Quantitative pharmacokinetic-pharmacodynamic and disease progression models are the core of the science of pharmacometrics which has been identified as one of the strategies that can make drug development more effective. To adequately develop and utilize these models one needs to carefully consider the nature of the data, choice of appropriate estimation methods, model evaluation strategies, and, most importantly, the intended use of the model. The general aim of this thesis was to investigate how the use of pharmacometric models can improve the design and analysis of clinical trials within drug development. The development of pharmacometric models for clinical assessment scales in stroke and graded severity events, in this thesis, show the benefit of describing data as close to its true nature as possible, as it increases the predictive abilities and allows for mechanistic interpretations of the models. Performance of three estimation methods implemented in the mixed-effects modeling software NONMEM; 1) Laplace, 2) SAEM, and 3) Importance sampling, applied when modeling repeated time-to-event data, was investigated. The two latter methods are to be preferred if less than approximately half of the individuals experience events. In addition, predictive performance of two validation procedures, internal and external validation, was explored, with internal validation being preferred in most cases. Model-based analysis was compared to conventional methods by the use of clinical trial simulations and the power to detect a drug effect was improved with a pharmacometric design and analysis. Throughout this thesis several examples have shown the possibility of significantly reducing sample sizes in clinical trials with a pharmacometric model-based analysis. This approach will reduce time and costs spent in the development of new drug therapies, but foremost reduce the number of healthy volunteers and patients exposed to experimental drugs.

Pharmacodynamic processes and disease progression are increasingly characterized with pharmacometric models. However, modelling options for discrete-type responses remain limited, although these response variables are commonly encountered clinical endpoints. Types of data defined as discrete data are generally ordinal, e.g. symptom severity, count, i.e. event frequency, and time-to-event, i.e. event occurrence. Underlying assumptions accompanying discrete data models need investigation and possibly adaptations in order to expand their use. Moreover, because these models are highly non-linear, estimation with linearization-based maximum likelihood methods may be biased. The aim of this thesis was to explore pharmacometric methods and novel models for discrete data through (i) the investigation of benefits of treating discrete data with different modelling approaches, (ii) evaluations of the performance of several estimation methods for discrete models, and (iii) the development of novel models for the handling of complex discrete data recorded during (pre-)clinical studies. A simulation study indicated that approaches such as a truncated Poisson model and a logit-transformed continuous model were adequate for treating ordinal data ranked on a 0-10 scale. Features that handled serial correlation and underdispersion were developed for the models to subsequently fit real pain scores. The performance of nine estimation methods was studied for dose-response continuous models. Other types of serially correlated count models were studied for the analysis of overdispersed data represented by the number of epilepsy seizures per day. For these types of models, the commonly used Laplace estimation method presented a bias, whereas the adaptive Gaussian quadrature method did not. Count models were also compared to repeated time-to-event models when the exact time of gastroesophageal symptom occurrence was known. Two new model structures handling repeated time-to-categorical events, i.e. events with an ordinal severity aspect, were introduced. Laplace and two expectation-maximisation estimation methods were found to be performing well for frequent repeated time-to-event models. In conclusion, this thesis presents approaches, estimation methods, and diagnostics adapted for treating discrete data. Novel models and diagnostics were developed when lacking and applied to biological observations.