Response Surface Modeling and Optimization to Elucidate the Differential Effects of Demographic Characteristics on HIV Prevalence in South Africa

Abstract

In this study, a Central Composite Face Centered (CCF) design was employed to study the individual and interaction effects of demographic characteristics on the spread of HIV in South Africa. The demographic characteristics studied for each pregnant mother attending an antenatal clinic in South Africa, were mother's age, partner's age, mother's level of education and parity. HIV status of an antenatal clinic attendee was found to be highly sensitive to changes in pregnant woman's age and partner's age, using the 2007 South African annual antenatal HIV and syphilis seroprevalence data. Individually the pregnant woman's level of education and parity had no significant effect on the HIV status. However, the latter two demographic characteristics exhibited significant effects on the HIV status of antenatal clinic attendees in two way interactions with other demographic characteristics. Using HIV as the optimization objective, the following summary statistics were obtained, R2 = 0.99 and two-factor interactions (2FI) model F-value of 63.77. The model F-value of 63.77 implied the 2FI model was significant and there was only a 0.01% chance this model value could occur due to noise. The model 'Lack of Fit' value of 0.01 implied that the 'Lack of Fit' was not significant relative to the pure error and thus there was a 99.88% chance that this 'Lack of Fit' F-value could occur due to noise. An adeq. precision value of 25 was obtained, suggesting that this 2FI model could be used to navigate the design space. A 3D response surface plot indicated that the highest rate of HIV positive individuals was obtainable at the highest age of the pregnant women and lowest age of their partners.