When we try to understand why some schools perform worse than others, if Covid-19 has struck harder on some demographics or whether income correlates with increased happiness, we may turn to regression to better understand how these variables are correlated. To capture the true relationship between variables we may use variable selection methods in order to ensure that the variables which have an actual effect have been included in the model. Choosing the right model for variable selection is vital. Without it there is a risk of including variables which have little to do with the dependent variable or excluding variables that are important. Failing to capture the true effects would paint a picture disconnected from reality and it would also give a false impression of what reality really looks like. To mitigate this risk a simulation study has been conducted to find out what variable selection algorithms to apply in order to make more accurate inference. The different algorithms being tested are stepwise regression, backward elimination and lasso regression. Lasso performed worst when applied to a small sample but performed best when applied to larger samples. Backward elimination and stepwise regression had very similar results.

The thesis project described in this report was conducted at Scania CV (Scania), which is a global company that delivers transport solutions to customers all around the globe. The project was conducted as a simulation study of the production flow of the output shaft manufacturing line UGA (Utgående Axel), located at the transmission department (DX) in Södertälje. The main objectives for the simulation study was to identify possible enhancements to increase the line-capacity and -OPE, and based on the findings provide a set of recommended actions Scania can take to increase the performance of the production line. To conduct the project was a simulation model developed in another master’s thesis back in 2019 provided to the authors. But since both the production line and the products manufactured at UGA line have been subjected to changes since 2019 was this model outdated and the validity of the model had to be confirmed. Therefore was a thorough current state description developed that was utilized to identify the gap between the simulation model from 2019 and the current state at the productionline. Based on the gap-analysis was it decided that the model from 2019 did not reflect UGA line in its current state to a satisfying degree. Therefore was a new simulation model developed, which then was updated with new input data. During the development of the new simulation model was the old model used as a template where the features that still accurately described UGA line was retained. The new simulation model was validated by a comparison between simulated throughput from the simulation model and historical throughput from UGA line. The validation showed a difference in mean weekly throughput of 0,3 %. It was therefore concluded that the simulation model accurately describe UGA line in its current state. The validated model was then used to simulate a number of different scenarios, and the result was analysed to find different areas for improvements. Finally was the result from the analysis compiled as recommended actions, that in turn was divided into short- and long-term actions. Where the actions categorised as short term concerns actions that could bring improvements to the existing production line, while the long-term actions require reconfigurations of the layout to be realized. The result showed that continue working on decreasing cycle times to achieve the defined goal cycletimes will have a positive effect on the lines capacity, but not on the overall line OPE. The reason for this is that the effect from other losses in the production line will increase when the cycle times become more uniform. But since the capacity will be significantly improved as the goal cycle time is reached, is Scania still recommended to continue their work with cycle time reduction, and if possible reduce the cycle times in some specific machines below the current goal. In addition is Scania in short-term recommended to identify and reduce the undefined stop time that frequently occur, reduce quality losses and improve machine availability. Regarding the long-term actions is Scania recommended to investigate the possibility to reconfigure UGA line. The simulations showed that both increasing buffer sizes at strategic positions to improve bottleneck utilization, or decouple the line to make it less sensitive will positively affect the capacity and OPE. In addition did the simulations of the combination of these two configurations show the greatest improvement among all simulations. Scania is therefore recommended to investigate the business case around either of these configurations or a combination of both. / Examensarbetet som beskrivs i denna rapport genomfördes hos Scania CV (Scania), vilket är ett globalt företag som levererar transportlösningar till kunder över hela världen. Projektet genomfördes som en simuleringsstudie av produktionsflödet hos produktionslinjen för utgående axlar, UGA-linjen (Utgående Axel), som är belägen på transmissionsavdelningen (DX) i Södertälje. De huvudsakliga målen för simuleringsstudien var att identifiera möjliga förbättringar för att öka linjekapaciteten och -OPE, och baserat på resultaten tillhandahålla en uppsättning rekommenderade åtgärder Scania kan vidta för att öka produktionslinjens prestanda. För att genomföra projektet tilldelades författarna en simuleringsmodell som utvecklats i ett tidigare examensarbete under 2019. Eftersom både produktionslinjen och produkterna som tillverkats på UGA-linjen har genomgått förändringar sedan 2019 ansågs modell vara föråldrad och modellens validitet behövde bekräftas. Därför arbetades en grundlig nulägesbeskrivning fram som sedan användes för att identifiera gapet mellan simuleringsmodellen från 2019 och nuläget vid produktionslinjen. Baserat på gap-analysen konstaterades det att modellen från 2019 inte återspeglade UGA-linjen till en tillfredsställande grad. Därför utvecklades en ny simulerings modell som sedan uppdaterades med ny indata. Under utvecklingen av den nya simuleringsmodellen användes den gamla modellen som en mall där de funktioner som fortfarande beskrev UGA-linjen på ett bra sätt bibehölls. Den nya simuleringsmodellen validerades genom en jämförelse mellan simulerad produktion och historiskt rapporterad produktion från UGA-linjen. Valideringen visade en skillnad i genomsnittligt antal producerade produkter per vecka på 0,3%. De konstaterades därför att simuleringsmodellen på ett tillförlitligt sätt beskriver UGA-linjen i sitt nuvarande tillstånd. Den validerade modellen användes sedan för att simulera ett antal olika scenarier vars resultat analyserades för att hitta olika förbättringsområden. Slutligen sammanställd resultaten från analysen som rekommenderade åtgärder, som i sin tur delades in i åtgärder på kort- och lång-sikt. De åtgärder som kategoriserats som kortsiktiga är åtgärder som kan medföra förbättringar av den befintliga produktionslinjen, medan de långsiktiga åtgärderna kräver förändring av layouten för att genomföras. Resultatet visade att fortsatta arbetet med att minska cykeltider för att uppnå de uppsatta målcykeltiderna kommer att ha en positiv effekt på linjekapaciteten, men inte på total OPE för linjen. Anledningen till detta är att effekten av andra förluster i produktionslinjen ökar när variationen i cykeltid mellan maskinerna minskar. Men eftersom kapaciteten kommer att öka markant om målcykeltiderna uppnås rekommenderas Scania att fortsätta arbeta med cykeltidsreducering och om möjligt minska cykeltiderna under det nuvarande målet för vissa maskiner. Dessutom rekommenderas Scania på kort sikt att; identifiera och minska den odefinierade stopptid som ofta förekommer, minska kvalitetsförluster och förbättra maskintillgängligheten. När det gäller de långsiktiga åtgärderna rekommenderas Scania att undersöka möjligheten att bygga om UGA-linjen. Detta eftersom simuleringarna visade att både ökade buffertstorlekar vid strategiska positioner för att förbättra utnyttjandegraden hos flaskhalsmaskinerna, och att koppla isär linjen för att göra den mindre känslig kommer att påverka både kapacitet och OPE positivt. Dessutom visade simuleringarna av kombinationen av dessa två konfigurationer den största förbättringen bland alla simuleringar. Scania rekommenderas därför att undersöka möjligheten kring någon av dessa konfigurationer eller en kombination av båda.

This is a sandwich thesis / In an interrupted time series (ITS) design, data are collected at multiple time points before and after the implementation of an intervention or program to investigate the effect of the intervention on an outcome of interest. ITS design is often implemented in healthcare settings and is considered the strongest quasi-experimental design in terms of internal and external validity as well as its ability to establish causal relationships. There are several statistical methods that can be used to analyze data from ITS studies. Nevertheless, limitations exist in practical applications, where researchers inappropriately apply the methods, and frequently ignore the assumptions and factors that may influence the optimality of the statistical analysis. Moreover, there is little to no guidance available regarding the application of the various methods, and a standardized framework for analysis of ITS studies does not exist. As such, there is a need to identify and compare existing ITS methods in terms of their strengths and limitations. Their methodological challenges also need to be investigated to inform and direct future research. In light of this, this PhD thesis addresses two main objectives: 1) to conduct a scoping review of the methods that have been employed in the analysis of ITS studies, and 2) to develop improved methods that address a major limitation of the statistical methods frequently used in ITS data analysis. These objectives are addressed in three projects. For the first project, a scoping review of the methods that have been used in analyzing ITS data was conducted, with the focus on ITS applications in health research. The review was based on the Arksey and O’Malley framework and the Joanna Briggs Handbook for scoping reviews. A total of 1389 studies were included in our scoping review. The articles were grouped into methods papers and applications papers based on the focus of the article. For the methods papers, we narratively described the identified methods and discussed their strengths and limitations. The application papers were summarized using frequencies and percentages. We identified some limitations of current methods and provided some recommendations useful in health research. In the second project, we developed and presented an improved method for ITS analysis when the data at each time point are aggregated across several participants, which is the most common case in ITS studies in healthcare settings. We considered the segmented linear regression approach, which our scoping review identified as the most frequently used method in ITS studies. When data are aggregated, heterogeneity is introduced due to variability in the patient population within sites (e.g. healthcare facilities) and this is ignored in the segmented linear regression method. Moreover, statistical uncertainty (imprecision) is introduced in the data because of the sample size (number of participants from whom data are aggregated). Ignoring this variability and uncertainty will likely lead to invalid estimates and loss of statistical power, which in turn leads to erroneous conclusions. Our proposed method incorporates patient variability and sample size as weights in a weighted segmented regression model. We performed extensive simulations and assessed the performance of our method using established performance criteria, such as bias, mean squared error, level and statistical power. We also compared our method with the segmented linear regression approach. The results indicated that the weighted segmented regression was uniformly more precise, less biased and more powerful than the segmented linear regression method. In the third project, we extended the weighted method to multisite ITS studies, where data are aggregated at two levels: across several participants within sites as well as across multiple sites. The extended method incorporates the two levels of heterogeneity using weights, where the weights are defined using patient variability, sample size, number of sites as well as site-to-site variability. This extended weighted regression model, which follows the weighted least squares approach is employed to estimate parameters and perform significance testing. We conducted extensive empirical evaluations using various scenarios generated from a multi-site ITS study and compared the performance of our method with that of the segmented linear regression model as well as a pooled analysis method previously developed for multisite studies. We observed that for most scenarios considered, our method produced estimates with narrower 95% confidence intervals and smaller p-values, indicating that our method is more precise and is associated with more statistical power. In some scenarios, where we considered low levels of heterogeneity, our method and the previously proposed method showed comparable results. In conclusion, this PhD thesis facilitates future ITS research by laying the groundwork for developing standard guidelines for the design and analysis of ITS studies. The proposed improved method for ITS analysis, which is the weighted segmented regression, contributes to the advancement of ITS research and will enable researchers to optimize their analysis, leading to more precise and powerful results. / Thesis / Doctor of Philosophy (PhD)

The Swedish health care system plays a vital role in satisfying the citizens’ demands for quality health care services. To deliver the right services in time in a hospital, an efficient admission plan is required, but this can be difficult to achieve. The Department of Pulmonary Medicine at the University Hospital in Linköping needs a better admission plan for their patients. In the department, the patient demand does not match the capacity, which leads to overcrowding at the ward. The aim of this thesis is to improve the admission plan of patients for the ward at the Department of Pulmonary Medicine by using discrete event simulation. To fulfil the aim, a simulation study is performed to understand how the system is working, where the problems emerged and how to prevent overcrowding. Different experiments are performed to check what could improve the admission plan at the ward. The results from this study shows that an improvement of the admission plan could be reached by better cooperation between involved units, improved documentation at the Department, a queue system of patients based on medical priorities and changed number of care beds. These solutions can prevent overcrowding and deliver health care services in time.

The Cox proportional hazards model is a standard tool for modelling the effect of covariates on time to event in the presence of censoring. The appropriateness of this model is conditioned by the validity of the proportional hazards assumption. The assumption is explained in the thesis and methods for its testing are described in detail. The tests are implemented in R, including self-written version of the Lin- Zhang-Davidian test. Their application is illustrated on medical data. The ability of the tests to reveal the violation of the proportional hazards assumption is investigated in a simulation study. The results suggest that the highest power is attained by the newly implemented Lin-Zhang-Davidian test in most cases. In contrast, the weighted version of the Lin-Wei-Ying test was found to have inadequate size for low sample sizes.

The Vrinnevi hospital in Norrköping faces a series of changes in conjunction with “Vision 2020”, the emergency ward is no exception. One of the goals that has been set up is to have 80 % of the arriving patients leave the ER within four hours, while having received the proper care. This study maps out the flow of patients through the ER, from arrival to discharge, as well as the process in between. The study also identifies the areas where bottlenecks in the patient flow are likely to appear and describes countermeasures to remedy such situations. In order to achieve this, a simulation model has been created. Facts used in the study are mainly based on previous studies, interviews with employees at the emergency ward, as well as some assumptions based on a theoretical background. Visits to the ER in question have been made, to gain a better understanding of the system that the simulation will illustrate. The study does not contain any deeper economic analysis. The focus is placed on examining whether the proposed changes to the system will affect the patient flow by measuring number of discharged patients within four hours, number of patients who receive a medical assessment within 30 minutes and the number of patients who get to meet a doctor within an hour. Five different scenarios, changing the work process at the ER, based on previous studies attempting to reduce patient throughput, have been created. The scenarios have been analyzed to form an understanding of how they may affect the different efficiency measurements of the emergency ward. The scenarios that have been simulated are: implementation of doctor-assisted triage, implementation on a “Clinical Initiative Nurse” in the waiting room, a reduction of administrative workload for the employees and adding resources to the emergency ward during specific hours of the day. Lastly, a combination scenario containing experiments with three of the most efficient measures has been created in order to achieve a discharge rate of 80 % within four hours. In conclusion, it is evident that all the scenarios have a positive effect on the efficiency measurements and that they all can be implemented so long as there is a positive attitude towards change and, in some cases, economic support.

Performance is key to survival. From day-to-day foraging events, to reproductive activities, to life-or-death crises, how well an organism performs these tasks can determine success or failure. Selection, therefore, both natural and sexual, act upon performance, and performance demands on individuals shape a population’s morphological and physiological trait distributions. While studies of morphological adaptations to ecological pressures implicitly center on the idea that responses to selection improve performance via changes in morphology, the relationships between morphology, performance, and fitness are not always well understood. In this dissertation, I investigate these relationships explicitly, as well as determine the effects that different ecological and genetic contexts have on selection and how populations respond to performance pressures. Using a model of lizard locomotor performance, I address three issues that may impact selection on performance that are often overlooked in performance studies. First, performance is not a static trait. Rather, individuals possess a range of performance abilities or intensities that can be expressed as needed. Using a novel, individual-based, quantitative genetic simulation model, I demonstrate the effects of variable performance expression and genetic constraints on how a population experiences and responds to selection on sprint and endurance performance. Second, sex differences in performance are expected in sexually dimorphic species, but empirical evidence for this is lacking. To this end, I measured and analyzed multivariate morphology and performance in Anolis carolinensis to identify sex-specific patterns in functional morphology and functional trade-offs within a broad suite of performance traits. Third, intralocus sexual conflict should constrain the evolution of the multivariate performance phenotype in both sexes. By extending the simulation model to include correlated trait inheritance between sexes and sex-specific selection on certain performance traits, I demonstrate the extent to which this sexual conflict constrains performance evolution. In combining studies of natural populations with simulation studies of selection, this dissertation embraces the complexity of performance to address the multiple contributing factors and constraints on performance evolution, and demonstrates the importance of accounting for such complexity when studying animal performance.

Previous solutions for the the Law of Categorical Judgment with category boundary variability have either constrained the standard deviations of the category boundaries in some way or have violated the assumptions of the scaling model. In the current work, a fully Bayesian Markov chain Monte Carlo solution for the Law of Categorical Judgment is given that estimates all model parameters (i.e. scale values, category boundaries, and the associated standard deviations). The importance of measuring category boundary standard deviations is discussed in the context of previous research in signal detection theory, which gives evidence of interindividual variability in how respondents perceive category boundaries and even intraindividual variability in how a respondent perceives category boundaries across trials. Although the measurement of category boundary standard deviations appears to be important for describing the way respondents perceive category boundaries on the latent scale, the inclusion of category boundary standard deviations in the scaling model exposes an inconsistency between the model and the rating method. Namely, with category boundary variability, the scaling model suggests that a respondent could experience disordinal category boundaries on a given trial. However, the idea that a respondent actually experiences disordinal category boundaries seems unlikely. The discrepancy between the assumptions of the scaling model and the way responses are made at the individual level indicates that the assumptions of the model will likely not be met. Therefore, the current work examined how well model parameters could be estimated when the assumptions of the model were violated in various ways as a consequence of disordinal category boundary perceptions. A parameter recovery study examined the effect of model violations on estimation accuracy by comparing estimates obtained from three response processes that violated the assumptions of the model with estimates obtained from a novel response process that did not violate the assumptions of the model. Results suggest all parameters in the Law of Categorical Judgment can be estimated reasonably well when these particular model violations occur, albeit to a lesser degree of accuracy than when the assumptions of the model are met.

This thesis discusses the changes in parameters of linear models and methods of their detection. It begins with a short introduction of the two basic types of change point detection procedures and bootstrap algorithms developed specifically to deal with dependent data. In the following chapter we focus on the location model - the simplest example of a linear model with a change in parameters. On this model we will illustrate a way of long-run variance estimation and implementation of selected bootstrap procedures. In the last chapter we show how to extend the applied methods to linear models with a change in parameters. We will compare the performance of change point tests based on asymptotic and bootstrap critical values through simulation studies in both our considered methods. The performance of selected long-run variance estimator will also be examined both for situations when the change in parameters occurs and when it does not. 1

Title: Tests of independence for multivariate data Author: Bc. Michal Kudlík Department: Department of Probability and Mathematical Statistics Supervisor: Ing. Marek Omelka, PhD., Department of Probability and Mathema- tical Statistics Abstract: This thesis is an overview of tests of independence for multidimensi- onal data. The report includes tests on independence of categorical and conti- nuous random variables, tests assuming normal distribution of data, asymptotic nonparametric tests and permutation tests with application of the Monte Carlo method. This thesis shows the suitability of tests with properly chosen real data and checks significance level and compares the strength of the selected tests by simulation study while using appropriate statistical software. Based on the simu- lation study the thesis discusses an appropriateness of the use of different tests for different situations. Keywords: independence, permutation and asymptotic tests of independence, Monte Carlo method, simulation study 1