On monotonic models for clinical event predictions

Predictors of clinical event rates frequently employ a monotonic
model, such as exponential, logistic or linear, fitted on cohort
datasets. Baseline  measurements are used as
independent variables and the rate of events observed later are the
dependent variabile. Such models assume a monotonic relationship
between the dependent and each of the indepedendent variables.

However, in observational studies, this relationship is often
`U-shaped' for parameters such as concentrations of blood
constituents, arterial pressure or body mass index. Most of these have
an optimal physiologic range, outside of which pathological phenomena
occur.

To provide an example, we calculated the univariate relationship
between blood cholesterol and systolic blood pressure with the SCORE2
predictions, which is monotonic when all other parameters are kept
constant. We compared it with the published results of large cohort
studies, where this relationship is U-shaped. We found a contrasting
tendency between predicted and measured event rates for low non-HDL
cholesterol or low systolic blood pressure.

Similar differences might characterise other applications of
monotonic regression for clinical event prediction. Parameter
adjustments cannot reduce such differences as the model function will
remain monotonic irrespective of its parameters.

As a possible aproach to this issue, we suggest the development of a
``direct predictor'' where a cohort dataset is used to select the
subset of data  with parameter configurations similar to the case of
interest and the event rate observed in the subset is taken as
prediction for the case.

In conclusion, we stress the importance of the parameter range and
specific population subgroup specification for the application of
existing monotonic prediction models.  More complex functions, or
completely different methods, may be needed in order to improve
clinical event risk predictions.