On monotonic models for clinical event predictions

Predictors of clinical event rates frequently employ a monotonicmodel, such as exponential, logistic or linear, fitted on cohortdatasets. Baseline measurements are used asindependent variables and the rate of events observed later are thedependent variabile. Such models assume a monotonic relationshipbetween the dependent and each of the indepedendent variables. However, in observational studies, this relationship is often`U-shaped' for parameters such as concentrations of bloodconstituents, arterial pressure or body mass index. Most of these havean optimal physiologic range, outside of which pathological phenomenaoccur. To provide an example, we calculated the univariate relationshipbetween blood cholesterol and systolic blood pressure with the SCORE2predictions, which is monotonic when all other parameters are keptconstant. We compared it with the published results of large cohortstudies, where this relationship is U-shaped. We found a contrastingtendency between predicted and measured event rates for low non-HDLcholesterol or low systolic blood pressure. Similar differences might characterise other applications ofmonotonic regression for clinical event prediction. Parameteradjustments cannot reduce such differences as the model function willremain 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 thesubset of data with parameter configurations similar to the case ofinterest and the event rate observed in the subset is taken asprediction for the case. In conclusion, we stress the importance of the parameter range andspecific population subgroup specification for the application ofexisting monotonic prediction models. More complex functions, orcompletely different methods, may be needed in order to improveclinical event risk predictions.