Method for modelling the number of HIV and AIDS cases using least square spline Biresponse nonparametric negative binomial regression

We propose a new statistical modeling method to analyze functional relationship between predictor variables and correlated response variables, and apply it for modeling the number of HIV and AIDS cases influenced by early-age marriages and contraceptive users. The proposed method is LS-Spline BNNBR that is a Biresponse Nonparametric Negative Binomial Regression (BNNBR) based on least squares spline (LS-Spline). To validate the proposed method, we compare it with classical method, namely Ordinary Least Square Biresponse Parametric Negative Binomial Regression (OLS-BPNBR). The results show that the LS-Spline BNNBR method provided deviance value of 7.542334 which is smaller than that of OLS-BPNBR method, namely 7.993935. Thus, the proposed method has better prediction fit than the classical method.•This study discusses new statistical modeling method for the number of HIV and AIDS cases influenced by early-age marriages and contraceptive users where the response variables are correlated with each other.•The model estimation results show that the number of HIV and AIDS cases in Indonesia will decrease if the early-age marriages percentage increases and the contraceptive users percentage decreases.•The results are useful to provide a scientific basis for making policies to control the number of HIV and AIDS cases in Indonesia.