Drug development is time consuming, expensive with high failure rates. It takes 10-15 years for a drug to go from discovery to approval, while the mean cost of developing a drug is $1.5 billions dollars. Pharmacometric models (PM) play a pivotal role in knowledge driven drug development and these models require validation prior to application. The purpose of the current study was to evaluate the posterior predictive check (PPC) and the bootstrap as population model validation tools. PPC was evaluated to determine, if it was able to distinguish between population pharmacokinetic (PPK) models that were developed/estimated from influence data versus models that were not derived/estimated from influence data. Bootstrap was examined to see if there was a correspondence between the root mean squared prediction errors (RMSPE) for serum concentrations when estimated by external prediction methods versus when estimated by the standard bootstrap. In the case of PPC, C last , C first -C last and C mid values from initial data sets were compared to corresponding posterior distributions. In the case of no influence data for C last , C first -C last and C mid on average 76%, 30% and 52% of the values from the posterior distributions were below the initial C last , C first -C last and C mid on average 93%, 13% and 67% of the values from the posterior distributions were below the initial C last , C first -C last and C mid respectively. PPC was able to classify models from influence versus no influence data. In the case of bootstrap when the original model was used to predict into the external data the WRMSPE for drug 1, drug 2, drug 3, drug 4 and simulated data set was 10.40 mg/L, 20.36 mg/L, 0.72 mg/L, 15.27 mg/L and 14.24 mg/L respectively. From the bootstrap the improved WRMSPE for drug 1 drug 2, drug 3, drug 4 and simulated data set was 9.35 mg/L, 19.85 mg/L, 0.50 mg/L, 14.44 mg/L and 13.98mg/L respectively. The bootstrap provided estimates of WRMSPE that corresponded to the external validation methods. From the results obtained, it was concluded that both the PPC and the Bootstrap were demonstrated to have value as validation tools.

<div>This dissertation addresses two significant issues in the effective application of machine learning algorithms and models for the physical and engineering sciences. The first is the broad challenge of automated modeling of data across different processes in a physical system. The second is the dilemma of obtaining insightful interpretations on the relationships between the inputs and outcome of a system as inferred from complex, black box machine learning models.</div><div><br></div><div><b>Automated Geometric Shape Deviation Modeling for Additive Manufacturing Systems</b></div><div><b><br></b></div><div>Additive manufacturing systems possess an intrinsic capability for one-of-a-kind manufacturing of a vast variety of shapes across a wide spectrum of processes. One major issue in AM systems is geometric accuracy control for the inevitable shape deviations that arise in AM processes. Current effective approaches for shape deviation control in AM involve the specification of statistical or machine learning deviation models for additively manufactured products. However, this task is challenging due to the constraints on the number of test shapes that can be manufactured in practice, and limitations on user efforts that can be devoted for learning deviation models across different shape classes and processes in an AM system. We develop an automated, Bayesian neural network methodology for comprehensive shape deviation modeling in an AM system. A fundamental innovation in this machine learning method is our new and connectable neural network structures that facilitate the transfer of prior knowledge and models on deviations across different shape classes and AM processes. Several case studies on in-plane and out-of-plane deviations, regular and free-form shapes, and different settings of lurking variables serve to validate the power and broad scope of our methodology, and its potential to advance high-quality manufacturing in an AM system.</div><div><br></div><div><b>Interpretable Machine Learning</b></div><div><b><br></b></div><div>Machine learning algorithms and models constitute the dominant set of predictive methods for a wide range of complex, real-world processes. However, interpreting what such methods effectively infer from data is difficult in general. This is because their typical black box natures possess a limited ability to directly yield insights on the underlying relationships between inputs and the outcome for a process. We develop methodologies based on new predictive comparison estimands that effectively enable one to ``mine’’ machine learning models, in the sense of (a) interpreting their inferred associations between inputs and/or functional forms of inputs with the outcome, (b) identifying the inputs that they effectively consider relevant, and (c) interpreting the inferred conditional and two-way associations of the inputs with the outcome. We establish Fisher consistent estimators, and their corresponding standard errors, for our new estimands under a condition on the inputs' distributions. The significance of our predictive comparison methodology is demonstrated with a wide range of simulation and case studies that involve Bayesian additive regression trees, neural networks, and support vector machines. Our extended study of interpretable machine learning for AM systems demonstrates how our method can contribute to smarter advanced manufacturing systems, especially as current machine learning methods for AM are lacking in their ability to yield meaningful engineering knowledge on AM processes. <br></div>

Several sophisticated techniques to study in vivo GI transit and regional absorption of pharmaceuticals are available and increasingly used. Examples of such methods are Magnetic Marker Monitoring (MMM) and local drug administration with remotely operated capsules. Another approach is the paracetamol and sulfapyridine double marker method which utilizes observed plasma concentrations of the two substances as markers for GI transit. Common for all of these methods is that they generate multiple types of observations e.g. tablet GI position, drug release and plasma concentrations of one or more substances. This thesis is based on the hypothesis that application of mechanistic nonlinear mixed-effect models could facilitate a better understanding of the interrelationship between such variables and result improved predictions of the processes involved in oral absorption. Mechanistic modeling approaches have been developed for application to data from MMM studies, paracetamol and sulfapyridine double marker studies and for linking in vitro and in vivo drug release. Models for integrating information about tablet GI transit, in vivo drug release and drug plasma concentrations measured in MMM studies was outlined and utilized to describe drug release and absorption properties along the GI tract for felodipine and the investigational drug AZD0837. A mechanistic link between in vitro and in vivo drug release was established by estimation of the mechanical stress in different regions of the GI tract in a unit equivalent to rotation speed in the in vitro experimental setup. The effect of atropine and erythromycin on gastric emptying and small intestinal transit was characterized with a semi-mechanistic model applied to double marker studies in fed and fasting dogs. The work with modeling of in vivo drug absorption has highlighted the need for, and led to, further development of mixed-effect modeling methodology with respect to model diagnostics and the handling of censored observations.