On the Use of Fractional Polynomial (FP) Models to Assess Preventive Aspect of Variables: an Example in Prevention of Mortality Following HIV infection

Abstract

Background: Identification of disease risk factors can help in the prevention of diseases. In assessing the predictive value of continuous variables, a routine procedure is to categorize the factors. This yield to inability to detect non‑linear relationship, if exist. Multivariate fractional polynomial (MFP) modeling is a flexible method to reveal non‑linear associations. We aim to demonstrate the impact of choice of risk function on the significance of variables.

Methods: We selected 6508 HIV‑infected persons registered in the Australia National HIV Registry between 1980 and 2003 to assess the predictors associated with the risk of death after HIV infection prior to AIDS. First, CD4 count as a categorical factor with three other categorical variables (age, sex, and HIV exposure category) was entered into the Cox regression model. Second, CD4 counts as a continuous variable along with other categorical variables were entered into the fractional polynomial (FP) model.

Results: Both the Cox and FP models showed age ≥ 40 years and hemophiliac patients were significantly associated with increased risk of death. In the categorized model, the CD4 variable did not reach the significance level. However, this variable was highly significant in the MFP model. The FP model showed slightly better performance in terms of discrimination ability and goodness of fit.

Conclusions: The FP model is a flexible method in detecting the predictive effect of continuous variables. This method enhances the ability to assess the predictive ability of variables and improves model performance.

Keywords: Continuous variables, fractional polynomial, HIV/AIDS, Modeling