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Adaptive clinical trial designs for survival outcomes testing the proportionality of hazards assumption
(09/11/2018) Stavropoulos, Charalampos; Σταυρόπουλος, Χαράλαμπος; Athens University of Economics and Business, Department of Statistics; Karlis, Dimitris
At this thesis we will examine a widely used assumption in the context of clinical trials, the assumption of proportional hazards. This assumption is about the relationship between the hazard functions of the groups that participate in the trial. More specifically, it is assumed that the ratio of hazard functions is constant through time. Based on that assumption, the researchers can use the Log Rank test and estimate the sample size that is needed. However, this is a very strict assumption and in this thesis we investigate its impact on the trial when it does not hold, in terms of power and sample size estimation. As an alternative, we investigate the Restricted Mean Survival Time (RMST), which is the mean survival time up to a certain point. We will use the difference between RMSTs for testing the difference between survival groups and we will compare this method to the Log Rank test under cases of proportional and non-proportional hazards. The comparison will be in terms of sample size estimation and power. Finally, we will provide a new clinical trial design that will start with the Log Rank test and at a certain point will test the proportionality assumption. If the assumption is rejected, the trial will adapt to testing the difference between RMSTs. The adaptive design’s performance will be compared to that of a simple design which does not test the proportionality assumption and uses the Log Rank test. The comparison will be in terms of sample size estimation and power.
Exploratory analysis, model selection and checking of structural assumptions in football data
Flakas, Ioannis A.; Φλάκας, Ιωάννης Α.; Athens University of Economics and Business, Department of Statistics; Karlis, Dimitris
Betting on the results of athletic competitions is very popular all over the world. Among sports, betting takes place mostly on football (soccer) and this is the reason for the vast application of statistical methodologies for the prediction of the outcome of a football game, like the number of goals scored by a team and several other characteristics of the game.In this thesis, we deal with the number of goals scored by a team. Our main aim is the evaluation of various models and the assessment of their predictive value. Research in soccer statistics has shown that the Poisson distribution can be used as the distribution of the number of goals scored by a team. So, we start by examining if the Poisson distribution is an appropriate for modeling such data. We base our conclusions on hypothesis testing making use of the index of dispersion, of the χ 2 test and a test proposed by Bohning (1994). We use data from 5 championships of different countries for 6 football seasons. Firstly, we investigate which variables should be included in our model in terms of statistical significance. We continue examining the independence between the goals scored by two opponents in a single match.For our purposes we use the Pearson chi-squared statistic and the Spearman’s and the Kendall’s correlation coefficients.Then we pursue a model comparison and by using AIC (Akaike, 1973)and BIC (Schwarz, 1978) we decide which of the bivariate Poisson models(Kocherlakota and Kocherlacota, 1992) fits best to our data. According to the selected model for each championship and for each season, we use the estimated parameters to generate replications of leagues. Each replication contains the same number of games with the corresponding league. For each league we generate 4,000 replications, and we calculate the average of the total team points and of the total number of goals scored and conceded by a team. These averages are used to check the agreement between the fitted distributions and the process that generated the actual data for each league,under the assumption that the model that is used is a sufficient summary of reality and the teams have the same performance as in observed league.At the end we examine the differences, in terms of fit, between the double Poisson model (two independent Poisson distributions) and the corresponding bivariate Poisson model.
Maximum likelihood estimation for overdispersed binomial and multinomial data through an EM algorithm
Mitsopoulos, Georgios D.; Karlis, Dimitris; Athens University of Economics and Business, Department of Statistics
The phenomenon of overdispersion is encountered very often when analyzing binomial/ multinomial data. Failure to take account of it may lead to inaccurate standard errors and misleading inference for the parameters of interest. A variety of models has been proposed to provide a solution to this problem,amongst of which are mixture models. The application of the latter, though,has been limited to a large extent by the complexity of the computations involved in fitting them. Hence, in the present thesis, logistic regression models based on beta-binomial and Dirichlet-multinomial distributions are presented, in order to fit overdispersed binomial and multinomial data,respectively. Interest is raised on the application of an Expectation-Maximization algorithm for finding maximum likelihood estimates, which proves to be a quite useful tool when trying to avoid computational difficulties that arise from applying these mixture models.
MCMC estimation of Poisson Bivariate Integer-Valued Autoregressive time series models
(Athens University of Economics and Business, 09-2012) Sofronas, Georgios; Athens University of Economics and Business, Department of Statistics; Karlis, Dimitris
Περιλαμβάνει περίληψη στην ελληνική και στην αγγλική
Model based clustering for young star clusters
(09/11/2018) Derezea, Efthymia; Δερεζέα, Ευθυμία; Vasdekis, Vassilis; Ntzoufras, Ioannis; Karlis, Dimitris
Model based clustering is a method of fitting finite mixtures models to data in order to identify clusters. It is widely used in many fields and has a variety of applications,one of those is the identification of young star clusters. We will examine four different models multivariate Gaussian, t, Skew Normal and Skew t mixtures and a method that suggests combining normal components to form a cluster. We will analyze their characteristics and we will then apply them to a real data set of young stars in order to evaluate their performance in this specific problem.
Surrogate markers in cancer clinical trials
Papadopoulou, Areti C.; Παπαδοπούλου, Αρετή Χ.; Athens University of Economics and Business, Department of Statistics; Karlis, Dimitris
Randomized clinical trials are the standard scientific method for evaluating new biological agents, drugs, devices or procedures that can improve medical practice including prolonging life time, improving life conditions or making the pain sustainable among other. Typically, these trials demand large sample size, long duration of treatment and follow-up, leading sometimes to drop-outs and some ethical conflicts. In many trials, the main outcome of interest is hard to be observed and thus other outcomes, which are considered surrogates of the one we would like to observe, are used for decision making. For example, in many cancer trials, while the overall survival of the patients is of interest, waiting until we observe death, can lead to lengthy in time trials with the danger that the decision to be late and thus, from an ethical point of view, to delay the use of a good drug. For this reason, in many cases, a surrogate of overall survival is considered, as for example the progression free survival or the disease free survival. Of course, before one proceed with the use of a surrogate endpoint, proper evaluation and validation of the surrogate endpoint must be conducted.In this thesis, we focus on time endpoints and in particular we restrict our interest in survival time endpoints in cancer trials. A natural procedure is to estimate some correlation between the two outcomes that are considered as surrogate and judge this surrogacy upon this correlation. With survival outcomes with censoring (as it is almost always the case) this is more demanding. A typical such procedure based on copulas will be examined in this thesis. However one main criticism on this method lies on the way the endpoints are defined. For example in breast cancer considering Disease Free Survival (DFS) as surrogate to Overall Survival (OS) may have a problem in the sense that DFS contains death in its definition and hence the observed correlation may be due to the fact that DFS is always smaller than OS. Current models do not make such an assumption/restriction and we want to see how this can affect our inference. For this purpose, we conducted an extensive simulation approach to examine how such a restriction can lead to different results when ignored. We have simulated three different scenarios and examine the impact. We have seen that the assumption is crucial and if we restrict the two variables to have some kind of ordering, i.e. DFS ≤ OS then we can observe correlation even if the two events are uncorrelated. We also examine a way to remedy this. The procedure described above was applied to datasets from real clinical trials such as Ovarian dataset available in R package surrogate and data simulated based on the published articles concerning HERA trial with respect the number of events and the observed HR as well as the patients characteristics.