Figure 8l.

Discussion

Haematotoxic side effects of cytotoxic chemotherapy are common but its severity is highly heterogeneous across patients. Intelligent strategies for individualized treatment decisions are required to optimize anti-cancer effect but limit toxicity to an acceptable level at the same time. However, predicting haematotoxic side effects on an individual level is a difficult task due to the underlying complex non-linear interactions of damaging and stimulating effects during cytotoxic drug treatment accompanied by a rapid turn-over of blood cells. Thus, sophisticated prediction models are required to capture essential biological features of these processes.
In the present paper, we compared the predictive potential of two dynamical models of thrombocytopoiesis under chemotherapy proposed in the literature, a semi-mechanistic model developed for general hematopoiesis and a more comprehensive model specifically developed for thrombocytopoiesis developed by us which also considers mechanisms of the bone marrow niche interaction .
Until recently, Friberg’s semi-mechanistic model was the only one applied to individual patient’s data to a larger extent . Based on a Bayesian a posteriori- approach, it was used for example to develop neutrophil-guided dose adaptations for etoposide and a respective computer tool was proposed . Sandström et al and Wallin et al treated IOV as a random effect affecting individual parameters which could not explain accumulating haematotoxicity. To improve this situation, Henrich et al recently introduced a slow bone-marrow exhaustion to the Friberg model. However other long range effects such as TPO activation of stem cells observed in animals as well as long-range effects on human megakaryocytes can make platelets dynamics much more complex and individually diverse implying necessity of more refined individualized mechanistic models of haematopoiesis.
Indeed, we found that our mechanistic model clearly outperforms the semi-mechanistic model regarding prediction of individual cycle toxicities especially in case of irregular platelet responses which are common for more intense chemotherapy regimens supported by growth-factor applications such as G-CSF. Combination of slow bone-marrow exhaustion with delayed TPO effects can result in a range of complex dynamical patterns, especially for short treatment cycles insufficient to fully replenish haematopoiesis. Our mechanistic model of bone marrow exhaustion is based on the observation that osteoblasts are depleted during multi-cycle chemotherapy . This aspect contributes to the better predictive power of the mechanistic model.
To fit this comprehensive model on individual level data, we applied the principle of “virtual participation”, which is superior to standard mixed-model analyses since it allows exploiting external data sets to re-inforce the learning of individual parameters. This approach is novel in the field since most of PK/PD modellers do not use prior information from other studies but fit exclusively clinical data of interest . Heterogeneity is then addressed by mixed effects modeling where parameters estimation is based on likelihood maximization for the entire population. In this case, assessment of algorithm’s convergence and overfitting are controlled exclusively for population parameters determining the distributions of individual parameters. Consequently, mixed effects modeling derives individual parameter estimates as a by-product implying high probability of insufficient fitting quality for a significant number of subjects. Moreover, pre-assumptions on the parameter distributions could spoil individual fits as well. This limits the usefulness of these methods to develop individualized therapy predictions. In contrast, our approach maximizes individual fitting precision without making any pre-assumptions on the underlying parameter distributions. We controlled convergence of fitting algorithm and reported standard errors on an individual level. We believe that such an individualized control of goodness of fit is more appropriate for the purpose of individualized treatment management than classical mixed effects modelling.
It is of high practical importance to compare the predictive power of models of different complexity since more complex models usually have more parameters, and with it, are more prone to over-fitting. Indeed, numbers of parameters with assumed IIV differed between the models and was determined on the basis of an identifiability analysis. Since the mechanistic model uses external data to stabilize parameter estimation, more individual parameters could be estimated for it.
Our proposed comparison framework is based on the prediction performance of next-cycle toxicities using individual parameter sets derived from individual blood counts observed so far. This situation is close to clinical practice where physicians have to decide upon treatment continuation after completion of a chemotherapy cycle. We used real patient data for our comparison but needed to restrict the analysis to patients with a sufficient number of observations per cycle, which are not commonly available in clinical practice though.
Models are fitted to data aiming at improving the agreement with observed thrombocytopenia grades. We used this approach to account for the fact that the degree of thrombopoenia is typically considered for clinical decision making. In contrast, agreement of model and data for large platelet counts is of lesser clinical utility. To achieve this goal, we introduced a novel transformation of platelets counts which continuously interpolates between thrombocytopenia grades. This transformation is characterized by an increased importance of correctly fitting low thrombocytopenia degrees as described in Supporting information S.4. The same fitness function was used for calibrating both models.
For comparisons of the predictive performance of our models, we defined two scores DD and LDD. Both measured deviations of predicted and observed degrees of thrombocytopenia, but the latter only counts deviations of more than one degree which is supposed to be of high clinical relevance. DD depended less than LDD on the number of cycles used for model calibration. We also determined the Youden index for the prediction of severe grade 3-4 thrombopoenia. It revealed that the MM outperforms the SMM irrespective of the evaluation function (DD, LDD, Youden index). Of note, the MM calibrated with only one cycle typically outperformed the SMM calibrated with a higher number of cycles except for highly unbalanced situations (e.g. where the SMM is calibrated on five cycles). The difference between models is less pronounced, when using standard errors of platelet counts as goal function (see supplement Figure S.6.1 in Supporting information S.6). This can be explained by the fact that the majority of data points are from periodic oscillations which are easy to capture by both models. However, for clinical utility it is much more important that critically low values are correctly predicted explaining our choice of goal functions.
We showed that regression analysis of clinical factors can be used to some extent to derive individual parameter estimates, e.g. when no platelet dynamics are not available. However, the predictive performance of these parameters is inferior compared to those obtained after calibrating the models to platelet data.

Conclusion

We conclude that our mechanistic model has superior predictive power regarding next cycle thrombotoxicity compared to the semi-mechanistic model proposed by Henrich et al. Time series data of only one cycle are required to achieve sufficiently accurate predictions of next-cycle toxicity. Based on our model, we developed a tool intended to support clinical decision making regarding next-cycle management in dependence on the individual therapy response . A prototype can be found elsewhere: (https://www.health-atlas.de/shiny-public/apps/thrombopenia/). We plan to assess its clinical utility in the future.