Development and evaluation of uncertainty quantifying machine learning models to predict piperacillin plasma concentrations in critically ill patients

Background: Beta-lactam antimicrobial concentrations are frequently suboptimal in critically ill patients. Population pharmacokinetic (PopPK) modeling is the golden standard to predict drug concentrations. However, currently available PopPK models often lack predictive accuracy, making them less suited to guide dosing regimen adaptations. Furthermore, many currently developed models for clinical applications often lack uncertainty quantification. We, therefore, aimed to develop machine learning (ML) models for the prediction of piperacillin plasma concentrations while also providing uncertainty quantification with the aim of clinical practice. Methods: Blood samples for piperacillin analysis were prospectively collected from critically ill patients receiving continuous infusion of piperacillin/tazobactam. Interpretable ML models for the prediction of piperacillin concentrations were designed using CatBoost and Gaussian processes. Distribution-based Uncertainty Quantification was added to the CatBoost model using a proposed Quantile Ensemble method, useable for any model optimizing a quantile function. These models are subsequently evaluated using the distribution coverage error, a proposed interpretable uncertainty quantification calibration metric. Development and internal evaluation of the ML models were performed on the Ghent University Hospital database (752 piperacillin concentrations from 282 patients). Ensuing, ML models were compared with a published PopPK model on a database from the University Medical Centre of Groningen where a different dosing regimen is used (46 piperacillin concentrations from 15 patients.). Results: The best performing model was the Catboost model with an RMSE and R-2 of 31.94-0.64 and 33.53-0.60 for internal evaluation with and without previous concentration. Furthermore, the results prove the added value of the proposed Quantile Ensemble model in providing clinically useful individualized uncertainty predictions and show the limits of homoscedastic methods like Gaussian Processes in clinical applications. Conclusions: Our results show that ML models can consistently estimate piperacillin concentrations with acceptable and high predictive accuracy when identical dosing regimens as in the training data are used while providing highly relevant uncertainty predictions. However, generalization capabilities to other dosing schemes are limited. Notwithstanding, incorporating ML models in therapeutic drug monitoring programs seems definitely promising and the current work provides a basis for validating the model in clinical practice

Parameter efficient neural networks with singular value decomposed kernels

Traditionally, neural networks are viewed from the perspective of connected neuron layers represented as matrix multiplications. We propose to compose these weight matrices from a set of orthogonal basis matrices by approaching them as elements of the real matrices vector space under addition and multiplication. Making use of the Kronecker product for vectors, this composition is unified with the singular value decomposition (SVD) of the weight matrix. The orthogonal components of this SVD are trained with a descent curve on the Stiefel manifold using the Cayley transform. Next, update equations for the singular values and initialization routines are derived. Finally, acceleration for stochastic gradient descent optimization using this formulation is discussed. Our proposed method allows more parameter-efficient representations of weight matrices in neural networks. These decomposed weight matrices achieve maximal performance in both standard and more complicated neural architectures. Furthermore, the more parameter-efficient decomposed layers are shown to be less dependent on optimization and better conditioned. As a tradeoff, training time is increased up to a factor of 2. These observations are consequently attributed to the properties of the method and choice of optimization over the manifold of orthogonal matrices

Context-aware deep learning with dynamically assembled weight matrices

Deep neural networks are static by nature, meaning they use a single set of parameters to process each data sample. However, for more complex and larger systems, for which samples can be obtained under a large variety of circumstances, a need for more dynamic networks that adapt to these variations seems apparent. To this end, the concept of context information and its integration in deep learning is considered. Contrary to current practices, that treat all modalities as equally informative to the decision process, contextual and feature information is considered to be vastly different in nature. A set of definitions and subsequent arguments are given in order to provide the necessary clarification regarding the interpretation of context with the purpose of using all information in a maximally efficient way. From this interpretation, a problem statement of context aware deep learning is constructed and consequently linked to its multiple model and transfer learning solutions. These solutions, however, are in-efficient since samples are spread across models. Based on the existence of this multiple model solution, a new approach, which integrates contextual information directly into a single context-dependent model, is proposed. This single model uses weight matrices that are dynamically assembled based on the contextual information to process each data sample individually. This allows for the single model to consume and learn from all samples. The corresponding training routine is constructed and evaluated on multiple benchmark problems. We start with an artificially generated problem on which the methods' ability to model multiple linear classification problems concurrently is confirmed. Next, both a time series forecasting and image classification dataset are used for evaluation. Evaluations of our proposed method are done and compared to standard context aware implementations based on concatenation and gating. These standard methods implement context information by adding additional parameters in order to try modeling all interactions between the context information and the samples. However, our proposed approach integrates the contextual information directly into the network weights, allowing parameter efficient modeling of dynamic contextual behavior. In both cases the proposed solution outperforms its standard counterparts with significant margins in both evaluation metrics and parameter efficiency. Specifically, a mean absolute error improvement of eleven standard deviations and an eight percent increase in classification accuracy, for the forecasting and image classification problems respectively, is observed, showing the potential of our approach

Evolution of Plant Defense Mechanisms RELATIONSHIPS OF PHENYLCOUMARAN BENZYLIC ETHER REDUCTASES TO PINORESINOL-LARICIRESINOL AND ISOFLAVONE REDUCTASES

Pinoresinol-lariciresinol and isoflavone reductase classes are phylogenetically related, as is a third, the so-called "isoflavone reductase homologs," This study establishes the first known catalytic function for the latter, as being able to engender the NADPH-dependent reduction of phenylcoumaran benzylic ethers, Accordingly, all three reductase classes are involved in the biosynthesis of important and related phenylpropanoid-derived plant defense compounds. In this investigation, the phenylcoumaran benzylic ether reductase from the gymnosperm, Pinus taeda, was cloned, with the recombinant protein heterologously expressed in Escherichia coli, The purified enzyme reduces the benzylic ether functionalities of both dehydrodiconiferyl alcohol and dihydrodehydrodiconiferyl alcohol, with a higher affinity for the former, as measured by apparent K-m and V-max values and observed kinetic H-3-isotope effects. It abstracts the 4R-hydride of the required NADPH cofactor in a manner analogous to that of the pinoresinol-lariciresinol reductases and isoflavone reductases. A similar catalytic function was observed for the corresponding recombinant reductase whose gene was cloned from the angiosperm, Populus trichocarpa. Interestingly, both pinoresinol-lariciresinol reductases and isoflavone reductases catalyze enantiospecific conversions, whereas the phenylcoumaran benzylic ether reductase only shows regiospecific discrimination. A possible evolutionary relationship among the three reductase classes is proposed, based on the supposition that phenylcoumaran benzylic ether reductases represent the progenitors of pinoresinol-lariciresinol and isoflavone reductases