Migrationsverket är en myndighet som prövar ansökningar från personer som vill söka skydd, ha medborgarskap, studera eller vill jobba i Sverige. Då det på senare tid varit en stor ökning i dessa ansökningar har tiden för vilket ett beslut tar ökat. Varje typ av ansökning (exempelvis medborgarskap) är en process som består av flera steg. Hur beslutet går igenom dessa steg kallas för flöde. Migrationsverket vill därför öka sin flödeseffektivitet. När beslutet är klart och personen tagit del av det men inte är nöjd kan denne överklaga. Detta är en av de mest komplexa processerna på Migrationsverket. Syftet är analysera hur lång tid denna process tar och vilka steg i processen som påverkar tiden. Ett steg (som senare visar sig ha en stor effekt på tiden) är yttranden. Det är när domstolen begär information om vad personen som överklagar har att säga om varför denne överklagar. För att analysera detta var två metoder relevanta, accelerated failure time (AFT) och \multi-state models (MSM). Den ena kan predicera tid till händelse (AFT) medan den andra kan analysera effekten av tidspåverkan (MSM) i stegen. Yttranden tidigt i processen har stor betydelse för hur snabbt en överklagan får en dom samtidigt som att antal yttranden ökar tiden enormt. Det finns andra faktorer som påverkar tiden men inte i så stor grad som yttranden. Då yttranden tidigt i processen samtidigt som antal yttranden har betydelse kan flödeseffektiviteten ökas med att ta tid på sig att skriva ett informativt yttrande som gör att domstolen inte behöver begära flera yttranden. / The Swedish Migration Board is an agency that review applications from individuals who wish to seek shelter, have citizenship, study or want to work in Sweden. In recent time there has been a large increase in applications and the time for which a decision is made has increased. Each type of application (such as citizenship) is a process consisting of several stages. How the decision is going through these steps is called flow. The Swedish Migration Board would therefore like to increase their flow efficiency. When the decision is made and the person has take part of it but is not satisfied, he can appeal. This is one of the most complex processes at the Board. The aim is to analyze how long this process will take and what steps in the process affects the time. One step (which was later found to have a significant effect on time) is opinions. This is when the court requests information on what the person is appealing has to say about why he is appealing. To analyze this, two methods were relevant, accelerated failure time (AFT) and the multi-state models (MSM). One can predict time to event (AFT), the other to analyze the effect of time-manipulation (MSM) in the flow. Opinions early in the process is crucial to how quickly an appeal get judgment while the number of opinions increases the time enormously. There are other factors that affect the time but not so much as opinions. The flow efficiency can be increased by taking time to write an informative opinion which allows the court need not to ask for more opinions.

Continuous-time multi-state models are widely used in modeling longitudinal data of disease processes with multiple transient states, yet the analysis is complex when subjects are observed periodically, resulting in interval censored data. Recently, most studies focused on modeling the true disease progression as a discrete time stationary Markov chain, and only a few studies have been carried out regarding non-homogenous multi-state models in the presence of interval-censored data. In this dissertation, several likelihood-based methodologies were proposed to deal with interval censored data in multi-state models. Firstly, a continuous time version of a homogenous Markov multi-state model with backward transitions was proposed to handle uneven follow-up assessments or skipped visits, resulting in the interval censored data. Simulations were used to compare the performance of the proposed model with the traditional discrete time stationary Markov chain under different types of observation schemes. We applied these two methods to the well-known Nun study, a longitudinal study of 672 participants aged ≥ 75 years at baseline and followed longitudinally with up to ten cognitive assessments per participant. Secondly, we constructed a non-homogenous Markov model for this type of panel data. The baseline intensity was assumed to be Weibull distributed to accommodate the non-homogenous property. The proportional hazards method was used to incorporate risk factors into the transition intensities. Simulation studies showed that the Weibull assumption does not affect the accuracy of the parameter estimates for the risk factors. We applied our model to data from the BRAiNS study, a longitudinal cohort of 531 subjects each cognitively intact at baseline. Last, we presented a parametric method of fitting semi-Markov models based on Weibull transition intensities with interval censored cognitive data with death as a competing risk. We relaxed the Markov assumption and took interval censoring into account by integrating out all possible unobserved transitions. The proposed model also allowed for incorporating time-dependent covariates. We provided a goodness-of-fit assessment for the proposed model by the means of prevalence counts. To illustrate the methods, we applied our model to the BRAiNS study.

Modelos multi-estados têm sido utilizados para descrever o comportamento de unidades amostrais cuja principal resposta é o tempo necessário para a ocorrência de seqüências de eventos. Consideramos um modelo multi-estados markoviano, não homogêneo, que incorpora covariáveis cujos efeitos podem variar ao longo do tempo (efeitos dinâmicos), o que permite a generalização dos modelos usualmente empregados. Resultados assintóticos mostram que procedimentos de estimação baseados no método histograma crivo convergem para um processo gaussiano. A metodologia proposta mostra-se adequada na modelagem de dados reais para comparação de desenvolvimento de recém-nascidos pré-termo com os a termo. Estudos com dados gerados artificialmente confirmam os resultados teóricos obtidos. / Multi-state models have been used to describe the behavior of sample units where the principal response is the time needed for the occurrence of a sequence of events. We consider a non-homogeneous Markovian multi-state model that incorporates covariates with time-dependent coefficient (dynamic effects), generalizing models usually employed. The asymptotic results show that the estimators based on the method of histogram sieves converge to a Gaussian process. The proposed methodology revels adequated for modeling data related to the comparison of developement of preterm infants with term infants. The studies with artificially generated data confirm the asymptotic results.

Modelos multi-estados têm sido utilizados para descrever o comportamento de unidades amostrais cuja principal resposta é o tempo necessário para a ocorrência de seqüências de eventos. Consideramos um modelo multi-estados markoviano, não homogêneo, que incorpora covariáveis cujos efeitos podem variar ao longo do tempo (efeitos dinâmicos), o que permite a generalização dos modelos usualmente empregados. Resultados assintóticos mostram que procedimentos de estimação baseados no método histograma crivo convergem para um processo gaussiano. A metodologia proposta mostra-se adequada na modelagem de dados reais para comparação de desenvolvimento de recém-nascidos pré-termo com os a termo. Estudos com dados gerados artificialmente confirmam os resultados teóricos obtidos. / Multi-state models have been used to describe the behavior of sample units where the principal response is the time needed for the occurrence of a sequence of events. We consider a non-homogeneous Markovian multi-state model that incorporates covariates with time-dependent coefficient (dynamic effects), generalizing models usually employed. The asymptotic results show that the estimators based on the method of histogram sieves converge to a Gaussian process. The proposed methodology revels adequated for modeling data related to the comparison of developement of preterm infants with term infants. The studies with artificially generated data confirm the asymptotic results.

Dementia is a clinical syndrome caused by neurodegeneration or cerebrovascular injury. Patients with dementia suffer from deterioration in memory, thinking, behavior and the ability to perform everyday activities. Since there are no cures or disease-modifying therapies for dementia, there is much interest in identifying modifiable risk factors that may help prevent or slow the progression of cognitive decline. Medications are a common focus of this type of research. Importantly, according to a report from the Centers for Disease Control and Prevention (CDC), 19.1% of the population aged 60 and over report taking antidepressants during 2011-2014, and this number tends to increase. However, antidepressant use among the elderly may be concerning because of the potentially harmful effects on cognition. To assess the impacts of antidepressants on the risk of dementia, we conducted three consecutive projects. In the first project, a retrospective cohort study using Marginal Structural Cox Proportional Hazards regression model with Inverse Probability Weighting (IPW) was conducted to evaluate the average causal effects of different classes of antidepressant on the risk of dementia. Potential causal effects of selective serotonin reuptake inhibitors (SSRIs), serotonin and norepinephrine reuptake inhibitors (SNRIs), atypical anti-depressants (AAs) and tri-cyclic antidepressants (TCAs) on the risk of dementia were observed at the 0.05 significance level. Multiple sensitivity analyses supported these findings. Unmeasured confounding is a threat to the validity of causal inference methods. In evaluating the effects of antidepressants, it is important to consider how common comorbidities of depression, such as sleep disorders, may affect both the exposure to anti-depressants and the onset of cognitive impairment. In this dissertation, sleep apnea and rapid-eye-movement behavior disorder (RBD) were unmeasured and thus uncontrolled confounders for the association between antidepressant use and the risk of dementia. In the second project, a bias factor formula for two binary unmeasured confounders was derived in order to account for these variables. Monte Carlo analysis was implemented to estimate the distribution of the bias factor for each class of antidepressant. The effects of antidepressants on the risk of dementia adjusted for both measured and unmeasured confounders were estimated. Sleep apnea and RBD attenuated the effect estimates for SSRI, SNRI and AA on the risk of dementia. In the third project, to account for potential time-varying confounding and observed time-varying treatment, a multi-state Markov chain with three transient states (normal cognition, mild cognitive impairment (MCI), and impaired but not MCI) and two absorbing states (dementia and death) was performed to estimate the probabilities of moving between finite and mutually exclusive cognitive state. This analysis also allowed participants to recover from mild impairments (i.e., mild cognitive impairment, impaired but not MCI) to normal cognition, and accounted for the competing risk of death prior to dementia. These findings supported the results of the main analysis in the first project.

The basic function of an electric power system is to supply its customers with electric energy as economically as possible and with a reasonable degree of continuity and quality. Power system reliability evaluation techniques are now highly developed through the work of many researchers and engineers. It is expected that the application of power system reliability evaluation in bulk power systems will continue to increase in the future especially in the newly deregulated power industry. This thesis presents research conducted on the three areas of incorporating multi-state generating unit models, evaluating system performance indices and identifying transmission deficiencies in composite system adequacy assessment. The research was done using a previously developed software package designated as MECORE. Many generating companies in both the traditionally regulated and newly deregulated electrical power industry have large generating units that can operate in one or more derated states. In this research work, load point and system reliability indices are evaluated using two-state and multi-state generating unit models to examine the impact of incorporating multi-state generating unit models in composite system adequacy assessment. The intention behind deregulation in the power industry is to increase competition in order to obtain better service quality and lower production costs. This research illustrates how Canadian power systems have performed in the past using data compiled by the Canadian Electricity Association. A procedure to predict similar indices is presented and used to estimate future performance and the effects of system modifications. The incentives for market participants to invest in new generation and transmission facilities are highly influenced by the market risk in a deregulation environment. An adequate transmission system is a key element in a dynamic competitive market. This thesis presents a procedure to identify transmission deficiencies in composite generation and transmission system. The research work illustrated in this thesis is focused on the application of probabilistic techniques in composite system adequacy assessment and particularly in the newly deregulated electric power industry. The conclusions and the techniques presented should prove valuable to those responsible for power system planning.

The basic function of an electric power system is to supply its customers with electric energy as economically as possible and with a reasonable degree of continuity and quality. Power system reliability evaluation techniques are now highly developed through the work of many researchers and engineers. It is expected that the application of power system reliability evaluation in bulk power systems will continue to increase in the future especially in the newly deregulated power industry. This thesis presents research conducted on the three areas of incorporating multi-state generating unit models, evaluating system performance indices and identifying transmission deficiencies in composite system adequacy assessment. The research was done using a previously developed software package designated as MECORE. Many generating companies in both the traditionally regulated and newly deregulated electrical power industry have large generating units that can operate in one or more derated states. In this research work, load point and system reliability indices are evaluated using two-state and multi-state generating unit models to examine the impact of incorporating multi-state generating unit models in composite system adequacy assessment. The intention behind deregulation in the power industry is to increase competition in order to obtain better service quality and lower production costs. This research illustrates how Canadian power systems have performed in the past using data compiled by the Canadian Electricity Association. A procedure to predict similar indices is presented and used to estimate future performance and the effects of system modifications. The incentives for market participants to invest in new generation and transmission facilities are highly influenced by the market risk in a deregulation environment. An adequate transmission system is a key element in a dynamic competitive market. This thesis presents a procedure to identify transmission deficiencies in composite generation and transmission system. The research work illustrated in this thesis is focused on the application of probabilistic techniques in composite system adequacy assessment and particularly in the newly deregulated electric power industry. The conclusions and the techniques presented should prove valuable to those responsible for power system planning.

In practice, data are frequently incomplete in one way or another. It can be a significant challenge to make valid inferences about the parameters of interest in this situation. In this thesis, three problems involving such data are addressed. The first two problems involve interval-censored life history data with mismeasured covariates. Data of this type are incomplete in two ways. First, the exact event times are unknown due to censoring. Second, the true covariate is missing for most, if not all, individuals. This work focuses primarily on the impact of covariate measurement error in progressive multi-state models with data arising from panel (i.e., interval-censored) observation. These types of problems arise frequently in clinical settings (e.g. when disease progression is of interest and patient information is collected during irregularly spaced clinic visits). Two and three state models are considered in this thesis. This work is motivated by a research program on psoriatic arthritis (PsA) where the effects of error-prone covariates on rates of disease progression are of interest and patient information is collected at clinic visits (Gladman et al. 1995; Bond et al. 2006). Information regarding the error distributions were available based on results from a separate study conducted to evaluate the reliability of clinical measurements that are used in PsA treatment and follow-up (Gladman et al. 2004). The asymptotic bias of covariate effects obtained ignoring error in covariates is investigated and shown to be substantial in some settings. In a series of simulation studies, the performance of corrected likelihood methods and methods based on a simulation-extrapolation (SIMEX) algorithm (Cook \& Stefanski 1994) were investigated to address covariate measurement error. The methods implemented were shown to result in much smaller empirical biases and empirical coverage probabilities which were closer to the nominal levels. The third problem considered involves an extreme case of interval censoring known as current status data. Current status data arise when individuals are observed only at a single point in time and it is then determined whether they have experienced the event of interest. To complicate matters, in the problem considered here, an unknown proportion of the population will never experience the event of interest. Again, this type of data is incomplete in two ways. One assessment is made on each individual to determine whether or not an event has occurred. Therefore, the exact event times are unknown for those who will eventually experience the event. In addition, whether or not the individuals will ever experience the event is unknown for those who have not experienced the event by the assessment time. This problem was motivated by a series of orthopedic trials looking at the effect of blood thinners in hip and knee replacement surgeries. These blood thinners can cause a negative serological response in some patients. This response was the outcome of interest and the only available information regarding it was the seroconversion time under current status observation. In this thesis, latent class models with parametric, nonparametric and piecewise constant forms of the seroconversion time distribution are described. They account for the fact that only a proportion of the population will experience the event of interest. Estimators based on an EM algorithm were evaluated via simulation and the orthopedic surgery data were analyzed based on this methodology.

In practice, data are frequently incomplete in one way or another. It can be a significant challenge to make valid inferences about the parameters of interest in this situation. In this thesis, three problems involving such data are addressed. The first two problems involve interval-censored life history data with mismeasured covariates. Data of this type are incomplete in two ways. First, the exact event times are unknown due to censoring. Second, the true covariate is missing for most, if not all, individuals. This work focuses primarily on the impact of covariate measurement error in progressive multi-state models with data arising from panel (i.e., interval-censored) observation. These types of problems arise frequently in clinical settings (e.g. when disease progression is of interest and patient information is collected during irregularly spaced clinic visits). Two and three state models are considered in this thesis. This work is motivated by a research program on psoriatic arthritis (PsA) where the effects of error-prone covariates on rates of disease progression are of interest and patient information is collected at clinic visits (Gladman et al. 1995; Bond et al. 2006). Information regarding the error distributions were available based on results from a separate study conducted to evaluate the reliability of clinical measurements that are used in PsA treatment and follow-up (Gladman et al. 2004). The asymptotic bias of covariate effects obtained ignoring error in covariates is investigated and shown to be substantial in some settings. In a series of simulation studies, the performance of corrected likelihood methods and methods based on a simulation-extrapolation (SIMEX) algorithm (Cook \& Stefanski 1994) were investigated to address covariate measurement error. The methods implemented were shown to result in much smaller empirical biases and empirical coverage probabilities which were closer to the nominal levels. The third problem considered involves an extreme case of interval censoring known as current status data. Current status data arise when individuals are observed only at a single point in time and it is then determined whether they have experienced the event of interest. To complicate matters, in the problem considered here, an unknown proportion of the population will never experience the event of interest. Again, this type of data is incomplete in two ways. One assessment is made on each individual to determine whether or not an event has occurred. Therefore, the exact event times are unknown for those who will eventually experience the event. In addition, whether or not the individuals will ever experience the event is unknown for those who have not experienced the event by the assessment time. This problem was motivated by a series of orthopedic trials looking at the effect of blood thinners in hip and knee replacement surgeries. These blood thinners can cause a negative serological response in some patients. This response was the outcome of interest and the only available information regarding it was the seroconversion time under current status observation. In this thesis, latent class models with parametric, nonparametric and piecewise constant forms of the seroconversion time distribution are described. They account for the fact that only a proportion of the population will experience the event of interest. Estimators based on an EM algorithm were evaluated via simulation and the orthopedic surgery data were analyzed based on this methodology.

Multi-state models are useful for modelling progression of a disease, where states represent the health status of a subject under study. In practice, patients may be observed when necessity strikes thus implying that the disease and observation processes are not independent. Often, clinical visits are postponed or advanced by the clinician or patient themselves based on the health status of the patient. In such situations, there is a potential for the frequency and timing of the examinations to be dependent on the latent transition times, and the observation process may be informative. We consider the case where the exact times of transitions between health states of the patient are not observed and so the disease process is interval censored. We model the disease and observation processes jointly to ensure valid inference. The transition intensities are modelled assuming proportional hazards and we link the two processes via random effects. Using a Bayesian framework we apply our joint model to the analysis of a large study examining cancer trajectories of palliative care patients. / Graduate