Empirical methods for the validation of time-to-event mathematical models taking into account uncertainty and...

Over the past several decades, metrics have been defined to assess the quality of various types of models and to compare their performance depending on their capacity to explain the variance found in real-life data. However, available validation methods are mostly designed for statistical regressions rather than for mechanistic models. To our knowledge, in the latter case, there are no consensus standards, for instance for the validation of predictions against real-world data given the variability and uncertainty of the data. In this work, we focus on the prediction of time-to-event curves using as an application example a mechanistic model of non-small cell lung cancer. We designed four empirical methods to assess both model performance and reliability of predictions: two methods based on bootstrapped versions of parametric statistical tests: log-rank and combined weighted log-ranks (MaxCombo); and two methods based on bootstrapped prediction intervals, referred to here as raw coverage and the juncture metric. We also introduced the notion of observation time uncertainty to take into consideration the real life delay between the moment when an event happens, and the moment when it is observed and reported.

We highlight the advantages and disadvantages of these methods according to their application context. We have shown that the context of use of the model has an impact on the model validation process. Thanks to the use of several validation metrics we have highlighted the limit of the model to predict the evolution of the disease in the whole population of mutations at the same time, and that it was more efficient with specific predictions in the target mutation populations. The choice and use of a single metric could have led to an erroneous validation of the model and its context of use.

With this work, we stress the importance of making judicious choices for a metric, and how using a combination of metrics could be more relevant, with the objective of validating a given model and its predictions within a specific context of use. We also show how the reliability of the results depends both on the metric and on the statistical comparisons, and that the conditions of application and the type of available information need to be taken into account to choose the best validation strategy.