Comparative Study of the Application of Box Behnken Design (BBD) and Binary Logistic Regression (BLR) toStudy the Effect of Demographic Characteristics on HIV Risk in South Africa

In this study, a Box Behnken Design (BBD) and a Binary Logistic Regression (BLR) were applied to study the effects of demographic characteristics on the risk 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 (father’s age), mother’s level of education and parity. Using the 2007 South African antenatal seroprevalence data, the BBD design showed that HIV status of a pregnant woman was highly sensitive to changes to her age and educational level. These results were independently confirmed by the BLR model. Individually the father’s age and parity had no significant effect on the HIV status. However, the latter two demographic characteristics showed significant effects on the HIV risk in two way interactions with other demographic characteristics. The results from the BBD provided the following summary statistics, R2 = 0.99 and two-factor interactions (2FI) model F-value of 88.29. The latter value of 88.29 for the BBD 2FI model is significant with only a 0.01% chance that this value could be due to noise. An adeq.precision value of 31.33 was obtained for the BBD further confirming that the 2FI model could be used to navigate the experimental design space. Finally, the 3-D response surface plots of HIV risk against mother’s age and her education were created.