@phdthesis{Aulbach2015,
  author    = {Aulbach, Stefan},
  title     = {Contributions to Extreme Value Theory in Finite and Infinite Dimensions: With a Focus on Testing for Generalized Pareto Models},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-127162},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2015},
  abstract  = {Extreme value theory aims at modeling extreme but rare events from a probabilistic point of view. It is well-known that so-called generalized Pareto distributions, which are briefly reviewed in Chapter 1, are the only reasonable probability distributions suited for modeling observations above a high threshold, such as waves exceeding the height of a certain dike, earthquakes having at least a certain intensity, and, after applying a simple transformation, share prices falling below some low threshold. However, there are cases for which a generalized Pareto model might fail. Therefore, Chapter 2 derives certain neighborhoods of a generalized Pareto distribution and provides several statistical tests for these neighborhoods, where the cases of observing finite dimensional data and of observing continuous functions on [0,1] are considered. By using a notation based on so-called D-norms it is shown that these tests consistently link both frameworks, the finite dimensional and the functional one. Since the derivation of the asymptotic distributions of the test statistics requires certain technical restrictions, Chapter 3 analyzes these assumptions in more detail. It provides in particular some examples of distributions that satisfy the null hypothesis and of those that do not. Since continuous copula processes are crucial tools for the functional versions of the proposed tests, it is also discussed whether those copula processes actually exist for a given set of data. Moreover, some practical advice is given how to choose the free parameters incorporated in the test statistics. Finally, a simulation study in Chapter 4 compares the in total three different test statistics with another test found in the literature that has a similar null hypothesis. This thesis ends with a short summary of the results and an outlook to further open questions.},
  subject      = {Extremwertstatistik},
  language  = {en}
}
@phdthesis{Bulitta2006,
  author    = {Bulitta, J{\"u}rgen},
  title     = {Innovative techniques for selecting the dose of antibiotics in empiric therapy - focus on beta-lactams and cystic fibrosis patients},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-19353},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2006},
  abstract  = {Background: Population pharmacokinetic-pharmacodynamic (PKPD) modeling and simulations were applied to identify optimal dosage regimens for antibiotics. As the emergence of bacterial resistance is increasing and as only a few new antibiotics became available during the last decade, optimal use of established agents and preserving their effectiveness seems vital. Objectives: 1) To find the descriptor of body size and body composition which allows to achieve target concentrations and target effects in patients with cystic fibrosis (CF) most precisely. 2) To identify the mode of administration with the highest probability of successful treatment for intravenous beta-lactams. 3) To develop formulas for optimal dose selection for patients of various body size. General methods: Drug analysis in plasma and urine was performed by HPLC or LC-MS/MS in a single laboratory, at the IBMP. Drug analysis was not done by the author of this thesis. We used non-compartmental analysis and parametric population PK analysis for all studies. We used non-parametric bootstrapping to assess the uncertainty of PK parameters for our meta-analysis of the PK in CF-patients and healthy volunteers. Plasma concentration time profiles for several thousand virtual subjects were simulated by MCS which account for average PK parameters, their between subject variability (BSV), and patient specific demographic data. Convincing literature data show that the duration of non-protein bound concentration above MIC (fT>MIC) best predicts the microbiological and clinical success of beta-lactams and the area under the non-protein bound concentration curve divided by the MIC (fAUC/MIC) best predicts success for quinolones. We used PKPD targets from literature that were based on the fT>MIC or fAUC/MIC, respectively. Achieving a PKPD target was used as a surrogate measure for successful treatment. In our MCS, we calculated the fT>MIC or fAUC/MIC for all simulated concentration profiles and compared it to the value of the PKPD target. The fraction of subjects who achieved the target at the respective MIC approximates the probability of target attainment (PTA). The PTA can be interpreted as probability of successful treatment under certain assumptions. Studies in CF-patients Methods: We had data from ten studies (seven beta-lactams and three quinolones) in CF-patients which all included a healthy volunteer control group. Clinical procedures were very similar for all ten studies. Both subject groups had study conditions as similar as possible. We had data on 90 CF-patients (average +/- SD, age: 21+/-3.6 yrs) and on 111 healthy volunteers (age: 25+/-3.5 yrs). We compared the average clearance and volume of distribution between CF-patients and healthy volunteers for various body size descriptors including total body weight (WT), fat-free mass (FFM), and predicted normal weight (PNWT). We considered linear and allometric scaling of PK parameters by body size and used a meta-analysis based on population PK parameters for the comparison of CF-patients and healthy volunteers. Target concentrations can be achieved more precisely, if a size descriptor reduces the random, unexplained BSV. Therefore, we studied the reduction of unexplained BSV for each size descriptor relative to linear scaling by WT, since doses for CF-patients are commonly selected as mg/kg WT. Results: Without accounting for body size, average total clearance was 15\% lower (p=0.005) and volume of distribution at steady-state was 17\% lower (p=0.001) in CF-patients compared to healthy volunteers. For linear scaling by WT, average total clearance in CF-patients divided by total clearance in healthy volunteers was 1.15 (p=0.013). This ratio was 1.06 (p=0.191) for volume of distribution. A ratio of 1.0 indicates that CF-patients and healthy volunteers of the same body size have identical average clearances or volumes of distribution. For allometric scaling by FFM or PNWT, the ratio of total clearance and volume of distribution between CF-patients and healthy volunteers was within 0.80 and 1.25 for almost all drugs and the average ratio was close to 1. Allometric scaling by FFM or PNWT reduced the unexplained BSV in renal clearance by 24 to 27\% (median of 10 drugs) relative to linear scaling by WT. The unexplained BSV was reduced for seven or eight of the ten drugs by more than 15\% and the remaining two or three drugs had essentially unchanged (+/-15\%) unexplained BSVs in renal clearance. Conclusions: The PK in CF-patients was comparable to the PK in healthy volunteers after accounting for body size and body composition by allometric scaling with FFM or PNWT. Target concentrations and target effects in CF-patients can be achieved most precisely by dose selection based on an allometric size model with FFM or PNWT. Future studies are warranted to study the clinical superiority of allometric dosing by FFM or PNWT compared to dose selection as mg/kg WT in CF-patients.},
  subject      = {Populationskinetik},
  language  = {en}
}