  Purpose: We propose a general framework for quantifying predictive
uncertainties of dose-related quantities and leveraging this information in a
dose mimicking problem in the context of automated radiation therapy treatment
planning.
  Methods: A three-step pipeline, comprising feature extraction, dose statistic
prediction and dose mimicking, is employed. In particular, the features are
produced by a convolutional variational autoencoder and used as inputs in a
previously developed nonparametric Bayesian statistical method, estimating the
multivariate predictive distribution of a collection of predefined dose
statistics. Specially developed objective functions are then used to construct
a probabilistic dose mimicking problem based on the produced distributions,
creating deliverable treatment plans.
  Results: The numerical experiments are performed using a dataset of 94
retrospective treatment plans of prostate cancer patients. We show that the
features extracted by the variational autoencoder capture geometric information
of substantial relevance to the dose statistic prediction problem and are
related to dose statistics in a more regularized fashion than hand-crafted
features. The estimated predictive distributions are reasonable and outperforms
a non-input-dependent benchmark method, and the deliverable plans produced by
the probabilistic dose mimicking agree better with their clinical counterparts
than for a non-probabilistic formulation.
  Conclusions: We demonstrate that prediction of dose-related quantities may be
extended to include uncertainty estimation and that such probabilistic
information may be leveraged in a dose mimicking problem. The treatment plans
produced by the proposed pipeline resemble their original counterparts well,
illustrating the merits of a holistic approach to automated planning based on
probabilistic modeling.
