Download Appendix For four Sub-Saharan African countries (Ghana, Lesotho

Appendix
For four Sub-Saharan African countries (Ghana, Lesotho, Malawi, and Rwanda) we use
mathematical modeling and empirical data to estimate the effect of treating discordant
couples on: (i) the annual HIV incidence rate and (ii) the annual number of infections
prevented (IP).
All of the models’ parameters are defined in Table S1; this Table also includes the
parameter values used to predict the impact of an intervention based on treating
discordant couples to prevent transmission in Ghana, Lesotho, Malawi, and Rwanda.
(i) Estimating the effect of treating discordant couples on the annual HIV
incidence rate
To estimate the reduction in the incidence rate due to treating discordant couples to
prevent transmission, we first estimated the overall incidence rate; i.e., the number of
new infections occurring in both stable couples and in short-term partnerships. We used
the model of Coburn et al.S1 to make estimates for Ghana, Lesotho, Malawi, and
Rwanda.
1. For stable discordant couples their incidence rate ( X c ) is determined by the
equation: X c   dc / 2 , where  d represents the proportion of stable couples
that are discordant and c represents the probability of HIV transmission
within a discordant couple. The parameter  d is estimated using data from
EwayoS2 (Table S2). The parameter c is estimated using the relationship
c  1  (1   )N , where
 represents the per act transmission probability and
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N represents the per capita annual number of sex acts. We set c to be 0.10,
assuming
 is 0.001 and N is 104.
2. For individuals in short-term partnerships their incidence rate ( X n ) is
determined by the equation: Xn  (1  an )n . The parameter a n represents the
prevalence of HIV in individuals who have short-term partnerships;
consequently ( 1  an ) represents the proportion of uninfected individuals that
are in short-term partnerships. The parameter n represents the probability of
transmission within a short-term partnership and is estimated using the
relationship n  1  (1   )a N . We use the same parameter values as for
n
stable couples for
 and N ; i.e.,  = 0.001 and N = 104. To estimate the
value of a n we used dataS3 on country-level prevalence ( A ) and the
equation: A  qac  (1  q)an , where q represents the proportion of the
population that is in stable couples and ac represents the prevalence of HIV
in stable couples. HIV prevalence in stable couples is given by the equation:
ac      d / 2 ; which we calculated using data from EwayoS2. We specified
values for q of 0.4 and 0.7 by assuming that 40% or 70%, respectively, of the
population are in stable couples.
3. We then estimated (for each of the four countries) the annual HIV incidence
rate (  ) using the expression: qXc  (1  q)Xn . This expression reflects the
annual incidence rate as a weighted average of the incidence rate in stable
couples and the incidence rate in short-term partnerships; the weight is the
proportion of individuals in these two groups (i.e., q and 1  q , respectively).
We then derived an expression for the annual HIV incidence rate (  ) that includes the
effect of an intervention based on treating discordant couples to prevent transmission:
(c)  (1  c   )qXc  (1  q)Xn .
where c represents treatment coverage (i.e., proportion of discordant couples that
receive ART to prevent transmission), and
 represents the protective efficacy of
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treatment in protecting against HIV infection. To make our calculations we set
 to be
0.96 (as in the HPTN 052S4 Study) and varied treatment coverage from 0% to 100%;
results shown in Table S3.
(ii) Estimating the number of IP by treating discordant couples to prevent
transmission
To estimate the annual number of IP, we first estimated the annual number of infections
that occur per year due to transmission in discordant couples. We made these
estimates for Ghana, Lesotho, Malawi, and Rwanda by:
1. Calculating, using demographic data from the World Health OrganizationS5
and from the Measure Demographic and Health SurveysS6 (data are
shown in Table 1 in the main text), the number of individuals in each of the
four countries that are between 15-49 years old.
2. Determining the number of individuals that are in couples, by assuming
that between 40% to 70% of the population (aged 15-49 years old) is in
stable couples.
3. Using data for Ghana, Lesotho, Malawi, and Rwanda from Ewayo et al.S2,
we classified couples into three groups based on their HIV serostatus:
concordant negative, concordant positive or serodiscordant. We denote
these three groups by   ,   , and  d , respectively. Results are shown in
Table 1 in the main text (in terms of numbers of individuals), and as
percentages in Table S2.
4. Estimating the probability of HIV transmission within a discordant couple
( c ) using the relationship c  1  (1   )N , where
 represents the per
act transmission probability and N is the per capita annual number of sex
acts. We estimate c to be 0.10, assuming
 is 0.001 and N is 104.
5. Estimating the annual number of infections that occur per year due to
transmission in discordant couples by multiplying c by the number of
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uninfected individuals in discordant couples. Note, the number of
uninfected individuals in serodiscordant couples is half of the population in
these partnerships.
We determined the number of infections prevented from a discordant couples treatment
intervention by multiplying the total number of infections in discordant couples by c   .
To make our calculations, we set
 to be 0.96 and vary treatment coverage from 0% to
100%; results are shown in Table S4.
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References
S1. Coburn BJ, Gerberry DJ, Blower S. Quantification of the role of discordant couples
in driving incidence of HIV in sub-Saharan Africa. Lancet Infect Dis 2011;11:263-4.
S2. Eyawo O, Walque Dd, Ford N, Gakii G, Lester RT, Mills EJ. HIV status in
discordant couples in sub-Saharan Africa: a systematic review and meta-analysis. The
Lancet Infectious Diseases 2010;10:770-7.
S3. The World Bank. World Development Indicators. 2009. (Accessed January, 24
2011, at http://data.worldbank.org/data-catalog/world-development-indicators)
S4. NIH News: Treating HIV-infected People with Antiretrovirals Protects Partners from
Infection. (Accessed May 12, 2011, at
http://www.niaid.nih.gov/news/newsreleases/2011/Pages/HPTN052.aspx)
S5. The World Health Organization (WHO). Country Profiles., 2011. (Accessed May 29,
2011, at http://www.who.int/countries/en/)
S6. Measure Household and Demographic Surveys. Calverton, MD. Measure DHS.
ICF Macro, 2011. (Accessed at http://www.measuredhs.com)
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Table S1. Model parameters: descriptions and values. The upper panel shows a list
of the symbol and description for each of the models’ parameters. The lower panel
provides the parameter values used for Lesotho, Malawi, Rwanda and Ghana.
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Table S2. Percent of couples classified by serostatus for Lesotho, Malawi,
Rwanda and Ghana. The percentages were determine from demographic and health
surveysS6. The table is based on data presented by Eyawo et al.S2
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Table S3. The effect of an intervention based on treating discordant couples to
prevent infection as a function of treatment coverage. The upper panel shows the
annual incidence that would occur in the presence of an intervention. The lower panel
shows the percentage reduction in the incidence that would occur in the presence of an
intervention. Calculations are based on the assumption that 40% (shown by the lower
end of the range) or 70% (shown by the upper end of the range) of the population is in
stable partnerships; stable partnerships include concordant positive, concordant
negative and discordant couples.
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Table S4. Total number of infections prevented per year due to treating
discordant couples to prevent infection. Calculations are based on the assumption
that 40% (shown by the lower end of the range) or 70% (shown by the upper end of the
range) of the population is in stable partnerships; stable partnerships include
concordant positive, concordant negative and discordant couples.
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