This Master Thesis report was written by Umeå University Engineering Physics student Richard Tano during his thesis work at Ericsson Luleå. Monitoring network quality is of utmost importance to network providers. This can be done with models evaluating QoS (Quality of Service) and conforming to ITU-T Recommendations. When determining video stream quality there is of more importance to evaluatethe QoE (Quality of Experience) to understand how the user perceives the quality. This isranked in MOS (Mean opinion scores) values. An important aspect of determining the QoEis the video content type, which is correlated to the coding complexity and MOS values ofthe video. In this work the possibilities to improve quality estimation models complying to ITU-T study group 12 (q.14) was investigated. Methods were evaluated and an algorithm was developed that applies time series analysis of packet statistics for determination of videostreams MOS scores. Methods used in the algorithm includes a novel assembling of frequentpattern analysis and regression analysis. A model which incorporates the algorithm for usage from low to high bitrates was dened. The new model resulted in around 20% improvedprecision in MOS score estimation compared to the existing reference model. Furthermore an algorithm using only regression statistics and modeling of related statistical parameters was developed. Improvements in coding estimation was comparable with earlier algorithm but efficiency increased considerably. / Detta examensarbete skrevs av Richard Tano student på Umeå universitet åt Ericsson Luleå. Övervakning av nätets prestanda är av yttersta vikt för nätverksleverantörer. Detta görs med modeller för att utvärdera QoS (Quality of Service) som överensstämmer med ITU-T rekommendationer. Vid bestämning av kvaliten på videoströmmar är det mer meningsfullt att utvärdera QoE (Quality of Experience) för att få insikt i hur användaren uppfattar kvaliten. Detta graderas i värden av MOS (Mean opinion score). En viktig aspekt för att bestämma QoE är typen av videoinnehåll, vilket är korrelerat till videons kodningskomplexitet och MOS värden. I detta arbete undersöktes möjligheterna att förbättra kvalitetsuppskattningsmodellerna under uppfyllande av ITU-T studygroup 12 (q.14). Metoder undersöktes och en algoritm utvecklades som använder tidsserieanalys av paketstatistik för uppskattning av videoströmmars MOS-värden. Metoder som ingår i algoritmen är en nyutvecklad frekventa mönster metod tillsammans med regressions analys. En modell som använder algoritmen från låg till hög bithastighet definierades. Den nya modellen gav omkring 20% förbättrad precision i uppskattning av MOS-värden jämfört med existerande referensmodell. Även en algoritm som enbart använder regressionsstatistik och modellerande av statistiska parametrar utvecklades. Denna algoritm levererade jämförbara resultat med föregående algoritm men gav även kraftigt förbättrad effektivitet.

La radiothérapie externe (EBRT en anglais pour External Beam Radiotherapy) est l'un des traitements référence du cancer de prostate. Les objectifs de la radiothérapie sont, premièrement, de délivrer une haute dose de radiations dans la cible tumorale (prostate et vésicules séminales) afin d'assurer un contrôle local de la maladie et, deuxièmement, d'épargner les organes à risque voisins (principalement le rectum et la vessie) afin de limiter les effets secondaires. Des modèles de probabilité de complication des tissus sains (NTCP en anglais pour Normal Tissue Complication Probability) sont nécessaires pour estimer sur les risques de présenter des effets secondaires au traitement. Dans le contexte de la radiothérapie externe, les objectifs de cette thèse étaient d'identifier des paramètres prédictifs de complications rectales et vésicales secondaires au traitement; de développer de nouveaux modèles NTCP permettant l'intégration de paramètres dosimétriques et de paramètres propres aux patients; de comparer les capacités prédictives de ces nouveaux modèles à celles des modèles classiques et de développer de nouvelles méthodologies d'identification de motifs de dose corrélés à l'apparition de complications. Une importante base de données de patients traités par radiothérapie conformationnelle, construite à partir de plusieurs études cliniques prospectives françaises, a été utilisée pour ces travaux. Dans un premier temps, la fréquence des symptômes gastro-Intestinaux et génito-Urinaires a été décrite par une estimation non paramétrique de Kaplan-Meier. Des prédicteurs de complications gastro-Intestinales et génito-Urinaires ont été identifiés via une autre approche classique : la régression logistique. Les modèles de régression logistique ont ensuite été utilisés dans la construction de nomogrammes, outils graphiques permettant aux cliniciens d'évaluer rapidement le risque de complication associé à un traitement et d'informer les patients. Nous avons proposé l'utilisation de la méthode d'apprentissage de machine des forêts aléatoires (RF en anglais pour Random Forests) pour estimer le risque de complications. Les performances de ce modèle incluant des paramètres cliniques et patients, surpassent celles des modèle NTCP de Lyman-Kutcher-Burman (LKB) et de la régression logistique. Enfin, la dose 3D a été étudiée. Une méthode de décomposition en valeurs populationnelles (PVD en anglais pour Population Value Decomposition) en 2D a été généralisée au cas tensoriel et appliquée à l'analyse d'image 3D. L'application de cette méthode à une analyse de population a été menée afin d'extraire un motif de dose corrélée à l'apparition de complication après EBRT. Nous avons également développé un modèle non paramétrique d'effets mixtes spatio-Temporels pour l'analyse de population d'images tridimensionnelles afin d'identifier une région anatomique dans laquelle la dose pourrait être corrélée à l'apparition d'effets secondaires. / External beam radiotherapy (EBRT) is one of the cornerstones of prostate cancer treatment. The objectives of radiotherapy are, firstly, to deliver a high dose of radiation to the tumor (prostate and seminal vesicles) in order to achieve a maximal local control and, secondly, to spare the neighboring organs (mainly the rectum and the bladder) to avoid normal tissue complications. Normal tissue complication probability (NTCP) models are then needed to assess the feasibility of the treatment and inform the patient about the risk of side effects, to derive dose-Volume constraints and to compare different treatments. In the context of EBRT, the objectives of this thesis were to find predictors of bladder and rectal complications following treatment; to develop new NTCP models that allow for the integration of both dosimetric and patient parameters; to compare the predictive capabilities of these new models to the classic NTCP models and to develop new methodologies to identify dose patterns correlated to normal complications following EBRT for prostate cancer treatment. A large cohort of patient treated by conformal EBRT for prostate caner under several prospective French clinical trials was used for the study. In a first step, the incidence of the main genitourinary and gastrointestinal symptoms have been described. With another classical approach, namely logistic regression, some predictors of genitourinary and gastrointestinal complications were identified. The logistic regression models were then graphically represented to obtain nomograms, a graphical tool that enables clinicians to rapidly assess the complication risks associated with a treatment and to inform patients. This information can be used by patients and clinicians to select a treatment among several options (e.g. EBRT or radical prostatectomy). In a second step, we proposed the use of random forest, a machine-Learning technique, to predict the risk of complications following EBRT for prostate cancer. The superiority of the random forest NTCP, assessed by the area under the curve (AUC) of the receiving operative characteristic (ROC) curve, was established. In a third step, the 3D dose distribution was studied. A 2D population value decomposition (PVD) technique was extended to a tensorial framework to be applied on 3D volume image analysis. Using this tensorial PVD, a population analysis was carried out to find a pattern of dose possibly correlated to a normal tissue complication following EBRT. Also in the context of 3D image population analysis, a spatio-Temporal nonparametric mixed-Effects model was developed. This model was applied to find an anatomical region where the dose could be correlated to a normal tissue complication following EBRT.

Cette thèse porte sur le développement de méthodes semi-paramétriques robustes pour l'inférence de paramètres complexes émergeant à l'interface de l'inférence causale et la biostatistique. Ses motivations sont les applications à la recherche épidémiologique et médicale à l'ère des Big Data. Nous abordons plus particulièrement deux défis statistiques pour réconcilier, dans chaque contexte, estimation adaptative et inférence statistique. Le premier défi concerne la maximisation de l'information tirée d'essais contrôlés randomisés (ECRs) grâce à la conception d'essais adaptatifs. Nous présentons un cadre théorique pour la construction et l'analyse d'ECRs groupes-séquentiels, réponses-adaptatifs et ajustés aux covariable (traduction de l'expression anglaise « group-sequential, response-adaptive, covariate-adjusted », d'où l'acronyme CARA) qui permettent le recours à des procédures adaptatives d'estimation à la fois pour la construction dynamique des schémas de randomisation et pour l'estimation du modèle de réponse conditionnelle. Ce cadre enrichit la littérature existante sur les ECRs CARA notamment parce que l'estimation des effets est garantie robuste même lorsque les modèles sur lesquels s'appuient les procédures adaptatives d'estimation sont mal spécificiés. Le second défi concerne la mise au point et l'étude asymptotique d'une procédure inférentielle semi-paramétrique avec estimation adaptative des paramètres de nuisance. A titre d'exemple, nous choisissons comme paramètre d'intérêt la différence des risques marginaux pour un traitement binaire. Nous proposons une version cross-validée du principe d'inférence par minimisation ciblée de pertes (« Cross-validated Targeted Mimum Loss Estimation » en anglais, d'où l'acronyme CV-TMLE) qui, comme son nom le suggère, marie la procédure TMLE classique et le principe de la validation croisée. L'estimateur CV-TMLE ainsi élaboré hérite de la propriété typique de double-robustesse et aussi des propriétés d'efficacité du TMLE classique. De façon remarquable, le CV-TMLE est linéairement asymptotique sous des conditions minimales, sans recourir aux conditions de type Donsker. / This dissertation focuses on developing robust semiparametric methods for complex parameters that emerge at the interface of causal inference and biostatistics, with applications to epidemiological and medical research in the era of Big Data. Specifically, we address two statistical challenges that arise in bridging the disconnect between data-adaptive estimation and statistical inference. The first challenge arises in maximizing information learned from Randomized Control Trials (RCT) through the use of adaptive trial designs. We present a framework to construct and analyze group sequential covariate-adjusted response-adaptive (CARA) RCTs that admits the use of data-adaptive approaches in constructing the randomization schemes and in estimating the conditional response model. This framework adds to the existing literature on CARA RCTs by allowing flexible options in both their design and analysis and by providing robust effect estimates even under model mis-specifications. The second challenge arises from obtaining a Central Limit Theorem when data-adaptive estimation is used to estimate the nuisance parameters. We consider as target parameter of interest the marginal risk difference of the outcome under a binary treatment, and propose a Cross-validated Targeted Minimum Loss Estimator (TMLE), which augments the classical TMLE with a sample-splitting procedure. The proposed Cross-Validated TMLE (CV-TMLE) inherits the double robustness properties and efficiency properties of the classical TMLE , and achieves asymptotic linearity at minimal conditions by avoiding the Donsker class condition.

Thesis Abstract Current Nuclear Power Plant (NPP) design does not account for Beyond Design Basis Events (BDBEs) and thus lack the provisions to effectively mitigates complete loss of AC power and total loss of heat sink. Furthermore, parametric models used in PRA studies to assess Nuclear Power Plant’s safety risk for BDBE and External Events (EE) have significant limitations and proved ineffective to provide solutions on how to mitigate in BDBE or EEs situations. The Fukushima accident is a good example where PRA assessments did not provide the necessary means to cool or contain the reactors effectively. In this thesis, Emergency Mitigation Preparedness (EMP) model and assessment is proposed. The EMP model is objective and practical in evaluating NPP’s mitigation readiness in BDBE and EEs situations and provide a practical NPP Vulnerability indicator gauge which can potentially be used in risk-informed decisions. This will aid further in the NPP to improve in areas of emergency planning, enhance site and reactor design and improve workers safety and readiness to execute effective mitigation procedures and emergency plans. / Thesis / Master of Engineering (ME)

This study investigates whether Gaussian Process Regression can be applied to evaluate buffer queue times in large scale data processing systems. It is additionally considered whether high-frequency data stream rates can be generalized into a small subset of the sample space. With the aim of providing basis for dynamic software optimization, a promising foundation for continued research is introduced. The study is intended to contribute to Direct Market Access financial trading systems which processes immense amounts of market data daily. Due to certain limitations, we shoulder a naïve approach and model latencies as a function of only data throughput in eight small historical intervals. The training and test sets are represented from raw market data, and we resort to pruning operations to shrink the datasets by a factor of approximately 0.0005 in order to achieve computational feasibility. We further consider four different implementations of Gaussian Process Regression. The resulting algorithms perform well on pruned datasets, with an average R2 statistic of 0.8399 over six test sets of approximately equal size as the training set. Testing on non-pruned datasets indicate shortcomings from the generalization procedure, where input vectors corresponding to low-latency target values are associated with less accuracy. We conclude that depending on application, the shortcomings may be make the model intractable. However for the purposes of this study it is found that buffer queue times can indeed be modelled by regression algorithms. We discuss several methods for improvements, both in regards to pruning procedures and Gaussian Processes, and open up for promising continued research. / Denna studie undersöker huruvida Gaussian Process Regression kan appliceras för att utvärdera buffer-kötider i storskaliga dataprocesseringssystem. Dessutom utforskas ifall dataströmsfrekvenser kan generaliseras till en liten delmängd av utfallsrymden. Medmålet att erhålla en grund för dynamisk mjukvaruoptimering introduceras en lovandestartpunkt för fortsatt forskning. Studien riktas mot Direct Market Access system för handel på finansiella marknader, somprocesserar enorma mängder marknadsdata dagligen. På grund av vissa begränsningar axlas ett naivt tillvägagångssätt och väntetider modelleras som en funktion av enbartdatagenomströmning i åtta små historiska tidsinterval. Tränings- och testdataset representeras från ren marknadsdata och pruning-tekniker används för att krympa dataseten med en ungefärlig faktor om 0.0005, för att uppnå beräkningsmässig genomförbarhet. Vidare tas fyra olika implementationer av Gaussian Process Regression i beaktning. De resulterande algorithmerna presterar bra på krympta dataset, med en medel R2 statisticpå 0.8399 över sex testdataset, alla av ungefär samma storlek som träningsdatasetet. Tester på icke krympta dataset indikerar vissa brister från pruning, där input vektorermotsvararande låga latenstider är associerade med mindre exakthet. Slutsatsen dras att beroende på applikation kan dessa brister göra modellen obrukbar. För studiens syftefinnes emellertid att latenstider kan sannerligen modelleras av regressionsalgoritmer. Slutligen diskuteras metoder för förbättrning med hänsyn till både pruning och GaussianProcess Regression, och det öppnas upp för lovande vidare forskning.

Neste trabalho, apresentamos os modelos simétricos parcialmente lineares AR(1), que generalizam os modelos parcialmente lineares para a presença de erros autocorrelacionados seguindo uma estrutura de autocorrelação AR(1) e erros seguindo uma distribuição simétrica ao invés da distribuição normal. Dentre as distribuições simétricas, podemos considerar distribuições com caudas mais pesadas do que a normal, controlando a curtose e ponderando as observações aberrantes no processo de estimação. A estimação dos parâmetros do modelo é realizada por meio do critério de verossimilhança penalizada, que utiliza as funções escore e a matriz de informação de Fisher, sendo todas essas quantidades derivadas neste trabalho. O número efetivo de graus de liberdade e resultados assintóticos também são apresentados, assim como procedimentos de diagnóstico, destacando-se a obtenção da curvatura normal de influência local sob diferentes esquemas de perturbação e análise de resíduos. Uma aplicação com dados reais é apresentada como ilustração. / In this master dissertation, we present the symmetric partially linear models with AR(1) errors that generalize the normal partially linear models to contain autocorrelated errors AR(1) following a symmetric distribution instead of the normal distribution. Among the symmetric distributions, we can consider heavier tails than the normal ones, controlling the kurtosis and down-weighting outlying observations in the estimation process. The parameter estimation is made through the penalized likelihood by using score functions and the expected Fisher information. We derive these functions in this work. The effective degrees of freedom and asymptotic results are also presented as well as the residual analysis, highlighting the normal curvature of local influence under different perturbation schemes. An application with real data is given for illustration.

Neste trabalho, apresentamos os modelos simétricos parcialmente lineares AR(1), que generalizam os modelos parcialmente lineares para a presença de erros autocorrelacionados seguindo uma estrutura de autocorrelação AR(1) e erros seguindo uma distribuição simétrica ao invés da distribuição normal. Dentre as distribuições simétricas, podemos considerar distribuições com caudas mais pesadas do que a normal, controlando a curtose e ponderando as observações aberrantes no processo de estimação. A estimação dos parâmetros do modelo é realizada por meio do critério de verossimilhança penalizada, que utiliza as funções escore e a matriz de informação de Fisher, sendo todas essas quantidades derivadas neste trabalho. O número efetivo de graus de liberdade e resultados assintóticos também são apresentados, assim como procedimentos de diagnóstico, destacando-se a obtenção da curvatura normal de influência local sob diferentes esquemas de perturbação e análise de resíduos. Uma aplicação com dados reais é apresentada como ilustração. / In this master dissertation, we present the symmetric partially linear models with AR(1) errors that generalize the normal partially linear models to contain autocorrelated errors AR(1) following a symmetric distribution instead of the normal distribution. Among the symmetric distributions, we can consider heavier tails than the normal ones, controlling the kurtosis and down-weighting outlying observations in the estimation process. The parameter estimation is made through the penalized likelihood by using score functions and the expected Fisher information. We derive these functions in this work. The effective degrees of freedom and asymptotic results are also presented as well as the residual analysis, highlighting the normal curvature of local influence under different perturbation schemes. An application with real data is given for illustration.

Submitted by Daniela Kubudi Glasman (dkubudi@gmail.com) on 2014-06-23T17:18:45Z No. of bitstreams: 1 tese_DanielaKubudi_final.pdf: 1329488 bytes, checksum: 78a5e9b2527544313ec47b6425dbeb07 (MD5) / Approved for entry into archive by BRUNA BARROS (bruna.barros@fgv.br) on 2014-10-27T16:31:57Z (GMT) No. of bitstreams: 1 tese_DanielaKubudi_final.pdf: 1329488 bytes, checksum: 78a5e9b2527544313ec47b6425dbeb07 (MD5) / Approved for entry into archive by Marcia Bacha (marcia.bacha@fgv.br) on 2014-11-13T13:38:37Z (GMT) No. of bitstreams: 1 tese_DanielaKubudi_final.pdf: 1329488 bytes, checksum: 78a5e9b2527544313ec47b6425dbeb07 (MD5) / Made available in DSpace on 2014-11-13T13:39:30Z (GMT). No. of bitstreams: 1 tese_DanielaKubudi_final.pdf: 1329488 bytes, checksum: 78a5e9b2527544313ec47b6425dbeb07 (MD5) Previous issue date: 2013-02-25 / This thesis consists of three works that analyses the term structure of interest rates using different datasets and models. Chapter 1 proposes a parametric interest rate model that allows for segmentation and local shocks in the term structure. Adopting U.S. Treasury data, two versions of this segmented model are implemented. Based on a sequence of 142 forecasting experiments, the proposed models are compared to established benchrnarks and find that they outperform in out-of-sample forecasting results, specially for short-term maturities and for the 12-month horizon forecast. Chapter 2 adds no-arbitrage restrictions when estimating a dynamic gaussian polynomial term structure model for the Brazilian interest rate market. This article propose an important approximation of the time series of term structure risk factors, that allows to extract the risk premium embedded in interest rate zero coupon instruments without having to run a fui! optimization of a dynamic model. This methodology has the advantage to be easily implemented and provides a good approximation for the term structure risk premia that can be used in many applications. Chapter 3 models the joint dynamic of nominal and real yields using an affine macro-finance no-arbitrage term structure model in order to decompose the break even inflation rates into inflation risk premiums and inflation expectations in the US market. The Yields-Only and the Macro version of this model are implemented and the estimated inflation risk premiums obtained are small and quite stable during the sample period, but have differences when comparing the two versions of the model. / Esta tese é composta de três artigos que analisam a estrutura a termo das taxas de juros usando diferentes bases de dados e modelos. O capítulo 1 propõe um modelo paramétrico de taxas de juros que permite a segmentação e choques locais na estrutura a termo. Adotando dados do tesouro americano, duas versões desse modelo segmentado são implementadas. Baseado em uma sequência de 142 experimentos de previsão, os modelos propostos são comparados à benchmarks e concluí-se que eles performam melhor nos resultados das previsões fora da amostra, especialmente para as maturidades curtas e para o horizonte de previsão de 12 meses. O capítulo 2 acrescenta restrições de não arbitragem ao estimar um modelo polinomial gaussiano dinâmico de estrutura a termo para o mercado de taxas de juros brasileiro. Esse artigo propõe uma importante aproximação para a série temporal dos fatores de risco da estrutura a termo, que permite a extração do prêmio de risco das taxas de juros sem a necessidade de otimização de um modelo dinâmico completo. Essa metodologia tem a vantagem de ser facilmente implementada e obtém uma boa aproximação para o prêmio de risco da estrutura a termo, que pode ser usada em diferentes aplicações. O capítulo 3 modela a dinâmica conjunta das taxas nominais e reais usando um modelo afim de não arbitagem com variáveis macroeconômicas para a estrutura a termo, afim de decompor a diferença entre as taxas nominais e reais em prêmio de risco de inflação e expectativa de inflação no mercado americano. Uma versão sem variáveis macroeconômicas e uma versão com essas variáveis são implementadas e os prêmios de risco de inflação obtidos são pequenos e estáveis no período analisado, porém possuem diferenças na comparação dos dois modelos analisados.

Cette thèse a été conçu pour explorer les modèles dynamiques de régression, d’évaluer les inférences statistiques pour l’analyse des données de survie et de fiabilité. Ces modèles de régression dynamiques que nous avons considérés, y compris le modèle des hasards proportionnels paramétriques et celui de la vie accélérée avec les variables qui peut-être dépendent du temps. Nous avons discuté des problèmes suivants dans cette thèse.Nous avons présenté tout d’abord une statistique de test du chi-deux généraliséeY2nquiest adaptative pour les données de survie et fiabilité en présence de trois cas, complètes,censurées à droite et censurées à droite avec les covariables. Nous avons présenté en détailla forme pratique deY2nstatistique en analyse des données de survie. Ensuite, nous avons considéré deux modèles paramétriques très flexibles, d’évaluer les significations statistiques pour ces modèles proposées en utilisantY2nstatistique. Ces modèles incluent du modèle de vie accélérés (AFT) et celui de hasards proportionnels (PH) basés sur la distribution de Hypertabastic. Ces deux modèles sont proposés pour étudier la distribution de l’analyse de la duré de survie en comparaison avec d’autre modèles paramétriques. Nous avons validé ces modèles paramétriques en utilisantY2n. Les études de simulation ont été conçus.Dans le dernier chapitre, nous avons proposé les applications de ces modèles paramétriques à trois données de bio-médicale. Le premier a été fait les données étendues des temps de rémission des patients de leucémie aiguë qui ont été proposées par Freireich et al. sur la comparaison de deux groupes de traitement avec des informations supplémentaires sur les log du blanc du nombre de globules. Elle a montré que le modèle Hypertabastic AFT est un modèle précis pour ces données. Le second a été fait sur l’étude de tumeur cérébrale avec les patients de gliome malin, ont été proposées par Sauerbrei & Schumacher. Elle a montré que le meilleur modèle est Hypertabastic PH à l’ajout de cinq variables de signification. La troisième demande a été faite sur les données de Semenova & Bitukov, à concernant les patients de myélome multiple. Nous n’avons pas proposé un modèle exactement pour ces données. En raison de cela était les intersections de temps de survie.Par conséquent, nous vous conseillons d’utiliser un autre modèle dynamique que le modèle de la Simple Cross-Effect à installer ces données. / This thesis was designed to explore the dynamic regression models, assessing the sta-tistical inference for the survival and reliability data analysis. These dynamic regressionmodels that we have been considered including the parametric proportional hazards andaccelerated failure time models contain the possibly time-dependent covariates. We dis-cussed the following problems in this thesis.At first, we presented a generalized chi-squared test statisticsY2nthat is a convenient tofit the survival and reliability data analysis in presence of three cases: complete, censoredand censored with covariates. We described in detail the theory and the mechanism to usedofY2ntest statistic in the survival and reliability data analysis. Next, we considered theflexible parametric models, evaluating the statistical significance of them by usingY2nandlog-likelihood test statistics. These parametric models include the accelerated failure time(AFT) and a proportional hazards (PH) models based on the Hypertabastic distribution.These two models are proposed to investigate the distribution of the survival and reliabilitydata in comparison with some other parametric models. The simulation studies were de-signed, to demonstrate the asymptotically normally distributed of the maximum likelihood estimators of Hypertabastic’s parameter, to validate of the asymptotically property of Y2n test statistic for Hypertabastic distribution when the right censoring probability equal 0% and 20%.n the last chapter, we applied those two parametric models above to three scenes ofthe real-life data. The first one was done the data set given by Freireich et al. on thecomparison of two treatment groups with additional information about log white blood cellcount, to test the ability of a therapy to prolong the remission times of the acute leukemiapatients. It showed that Hypertabastic AFT model is an accurate model for this dataset.The second one was done on the brain tumour study with malignant glioma patients, givenby Sauerbrei & Schumacher. It showed that the best model is Hypertabastic PH onadding five significance covariates. The third application was done on the data set given by Semenova & Bitukov on the survival times of the multiple myeloma patients. We did not propose an exactly model for this dataset. Because of that was an existing oneintersection of survival times. We, therefore, suggest fitting other dynamic model as SimpleCross-Effect model for this dataset.