The Analysis of interval censoring and double censoring via Markov chain Monte Carlo methods

L'Anàlisi de la supervivència s'utilitza en diferents camps per analitzar el temps transcorregut entre dos esdeveniments. El que distingeix l'anàlisi de la supervivència d'altres àrees de l'estadística és que les dades normalment estan censurades. La censura en un interval apareix quan l'esdeveniment final d'interès no és directament observable i només se sap que el temps de fallada està en un interval concret. Un esquema de censura més complex encara apareix quan tant el temps inicial com el temps final estan censurats en un interval. Aquesta situació s'anomena doble censura. En aquest article donem una descripció formal d'un mètode bayesà paramètric per a l'anàlisi de dades censurades en un interval i dades doblement censurades així com unes indicacions clares de la seva utilització o pràctica. La metodologia proposada s'ilustra amb dades d'una cohort de pacients hemofílics que es varen infectar amb el virus VIH a principis dels anys 1980's.

Simulación Monte Carlo de las dosis en tumores de pulmón en tratamientos de radioterapia estereotáxica extracraneal

Estudio elaborado a partir de una estancia en el Karolinska University Hospital, Suecia, entre marzo y junio del 2006. En la radioterapia estereotáxica extracraneal (SBRT) de tumores de pulmón existen principalmente dos problemas en el cálculo de la dosis con los sistemas de planificación disponibles: la precisión limitada de los algoritmos de cálculo en presencia de tejidos con densidades muy diferentes y los movimientos debidos a la respiración del paciente durante el tratamiento. El objetivo de este trabajo ha sido llevar a cabo la simulación con el código Monte Carlo PENELOPE de la distribución de dosis en tumores de pulmón en casos representativos de tratamientos con SBRT teniendo en cuenta los movimientos respiratorios y su comparación con los resultados de varios planificadores. Se han estudiado casos representativos de tratamientos de SBRT en el Karolinska University Hospital. Los haces de radiación se han simulado mediante el código PENELOPE y se han usado para la obtención de los resultados MC de perfiles de dosis. Los resultados obtenidos para el caso estático (sin movimiento respiratorio ) ponen de manifiesto que, en comparación con la MC, la dosis (Gy/MU) calculada por los planificadores en el tumor tiene una precisión del 2-3%. En la zona de interfase entre tumor y tejido pulmonar los planificadores basados en el algoritmo PB sobrestiman la dosis en un 10%, mientras que el algoritmo CC la subestima en un 3-4%. Los resultados de la simulación mediante MC de los movimientos respiratorios indican que los resultados de los planificadores son suficientemente precisos en el tumor, aunque en la interfase hay una mayor subestimación de la dosis en comparación con el caso estático. Estos resultados son compatibles con la experiencia clínica adquirida durante 15 años en el Karolinska University Hospital. Los resultados se han publicado en la revista Acta Oncologica.

Estimation of the radiation risks in diagnostic procedures to populations and patients

Since 1895, when X-rays were discovered, ionizing radiation became part of our life. Its use in medicine has brought significant health benefits to the population globally. The benefit of any diagnostic procedure is to reduce the uncertainty about the patient's health. However, there are potential detrimental effects of radiation exposure. Therefore, radiation protection authorities have become strict regarding the control of radiation risks.¦There are various situations where the radiation risk needs to be evaluated. International authority bodies point to the increasing number of radiologic procedures and recommend population surveys. These surveys provide valuable data to public health authorities which helps them to prioritize and focus on patient groups in the population that are most highly exposed. On the other hand, physicians need to be aware of radiation risks from diagnostic procedures in order to justify and optimize the procedure and inform the patient.¦The aim of this work was to examine the different aspects of radiation protection and investigate a new method to estimate patient radiation risks.¦The first part of this work concerned radiation risk assessment from the regulatory authority point of view. To do so, a population dose survey was performed to evaluate the annual population exposure. This survey determined the contribution of different imaging modalities to the total collective dose as well as the annual effective dose per caput. It was revealed that although interventional procedures are not so frequent, they significantly contribute to the collective dose. Among the main results of this work, it was shown that interventional cardiological procedures are dose-intensive and therefore more attention should be paid to optimize the exposure.¦The second part of the project was related to the patient and physician oriented risk assessment. In this part, interventional cardiology procedures were studied by means of Monte Carlo simulations. The organ radiation doses as well as effective doses were estimated. Cancer incidence risks for different organs were calculated for different sex and age-at-exposure using the lifetime attributable risks provided by the Biological Effects of Ionizing Radiations Report VII. Advantages and disadvantages of the latter results were examined as an alternative method to estimate radiation risks. The results show that this method is the most accurate, currently available, to estimate radiation risks. The conclusions of this work may guide future studies in the field of radiation protection in medicine.¦-¦Depuis la découverte des rayons X en 1895, ce type de rayonnement a joué un rôle important dans de nombreux domaines. Son utilisation en médecine a bénéficié à la population mondiale puisque l'avantage d'un examen diagnostique est de réduire les incertitudes sur l'état de santé du patient. Cependant, leur utilisation peut conduire à l'apparition de cancers radio-induits. Par conséquent, les autorités sanitaires sont strictes quant au contrôle du risque radiologique.¦Le risque lié aux radiations doit être estimé dans différentes situations pratiques, dont l'utilisation médicale des rayons X. Les autorités internationales de radioprotection indiquent que le nombre d'examens et de procédures radiologiques augmente et elles recommandent des enquêtes visant à déterminer les doses de radiation délivrées à la population. Ces enquêtes assurent que les groupes de patients les plus à risque soient prioritaires. D'un autre côté, les médecins ont également besoin de connaître le risque lié aux radiations afin de justifier et optimiser les procédures et informer les patients.¦Le présent travail a pour objectif d'examiner les différents aspects de la radioprotection et de proposer une manière efficace pour estimer le risque radiologique au patient.¦Premièrement, le risque a été évalué du point de vue des autorités sanitaires. Une enquête nationale a été réalisée pour déterminer la contribution des différentes modalités radiologiques et des divers types d'examens à la dose efficace collective due à l'application médicale des rayons X. Bien que les procédures interventionnelles soient rares, elles contribuent de façon significative à la dose délivrée à la population. Parmi les principaux résultats de ce travail, il a été montré que les procédures de cardiologie interventionnelle délivrent des doses élevées et devraient donc être optimisées en priorité.¦La seconde approche concerne l'évaluation du risque du point de vue du patient et du médecin. Dans cette partie, des procédures interventionnelles cardiaques ont été étudiées au moyen de simulations Monte Carlo. La dose délivrée aux organes ainsi que la dose efficace ont été estimées. Les risques de développer des cancers dans plusieurs organes ont été calculés en fonction du sexe et de l'âge en utilisant la méthode établie dans Biological Effects of Ionizing Radiations Report VII. Les avantages et inconvénients de cette nouvelle technique ont été examinés et comparés à ceux de la dose efficace. Les résultats ont montré que cette méthode est la plus précise actuellement disponible pour estimer le risque lié aux radiations. Les conclusions de ce travail pourront guider de futures études dans le domaine de la radioprotection en médicine.

A correlation sensitivity analysis of non-life underwriting risk in solvency capital requirement estimation

This paper analyses the impact of using different correlation assumptions between lines of business when estimating the risk-based capital reserve, the Solvency Capital Requirement (SCR), under Solvency II regulations. A case study is presented and the SCR is calculated according to the Standard Model approach. Alternatively, the requirement is then calculated using an Internal Model based on a Monte Carlo simulation of the net underwriting result at a one-year horizon, with copulas being used to model the dependence between lines of business. To address the impact of these model assumptions on the SCR we conduct a sensitivity analysis. We examine changes in the correlation matrix between lines of business and address the choice of copulas. Drawing on aggregate historical data from the Spanish non-life insurance market between 2000 and 2009, we conclude that modifications of the correlation and dependence assumptions have a significant impact on SCR estimation.

Solvency Capital estimation and Risk Measures

This paper examines why a financial entity’s solvency capital estimation might be underestimated if the total amount required is obtained directly from a risk measurement. Using Monte Carlo simulation we show that, in some instances, a common risk measure such as Value-at-Risk is not subadditive when certain dependence structures are considered. Higher risk evaluations are obtained for independence between random variables than those obtained in the case of comonotonicity. The paper stresses, therefore, the relationship between dependence structures and capital estimation.

Monte Carlo simulations of metasomatic enrichment in the lithosphere and implications for the source of alkaline basalts

One hypothesis for the origin of alkaline lavas erupted on oceanic islands and in intracontinental settings is that they represent the melts of amphibole-rich veins in the lithosphere (or melts of their dehydrated equivalents if metasomatized lithosphere is recycled into the convecting mantle). Amphibole-rich veins are interpreted as cumulates produced by crystallization of low-degree melts of the underlying asthenosphere as they ascend through the lithosphere. We present the results of trace-element modelling of the formation and melting of veins formed in this way with the goal of testing this hypothesis and for predicting how variability in the formation and subsequent melting of such cumulates (and adjacent cryptically and modally metasomatized lithospheric peridotite) would be manifested in magmas generated by such a process. Because the high-pressure phase equilibria of hydrous near-solidus melts of garnet lherzolite are poorly constrained and given the likely high variability of the hypothesized accumulation and remelting processes, we used Monte Carlo techniques to estimate how uncertainties in the model parameters (e.g. the compositions of the asthenospheric sources, their trace-element contents, and their degree of melting; the modal proportions of crystallizing phases, including accessory phases, as the asthenospheric partial melts ascend and crystallize in the lithosphere; the amount of metasomatism of the peridotitic country rock; the degree of melting of the cumulates and the amount of melt derived from the metasomatized country rock) propagate through the process and manifest themselves as variability in the trace-element contents and radiogenic isotopic ratios of model vein compositions and erupted alkaline magma compositions. We then compare the results of the models with amphibole observed in lithospheric veins and with oceanic and continental alkaline magmas. While the trace-element patterns of the near-solidus peridotite melts, the initial anhydrous cumulate assemblage (clinopyroxene +/- garnet +/- olivine +/- orthopyroxene), and the modelled coexisting liquids do not match the patterns observed in alkaline lavas, our calculations show that with further crystallization and the appearance of amphibole (and accessory minerals such as rutile, ilmenite, apatite, etc.) the calculated cumulate assemblages have trace-element patterns that closely match those observed in the veins and lavas. These calculated hydrous cumulate assemblages are highly enriched in incompatible trace elements and share many similarities with the trace-element patterns of alkaline basalts observed in oceanic or continental setting such as positive Nb/La, negative Ce/Pb, and similiar slopes of the rare earth elements. By varying the proportions of trapped liquid and thus simulating the cryptic and modal metasomatism observed in peridotite that surrounds these veins, we can model the variations in Ba/Nb, Ce/Pb, and Nb/U ratios that are observed in alkaline basalts. If the isotopic compositions of the initial low-degree peridotite melts are similar to the range observed in mid-ocean ridge basalt, our model calculations produce cumulates that would have isotopic compositions similar to those observed in most alkaline ocean island basalt (OIB) and continental magmas after similar to 0 center dot 15 Gyr. However, to produce alkaline basalts with HIMU isotopic compositions requires much longer residence times (i.e. 1-2 Gyr), consistent with subduction and recycling of metasomatized lithosphere through the mantle. such as a heterogeneous asthenosphere. These modelling results support the interpretation proposed by various researchers that amphibole-bearing veins represent cumulates formed during the differentiation of a volatile-bearing low-degree peridotite melt and that these cumulates are significant components of the sources of alkaline OIB and continental magmas. The results of the forward models provide the potential for detailed tests of this class of hypotheses for the origin of alkaline magmas worldwide and for interpreting major and minor aspects of the geochemical variability of these magmas.

Bayesian Markov chain Monte Carlo inversion of geophysical data for the purpose of estimating the hydraulic properties of the unsaturated zone

Ground-penetrating radar (GPR) has the potential to provide valuable information on hydrological properties of the vadose zone because of their strong sensitivity to soil water content. In particular, recent evidence has suggested that the stochastic inversion of crosshole GPR data within a coupled geophysical-hydrological framework may allow for effective estimation of subsurface van-Genuchten-Mualem (VGM) parameters and their corresponding uncertainties. An important and still unresolved issue, however, is how to best integrate GPR data into a stochastic inversion in order to estimate the VGM parameters and their uncertainties, thus improving hydrological predictions. Recognizing the importance of this issue, the aim of the research presented in this thesis was to first introduce a fully Bayesian inversion called Markov-chain-Monte-carlo (MCMC) strategy to perform the stochastic inversion of steady-state GPR data to estimate the VGM parameters and their uncertainties. Within this study, the choice of the prior parameter probability distributions from which potential model configurations are drawn and tested against observed data was also investigated. Analysis of both synthetic and field data collected at the Eggborough (UK) site indicates that the geophysical data alone contain valuable information regarding the VGM parameters. However, significantly better results are obtained when these data are combined with a realistic, informative prior. A subsequent study explore in detail the dynamic infiltration case, specifically to what extent time-lapse ZOP GPR data, collected during a forced infiltration experiment at the Arrenaes field site (Denmark), can help to quantify VGM parameters and their uncertainties using the MCMC inversion strategy. The findings indicate that the stochastic inversion of time-lapse GPR data does indeed allow for a substantial refinement in the inferred posterior VGM parameter distributions. In turn, this significantly improves knowledge of the hydraulic properties, which are required to predict hydraulic behaviour. Finally, another aspect that needed to be addressed involved the comparison of time-lapse GPR data collected under different infiltration conditions (i.e., natural loading and forced infiltration conditions) to estimate the VGM parameters using the MCMC inversion strategy. The results show that for the synthetic example, considering data collected during a forced infiltration test helps to better refine soil hydraulic properties compared to data collected under natural infiltration conditions. When investigating data collected at the Arrenaes field site, further complications arised due to model error and showed the importance of also including a rigorous analysis of the propagation of model error with time and depth when considering time-lapse data. Although the efforts in this thesis were focused on GPR data, the corresponding findings are likely to have general applicability to other types of geophysical data and field environments. Moreover, the obtained results allow to have confidence for future developments in integration of geophysical data with stochastic inversions to improve the characterization of the unsaturated zone but also reveal important issues linked with stochastic inversions, namely model errors, that should definitely be addressed in future research.

Main results of the Monte Carlo studies carried out for nuclear medicine practices within the ORAMED project

The aim of ORAMED work package 4 was the optimization of the medical practices in nuclear medicine during the preparation of radiopharmaceuticals and their administration to the patient. During the project a wide campaign of measurements was performed in the nuclear medicine departments of the collaborating hospitals. Such data were intrinsically characterized by a large variability that depended on the procedure, the employed techniques and the operator's habits. That variability could easily hide some important parameter, for example, the effectiveness of the adopted shielding (for syringe and vial) or the effect of the distances from the source. This information is necessary for a valuable optimization purpose of radiation protection. To this end a sensitivity analysis was carried out through Monte Carlo simulations employing voxel models, representing operator's hand during the considered practices. Such analysis allowed understanding at what extent the range of personal dose equivalent evaluated during measurements can be considered intrinsically related to the procedures. Furthermore, with the Monte Carlo simulations it was possible to study the appropriateness of the shielding usually utilized in these practices.

A model of cellular dosimetry for macroscopic tumors in radiopharmaceutical therapy.

PURPOSE: In the radiopharmaceutical therapy approach to the fight against cancer, in particular when it comes to translating laboratory results to the clinical setting, modeling has served as an invaluable tool for guidance and for understanding the processes operating at the cellular level and how these relate to macroscopic observables. Tumor control probability (TCP) is the dosimetric end point quantity of choice which relates to experimental and clinical data: it requires knowledge of individual cellular absorbed doses since it depends on the assessment of the treatment's ability to kill each and every cell. Macroscopic tumors, seen in both clinical and experimental studies, contain too many cells to be modeled individually in Monte Carlo simulation; yet, in particular for low ratios of decays to cells, a cell-based model that does not smooth away statistical considerations associated with low activity is a necessity. The authors present here an adaptation of the simple sphere-based model from which cellular level dosimetry for macroscopic tumors and their end point quantities, such as TCP, may be extrapolated more reliably. METHODS: Ten homogenous spheres representing tumors of different sizes were constructed in GEANT4. The radionuclide 131I was randomly allowed to decay for each model size and for seven different ratios of number of decays to number of cells, N(r): 1000, 500, 200, 100, 50, 20, and 10 decays per cell. The deposited energy was collected in radial bins and divided by the bin mass to obtain the average bin absorbed dose. To simulate a cellular model, the number of cells present in each bin was calculated and an absorbed dose attributed to each cell equal to the bin average absorbed dose with a randomly determined adjustment based on a Gaussian probability distribution with a width equal to the statistical uncertainty consistent with the ratio of decays to cells, i.e., equal to Nr-1/2. From dose volume histograms the surviving fraction of cells, equivalent uniform dose (EUD), and TCP for the different scenarios were calculated. Comparably sized spherical models containing individual spherical cells (15 microm diameter) in hexagonal lattices were constructed, and Monte Carlo simulations were executed for all the same previous scenarios. The dosimetric quantities were calculated and compared to the adjusted simple sphere model results. The model was then applied to the Bortezomib-induced enzyme-targeted radiotherapy (BETR) strategy of targeting Epstein-Barr virus (EBV)-expressing cancers. RESULTS: The TCP values were comparable to within 2% between the adjusted simple sphere and full cellular models. Additionally, models were generated for a nonuniform distribution of activity, and results were compared between the adjusted spherical and cellular models with similar comparability. The TCP values from the experimental macroscopic tumor results were consistent with the experimental observations for BETR-treated 1 g EBV-expressing lymphoma tumors in mice. CONCLUSIONS: The adjusted spherical model presented here provides more accurate TCP values than simple spheres, on par with full cellular Monte Carlo simulations while maintaining the simplicity of the simple sphere model. This model provides a basis for complementing and understanding laboratory and clinical results pertaining to radiopharmaceutical therapy.

DNA supercoiling inhibits DNA knotting.

Despite the fact that in living cells DNA molecules are long and highly crowded, they are rarely knotted. DNA knotting interferes with the normal functioning of the DNA and, therefore, molecular mechanisms evolved that maintain the knotting and catenation level below that which would be achieved if the DNA segments could pass randomly through each other. Biochemical experiments with torsionally relaxed DNA demonstrated earlier that type II DNA topoisomerases that permit inter- and intramolecular passages between segments of DNA molecules use the energy of ATP hydrolysis to select passages that lead to unknotting rather than to the formation of knots. Using numerical simulations, we identify here another mechanism by which topoisomerases can keep the knotting level low. We observe that DNA supercoiling, such as found in bacterial cells, creates a situation where intramolecular passages leading to knotting are opposed by the free-energy change connected to transitions from unknotted to knotted circular DNA molecules.

DNA-DNA interactions in bacteriophage capsids are responsible for the observed DNA knotting.

Recent experiments showed that the linear double-stranded DNA in bacteriophage capsids is both highly knotted and neatly structured. What is the physical basis of this organization? Here we show evidence from stochastic simulation techniques that suggests that a key element is the tendency of contacting DNA strands to order, as in cholesteric liquid crystals. This interaction favors their preferential juxtaposition at a small twist angle, thus promoting an approximately nematic (and apolar) local order. The ordering effect dramatically impacts the geometry and topology of DNA inside phages. Accounting for this local potential allows us to reproduce the main experimental data on DNA organization in phages, including the cryo-EM observations and detailed features of the spectrum of DNA knots formed inside viral capsids. The DNA knots we observe are strongly delocalized and, intriguingly, this is shown not to interfere with genome ejection out of the phage.