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. 2015 Apr;68(4):426-34.
doi: 10.1016/j.jclinepi.2014.11.022. Epub 2014 Nov 29.

Nonlinear modeling was applied thoughtfully for risk prediction: the Prostate Biopsy Collaborative Group

Daan Nieboer  1 , Yvonne Vergouwe  2 , Monique J Roobol  3 , Donna P Ankerst  4 , Michael W Kattan  5 , Andrew J Vickers  6 , Ewout W Steyerberg  2 ; Prostate Biopsy Collaborative Group
Collaborators, Affiliations

Nonlinear modeling was applied thoughtfully for risk prediction: the Prostate Biopsy Collaborative Group

Daan Nieboer et al. J Clin Epidemiol. 2015 Apr.

Abstract

Objectives: We aimed to compare nonlinear modeling methods for handling continuous predictors for reproducibility and transportability of prediction models.

Study design and setting: We analyzed four cohorts of previously unscreened men who underwent prostate biopsy for diagnosing prostate cancer. Continuous predictors of prostate cancer included prostate-specific antigen and prostate volume. The logistic regression models included linear terms, logarithmic terms, fractional polynomials of degree one or two (FP1 and FP2), or restricted cubic splines (RCS) with three or five knots (RCS3 and RCS5). The resulting models were internally validated by bootstrap resampling and externally validated in the cohorts not used at model development. Performance was assessed with the area under the receiver operating characteristic curve (AUC) and the calibration component of the Brier score (CAL).

Results: At internal validation models with FP2 or RCS5 showed slightly better performance than the other models (typically 0.004 difference in AUC and 0.001 in CAL). At external validation models containing logarithms, FP1, or RCS3 showed better performance (differences 0.01 and 0.002).

Conclusion: Flexible nonlinear modeling methods led to better model performance at internal validation. However, when application of the model is intended across a wide range of settings, less flexible functions may be more appropriate to maximize external validity.

Keywords: Calibration; Discrimination; External validation; Internal validation; Nonlinear modeling; Prediction models.

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Conflict of interest statement

Conflicts of interest: The authors declare that they have no conflict of interest.

Figures

Figure 1
Figure 1
The association between PSA and the log-odds of cancer according to the different multivariable models. Prostate volume was set to 40 cm3. Linear: using linear terms; Log: using a logarithmic transformation; FP1: Fractional polynomial of degree 1; FP2: Fractional polynomials of degree 2; RCS3: restricted cubic splines with 3 knots; RCS5: restricted cubic splines with 5 knots.
Figure 2
Figure 2
The association between prostate volume and the log-odds of cancer according to the different multivariable models. PSA was set to 4 ng/ml. Linear: using linear terms; Log: using a logarithmic transformation; FP1: Fractional polynomial of degree 1; FP2: Fractional polynomials of degree 2; RCS3: restricted cubic splines with 3 knots; RCS5: restricted cubic splines with 5 knots.
See this image and copyright information in PMC

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