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The analysis presented in this paper applies to experimental situations where observers or objects to be studied, all at stationary positions, are located in environments the optical thickness of which is strongly different. Non-transparent media comprise thin metallic films, packed or fluidised beds, superconductors, the Earth’s crust, and even dark clouds and other cosmological objects. The analysis applies mapping functions that correlate physical events, e, in non-transparent media, with their images, f(e), tentatively located on standard physical time scale. The analysis demonstrates, however, that physical time, in its rigorous sense, does not exist under non-transparency conditions. A proof of this conclusion is attempted in three steps: i) the theorem “there is no time without space and events” is accepted, (ii) images f[e(s,t)] do not constitute a dense, uncountably infinite set, and (iii) sets of images that are not uncountably infinite do not create physical time but only time-like sequences. As a consequence, mapping f[e(s,t)] in non-transparent space does not create physical analogues to the mathematical structure of the ordered, dense half-set R+ of real numbers, and reverse mapping, f-1f[e(s,t)], the mathematical inverse problem, would not allow unique identification and reconstruction of original events from their images. In these cases, causality as well as invariance of physical processes under time reversal, might be violated. An interesting problem is whether temporal cloaking (a time hole) in a transparent medium, as very recently reported in the literature, can be explained by the present analysis. Existence of time holes could perhaps be possible, not in transparent but in non-transparent media, as follows from the sequence of images, f[e(s,t)], that is not uncountably infinite, in contrast to R+. Impacts are expected for understanding physical diffusion-like, radiative transfer processes and stability models to protect superconductors against quenchs. There might be impacts also in relativity, quantum mechanics, nuclear decay, or in systems close to their phase transitions. The analysis is not restricted to objects of laboratory dimensions.
Purpose The purpose of this paper is to enhance consistent partial least squares (PLSc) to yield consistent parameter estimates for population models whose indicator blocks contain a subset of correlated measurement errors. Design/methodology/approach Correction for attenuation as originally applied by PLSc is modified to include a priori assumptions on the structure of the measurement error correlations within blocks of indicators. To assess the efficacy of the modification, a Monte Carlo simulation is conducted. Findings In the presence of population measurement error correlation, estimated parameter bias is generally small for original and modified PLSc, with the latter outperforming the former for large sample sizes. In terms of the root mean squared error, the results are virtually identical for both original and modified PLSc. Only for relatively large sample sizes, high population measurement error correlation, and low population composite reliability are the increased standard errors associated with the modification outweighed by a smaller bias. These findings are regarded as initial evidence that original PLSc is comparatively robust with respect to misspecification of the structure of measurement error correlations within blocks of indicators. Originality/value Introducing and investigating a new approach to address measurement error correlation within blocks of indicators in PLSc, this paper contributes to the ongoing development and assessment of recent advancements in partial least squares path modeling.
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.