with characteristics representative of many countries in the developing world. The model can be adapted to other settings by modifying input parameters, specifically *M*_{B+} and the range of *R*. Finally, for decision-making about interventions, cost-effectiveness will be an important consideration. The output from our model (prevented deaths) might be used in a cost-effectiveness analysis.

We have presented a simple, locally adaptable spreadsheet model for use in evaluating the effectiveness of various interventions and combinations of interventions to prevent MTCT of HIV. In choosing an intervention strategy, local decision-makers must also take into consideration cost, adherence to and acceptance of various interventions in the target population, and the likelihood that a given intervention can be delivered at the appropriate time. (If most women do not come for prenatal care, an intervention such as prenatal short-course zidovudine may not be feasible.) This analysis emphasizes the theoretical usefulness of an antiretroviral regimen that can be administered to a breastfeeding infant, especially when compared with early weaning.

#### Acknowledgements

The authors would like to thank Alan Greenberg and John Karon for their careful review of this manuscript. John Karon is also acknowledged for his assistance with confidence interval estimation.