Combined Impact of Sexual Risk Behaviors for HIV Seroconversion Among Women in Durban, South Africa: Implications for Prevention Policy and Planning

Abstract

The objective of this study was to estimate the joint impact of demographic and sexual risk behaviors on HIV acquisition. A total of 2,523 HIV seronegative women were recruited through three community based studies in Durban, South Africa. Point and interval estimates of partial population attributable risk (PAR) were used to quantify the proportion of HIV seroconversions which can be prevented if a combination of risk factors is eliminated from a target population. More than 80% of the observed HIV acquisitions were attributed to five risk factors: lack of cohabitation, frequency of sex, sexually transmitted infections (STIs), incidence of pregnancy and not being employed/no income. Structural factors such as minimizing migratory patterns by ensuring cohabitation of partners, access to treatment of STIs, income generation and safe sex negotiation skills are likely to play an important role in future prevention strategies.

Appendix

The PAR is formulated as a function of hazard ratio (HR) (s) and the prevalence (p)(s) of the risk factor(s). When there is only one risk factor at two levels (1 vs. 0)

$$ PAR = {\frac{p(HR - 1)}{p(HR - 1) + 1}} = 1 - {\frac{1}{{\sum\nolimits_{s = 1}^{2} {p_{s} HR_{s}}}}} $$

(1)

Where HR is the hazard ratios, p is the prevalence of the risk factor in the population and sindexes the two strata determined by the value of the risk factor. Equation 1 can be generalized to the multi-factorial setting when there are more than one risk factors at multiple levels, as

$$ PAR_{F} = {\frac{{\sum\nolimits_{s = 1}^{S} {} p_{s} (HR_{s} - 1)}}{{1 + \sum\nolimits_{s = 1}^{S} {} p_{s} (HR_{s}^{{}} - 1) + 1}}} = 1 - {\frac{1}{{\sum\nolimits_{s = 1}^{2} {p_{s} HR_{s}}}}} $$

(2)

where HR _s and p _s , s = 1,…, S, are the hazard ratios and the prevalences in the target population for the sth combination of the risk factors. Full PAR (PAR _F ) can be estimated by using Eq. 2 and interpreted as the percent reduction expected in the number of HIV seroconversion if all the known risk factors were eliminated from the target population.

In a multifactorial disease setting, at least some key risk factors such as age and sex are not modifiable. This limits the practical utility of the full PAR which is based on modification of all variables of interests. In an evaluation of a preventive intervention in a multifactorial disease setting, the interest is in the percent of cases associated with the exposures to be modified, when other risk factors, particularly non-modifiable, exist but do not change as a result of the intervention. Therefore we derived and used partial PAR which kept unmodifiable variable(s) unchanged.

Under the assumption of no interaction between the modifiable and non-modifiable risk factors of interest, the partial PAR(PAR _p ) is formulated as

$$ PAR_{p} = {\frac{{\sum\nolimits_{s = 1}^{S} {\sum\nolimits_{t = 1}^{T} {p_{st} HR_{1s} HR_{2t} - \sum\nolimits_{s = 1}^{S} {} \sum\nolimits_{t = 1}^{T} {p_{st} HR_{2t}}}}}}{{\sum\nolimits_{s = 1}^{S} {\sum\nolimits_{t - 1}^{T} {p_{st} HR_{1s} HR_{2t}}}}}} = 1 - {\frac{{\sum\nolimits_{t = 1}^{T} {p_{\bullet t} HR_{2t}}}}{{\sum\nolimits_{s = 1}^{S} {\sum\nolimits_{t = 1}^{T} {p_{st} HR_{1s} HR_{2t}}}}}} $$

(3)

where t denotes a stratum of unique combinations of levels of all background risk factors which are not modifiable and/or not under study, t = 1, …, T and HR _2t is the hazard ratio in combination t relative to the lowest risk level, where HR _{2, 1}=1. As previously, s indicates a risk factor defined by each of the unique combinations of the levels of the modifiable risk factors, that is, those risk factors to which the PAR _p applies, s = 1,…, S, and HR _1s is the relative risk corresponding to combinations relative to the lowest risk combination, HR _1,1 = 1. The joint prevalence of exposure group s and stratum tis denoted by p _st , and$p_{.t} = \Upsigma_{s = 1}^{S} p_{st}$. The PAR _p represents the difference between the number of cases expected in the original cohort and the number of cases expected if all subsets of the cohort who were originally exposed to the modifiable risk factor(s) had eliminated their exposure(s) so that their relative risk compared to the unexposed was 1, divided by the number of cases expected in the original cohort.

Derivation of the Variance of PAR

$$ \begin{aligned} Var(PAR_{p}) =& Var\left({{\frac{{\sum\nolimits_{t = 1}^{T} {p_{\cdot t} HR_{2t}}}}{{\sum\nolimits_{S = 1}^{S} {\sum\nolimits_{t = 1}^{T} {p_{st} HR}_{1s} HR_{2t}}}}}} \right) \\ &- Var(f({\varvec{p}},{\user2{HR}}_{{\user2{1}}},{\user2{HR}}_{{\mathbf{2}}})) \approx \left[{{\frac{{\partial f({\user2{p}},{\user2{HR}}_{{\mathbf{1}}},{\user2{HR}}_{{\user2{2}}})}}{{\partial {\user2{p}}}}}} \right]^{\prime} |_{p,HR} \\&\times Var({\user2{p}})\left[{{\frac{{\partial f\left({{\user2{p}},{\user2{HR}}_{{\mathbf{1}}},{\user2{HR}}_{{\mathbf{2}}}} \right)}}{{\partial {\user2{p}}}}}} \right]|_{p,HR} \\& + \left[{{\frac{{\partial f\left({{\user2{p}},{\user2{HR}}_{\mathbf1},{\user2{HR}}_{\mathbf2}} \right)}}{{\partial \left({{\user2{HR}^{\prime}}_{\mathbf1},{\user2{HR}^{\prime}}_{\mathbf2}} \right)}}}} \right]|_{{p,{\user2{RR}}}} \text{var} \left[{\left({{\user2{HR}^{\prime}}_{\mathbf1},{\user2{HR}^{\prime}}_{\mathbf2}} \right)^{\prime}} \right]\\ &\times \left[{{\frac{{\partial f\left({{\user2{p}},{\user2{HR}}_{\mathbf1},{\user2{HR}}_{\mathbf2}} \right)}}{{\partial \left({{\user2{HR}^{\prime}}_{\mathbf1},{\user2{HR}^{\prime}}_{\mathbf2}} \right)}}}} \right]|_{p,RR} \\ \end{aligned} $$

Where

$$ \begin{gathered} {\frac{{\partial f\left({{\varvec{p}},{\varvec{HR}}_{\mathbf1},{\varvec{HR}}_{\mathbf2}} \right)}}{{\partial p_{st}}}} = {\frac{{bHR_{2t} - aHR_{2t} HR_{1s}}}{{b^{2}}}} \hfill \\ {\frac{{\partial f\left({{\varvec{p}},{\varvec{HR}}_{\mathbf1},{\varvec{HR}}_{\mathbf2}} \right)}}{{\partial p_{1s}}}} = - {\frac{{a\sum\nolimits_{t = 1}^{T} {p_{st} HR_{2t}}}}{{b^{2}}}}, \hfill \\ {\frac{{\partial f\left({{\varvec{p}},{\varvec{HR}}_{\mathbf1},{\varvec{HR}}_{\mathbf2}} \right)}}{{\partial RR_{2t}}}} = {\frac{{bp_{\cdot t} - a\sum\nolimits_{s = 1}^{S} {p_{st} HR_{1s}}}}{{b^{2}}}} \hfill \\ a = \sum\nolimits_{t = 1}^{T} {p_{\cdot t} HR_{2t}, \, b = \sum\nolimits_{s = 1}^{S} {\sum\nolimits_{t = 1}^{T} {p_{st} HR_{1s} HR_{2t}}}} \hfill \\ \end{gathered} $$

where

$$ \sum\nolimits_{s} {p_{st} = p.t} $$

${\mathbf{HR}}_{1} = \left({HR_{1,1}, HR_{1,2}, \ldots, HR_{1,s}} \right)^{\prime}$ and ${\mathbf{HR}}_{ 2} = \left({HR_{2,1}, HR_{2,2}, \ldots, HR_{2,T}} \right)$ are the vectors of the hazard ratios corresponding to the modifiable and unmodifiable risk factors respectively. Under the proportional hazards model, $HR_{1s} = e^{{\beta^{\prime}_{1} x_{s} }}$ where $x_{s}$ is the vector of values of binary indicators corresponding to the sth combination of modifiable exposure variables, of which there are S combinations, and $HR_{2t} = e^{{\beta^{\prime}_{2} x_{t} }}$ where $x_{t}$ is the vector of values of the tth combination of unmodifiable background risk, of which there are T combinations.

The PAR estimates for individual risk factors and combination of risk factors based on a multiplicative model therefore the may total more than that 100%. Consequently, they can be interpreted as estimating the relative importance of individual and combination of risk factors.