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Improved ICU risk prediction modelling using a multivariable fractional polynomial approach


Mortality risk prediction models are used worldwide as a means of benchmarking ICU quality. Most models use logistic regression, with a cardinal assumption being linearity in the relationship between continuous predictors (for example, blood pressure) and the log odds of outcome (death). However, such linear relationships rarely exist in clinical practice. Several new statistical methods are available that allow nonlinear modelling for continuous predictors. We have applied one such method, multivariable fractional polynomials (MFP), to a paediatric ICU risk score (PIM2), to investigate whether this would improve the performance of PIM2.


All admissions to a single paediatric ICU over a 6-year period (2000–2006) were examined (n = 7,472, deaths = 380). PIM2 comprises 10 variables, of which three are continuous (base excess, systolic blood pressure, and FIO2/PO2); these were examined via a customised MFP macro [1] using SAS 9.1.


Application of the MFP approach resulted in improved model discrimination (c statistic = 0.843 versus 0.835 for the standard model), as well as excellent fit (Hosmer–Lemeshow P = 0.71). The MFP algorithm demonstrated a nonlinear relationship for all three continuous predictors, which also altered between the univariable and multivariable logistic models (Figure 1). A hitherto unsuspected interaction between blood pressure and 'high-risk' diagnostic category was revealed. Bootstrapping showed that similar nonlinear relationships were preserved across a range of datasets.

Figure 1
figure 1

Univariable (left) and multivariable (right) risk profile for base excess.


The MFP approach offers several advantages over linear modelling, both in model fit and a better elucidation of risk profiles for individual predictors. This requires confirmation in a national dataset.


  1. Multivariable Fractional Polynomial Approach[]

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Tibby, S., Durward, A. Improved ICU risk prediction modelling using a multivariable fractional polynomial approach. Crit Care 12 (Suppl 2), P486 (2008).

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