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.