Visualising statistical models using dynamic nomograms

Abstract

Translational Statistics proposes to promote the use of Statistics within research and improve the communication of statistical findings in an accurate and accessible manner to diverse audiences. When statistical models become more complex, it becomes harder to evaluate the role of explanatory variables on the response. For example, the interpretation and communication of the effect of predictors in regression models where interactions or smoothing splines are included can be challenging. Informative graphical representations of statistical models play a critical translational role; static nomograms are one such useful tool to visualise statistical models. In this paper, we propose the use of dynamic nomogram as a translational tool which can accommodate models of increased complexity. In theory, all models appearing in the literature could be accompanied by the corresponding dynamic nomogram to translate models in an informative manner. The R package presented will facilitate this communication for a variety of linear and non-linear models.

Conflict of interest statement

The authors have declared that no competing interests exist.

Figures

Fig 1. A nomogram to calculate the p-value for a chi-square test statistic [10].

To use the nomogram draw a straight line from the value of the chi-square test statistic through the required degrees to read off the corresponding p-value.

Fig 2. Nomograms for calculating the probability of surviving the Titanic disaster using the rms package.

A logistic regression model containing age, sex and passenger class as main effects is displayed on top while a model including all their two-way interactions is shown at the bottom.

Fig 3. Colour-based nomogram representing the probability of surviving the Titanic disaster in the main effect model using the VRPM package.

Fig 4. Dynamic nomogram of the logistic model with all three-way interactions fitted to the Titanic data using DynNom function.

The plot represents survival probability (with 95% confidence interval) of 30-year-old females with different ticket classes. The actual explanatory values and their corresponding predictions are given in the ‘Numerical Summary’ tab in S1 Fig, and the ‘Model Summary’ tab is provided in S2 Fig.

Fig 5. Dynamic nomogram for a Poisson regression model fitted to the crabs data.

The plot displays the predicted number of additional male partners of female crabs of 24, 28 or 32 centimetres width of either dark or light colour. The actual explanatory values/levels and predictions are given in the ‘Numerical Summary’ tab in S3 Fig.

Fig 6. Relationships between the square root of ragweed level and the other variables.

Fig 7. Dynamic nomogram for a regression model with a smoothing spline fitted to the ragweed data.

The plot displays the predicted response for ‘day in season’ set at 1, 11, 21, 31, 41, 51, 61, 71, 81 and 91 respectively while fixing all other explanatory variables at the mean/mode as appropriate. The actual explanatory values/levels and predictions are given in the ‘Numerical Summary’ tab in S4 Fig.

Fig 8. Dynamic nomogram for the Cox proportional hazards model fitted to the lung cancer data.

The Kaplan-Meier plot displays survival curves correspond to 55 and 60 years old males/females (ECOG and weight loss set at their mean). The predicted survival time (with 95% confidence interval) at 250 days is given in the ‘Predicted survival’ tab (S5 Fig) and the actual explanatory values/levels and predictions are given in the ‘Numerical Summary’ tab (S6 Fig).