This thesis makes contributions to the statistical research field of causal inference in observational studies. The results obtained are directly applicable in many scientific fields where effects of treatments are investigated and yet controlled experiments are difficult or impossible to implement. In the first paper we define a partially specified directed acyclic graph (DAG) describing the independence structure of the variables under study. Using the DAG we show that given that unconfoundedness holds we can use the observed data to select minimal sets of covariates to control for. General covariate selection algorithms are proposed to target the defined minimal subsets. The results of the first paper are generalized in Paper II to include the presence of unobserved covariates. Morevoer, the identification assumptions from the first paper are relaxed. To implement the covariate selection without parametric assumptions we propose in the third paper the use of a model-free variable selection method from the framework of sufficient dimension reduction. By simulation the performance of the proposed selection methods are investigated. Additionally, we study finite sample properties of treatment effect estimators based on the selected covariate sets. In paper IV we investigate misspecifications of parametric models of a scalar summary of the covariates, the propensity score. Motivated by common model specification strategies we describe misspecifications of parametric models for which unbiased estimators of the treatment effect are available. Consequences of the misspecification for the efficiency of treatment effect estimators are also studied.

Charnigo and Srinivasan originally developed compound estimators to nonparametrically estimate mean response functions and their derivatives simultaneously when there is one response variable and one covariate. The compound estimator maintains self consistency and almost optimal convergence rate. This dissertation studies, in part, compound estimation with multiple responses and/or covariates. An empirical comparison of compound estimation, local regression and spline smoothing is included, and near optimal convergence rates are established in the presence of multiple covariates. James and Stein proposed an estimator of the mean vector of a p dimensional multivariate normal distribution, which produces a smaller risk than the maximum likelihood estimator if p is at least 3. In this dissertation, we also extend their idea to a nonparametric regression setting. More specifically, we present Steinized local regression estimators of p mean response functions and their derivatives. We consider different covariance structures for the error terms, and whether or not a known upper bound for the estimation bias is assumed. We also apply Steinization to compound estimation, considering the application of Steinization to both pointwise estimators (for example, as obtained through local regression) and weight functions. Finally, the new methodology introduced in this dissertation will be demonstrated on numerical data illustrating the outcomes of a laboratory experiment in which radiation induces nanoparticles to scatter evanescent waves. The patterns of scattering, as represented by derivatives of multiple mean response functions, may be used to classify nanoparticles on their sizes and structures.

This thesis contributes to the research area of causal inference, where estimation of the effect of a treatment on an outcome of interest is the main objective. Some aspects of the estimation of average causal effects in observational studies in general, and case-control studies in particular, are explored. An important part of estimating causal effects in an observational study is to control for covariates. The first paper of this thesis concerns the selection of minimal covariate sets sufficient for unconfoundedness of the treatment assignment. A data-driven implementation of two covariate selection algorithms is proposed and evaluated. A common sampling scheme in epidemiology, and when investigating rare events, is the case-control design. In the second paper we study estimators of the marginal causal odds ratio in matched and independent case-control designs. Estimators that, under a logistic regression model, utilize information about the known prevalence of being a case is examined and compared through simulations. The third paper investigates the particular situation where case-control sampled data is reused to estimate the effect of the case-defining event on an outcome of interest. The consequence of ignoring the design when estimating the average causal effect is discussed and a design-weighted matching estimator is proposed. The performance of the estimator is evaluated with simulation experiments, when matching on the covariates directly and when matching on the propensity score. The last paper studies the effect of type 1 diabetes mellitus (T1DM) on school achievements using data from the Swedish Childhood Diabetes Register, a population-based incidence register. We apply theoretical results from the second and third papers in the estimation of the average causal effect within the T1DM population. A matching estimator that accounts for the matched case-control design is used.

Causal graphs are essential tools to find sufficient adjustment sets in observational studies. Subject matter experts can sometimes specify these graphs, but often the dependence structure of the variables, and thus the graph, is unknown even to them. In such cases, structure learning algorithms can be used to learn the graph. Early structure learning algorithms were implemented for either exclusively discrete or continuous variables. Recently, methods have been developed for structure learning on mixed data, including both continuous and discrete variables. In this thesis, three structure learning algorithms for mixed data are evaluated through a simulation study. The evaluation is based on graph recovery metrics and the ability to find a sufficient adjustment set for the average treatment effect (ATE). Depending on the intended purpose of the learned graph, the different evaluation metrics should be given varying attention. It is also concluded that the pcalg+micd algorithm learns graphs such that it is possible to find a sufficient adjustment set for the ATE in more than 99% of the cases. Moreover, the learned graphs from pcalg+micd are the most accurate compared to the true graph using the largest sample size.

Machine learning (ML) has become ubiquitous in various disciplines and applications, serving as a powerful tool for developing predictive models to analyze diverse variables of interest. With the advent of the digital era, the proliferation of data has presented numerous opportunities for growth and expansion across various domains. However, along with these opportunities, there is a unique set of challenges that arises due to the dynamic and ever-changing nature of data. These challenges include concept drift, which refers to shifting data distributions over time, and other data-related issues that can be framed as learning problems. Traditional static models are inadequate in handling these issues, underscoring the need for novel approaches to enhance the performance robustness and reliability of ML models to effectively navigate the inherent non-stationarity in the online world. The field of concept drift is characterized by several intricate aspects that challenge learning algorithms, including the analysis of model performance, which requires evaluating and understanding how the ML model's predictive capability is affected by different problem settings. Additionally, determining the magnitude of drift necessary for change detection is an indispensable task, as it involves identifying substantial shifts in data distributions. Moreover, the integration of adaptive methodologies is essential for updating ML models in response to data dynamics, enabling them to maintain their effectiveness and reliability in evolving environments. In light of the significance and complexity of the topic, this dissertation offers a fresh perspective on the performance robustness and adaptivity of ML models in non-stationary environments. The main contributions of this research include exploring and organizing the literature, analyzing the performance of ML models in the presence of different types of drift, and proposing innovative methodologies for drift detection and adaptation that solve real-world problems. By addressing these challenges, this research paves the way for the development of more robust and adaptive ML solutions capable of thriving in dynamic and evolving data landscapes. / Machine learning (ML) is widely used in various disciplines as a powerful tool for developing predictive models to analyze diverse variables. In the digital era, the abundance of data has created growth opportunities, but it also brings challenges due to the dynamic nature of data. One of these challenges is concept drift, the shifting data distributions over time. Consequently, traditional static models are inadequate for handling these challenges in the online world. Concept drift, with its intricate aspects, presents a challenge for learning algorithms. Analyzing model performance and detecting substantial shifts in data distributions are crucial for integrating adaptive methodologies to update ML models in response to data dynamics, maintaining effectiveness and reliability in evolving environments. In this dissertation, a fresh perspective is offered on the robustness and adaptivity of ML models in non-stationary environments. This research explores and organizes existing literature, analyzes ML model performance in the presence of drift, and proposes innovative methodologies for detecting and adapting to drift in real-world problems. The aim is to develop more robust and adaptive ML solutions capable of thriving in dynamic and evolving data landscapes.

No description available.

<p>Background: Post-operative pain management in total joint replacement surgery remains to be ineffective in up to 50% of patients and remains to have overwhelming impacts in terms of patient well-being and healthcare burden. The MOBILE trial was designed to assess whether the addition of gabapentin to a multimodal perioperative analgesia regimen can reduce morphine consumption or improve analgesia of patients following total joint arthroplasty. We present here empirical application of these various statistical methods to the MOBILE trial.</p> <p>Methods: Part 1: Analysis of covariance (ANCOVA) was used to adjust for baseline measures and to provide an unbiased estimate of the mean group difference of the one year post-operative knee flexion scores in knee arthroplasty patients. Robustness test were done by comparing ANCOVA to three comparative methods: i) the post-treatment scores, ii) change in scores, iii) percentage change from baseline.</p> <p>Part 2: Morphine consumption, taken at 4 time periods, of both the total hip and total knee arthroplasty patients was analyzed using linear mixed-effects model (LMEM) to provide a longitudinal estimate of the group difference. Repeated measures ANOVA and generalized estimating equations were used in a sensitivity analysis to compare robustness of the methods. Additionally, robustness of different covariance matrix structures in the LMEM were tested, namely first order auto-regressive compared to compound symmetry and unstructured.</p> <p>Results: Part 1: All four methods showed similar direction of effect, however ANCOVA (-3.9, 95% CI -9.5, 1.6, p=0.15) and post-treatment score (-4.3, 95% CI -9.8, 1.2, p=0.12) method provided the highest precision of estimate compared to change score (-3.0, 95% CI -9.9, 3.8, p=0.38) and percent change (-0.019, 95% CI -0.087, 0.050, p=0.58).</p> <p>Part 2: There was no statistically significant difference between the morphine consumption in the treatment group and the control group (1.0, 95% CI -4.7, 6.7, p=0.73). The results remained robust across different longitudinal methods and different covariance matrix structures.</p> <p>Conclusion: ANCOVA, through both simulation and empirical studies, provides the best statistical estimation for analyzing continuous outcomes requiring covariate adjustment. More wide-spread of the use of ANCOVA should be recommended amongst not only biostatisticians but also clinicians and trialists. The re-analysis of the morphine consumption aligns with the results of the MOBILE trial that gabapentin did not significantly reduce morphine consumption in patients undergoing major replacement surgeries. More work in area of post-operative pain is required to provide sufficient management for this patient population.</p> / Master of Science (MSc)

Educational researchers are often interested in phenomena that unfold over time within a person and at the same time, relationships between their characteristics that are stable over time. Since variables in a longitudinal study reflect both within- and between-person effects, researchers need to disaggregate them to understand the phenomenon of interest correctly. Although the person-mean centering technique has been believed as the gold standard of the disaggregation method, recent studies found that the centering did not work when there was a trend in the predictor. Hence, they proposed some detrending techniques to remove the systematic change; however, they were only applicable to multilevel models. Therefore, this dissertation develops novel detrending methods based on structural equation modeling (SEM). It also establishes the links between centering and detrending by reviewing a broad range of literature. The proposed SEM-based detrending methods are compared to the existing centering and detrending methods through a series of Monte Carlo simulations. The results indicate that (a) model misspecification for the time-varying predictors or outcomes leads to large bias of and standard error, (b) statistical properties of estimates of the within- and between-person effects are mostly determined by the type of between-person predictors (i.e., observed or latent), and (c) for unbiased estimation of the effects, models with latent between-person predictors require nonzero growth factor variances, while those with observed predictors at the between level need either nonzero or zero variance, depending on the parameter. As concluding remarks, some practical recommendations are provided based on the findings of the present study. / Doctor of Philosophy / Educational researchers are often interested in longitudinal phenomena within a person and relations between the person's characteristics. Since repeatedly measured variables reflect their within- and between-person aspects, researchers need to disaggregate them statistically to understand the phenomenon of interest. Recent studies found that the traditional centering method, where the individual's average of a predictor was subtracted from the original predictor value, could not correctly disentangle the within- and between-person effects when the predictor showed a systematic change over time (i.e., trend). They proposed some techniques to remove the trend; however, the detrending methods were only applicable to multilevel models. Therefore, the present study develops novel detrending methods using structural equation modeling. The proposed models are compared to the existing methods through a series of Monte Carlo simulations, where we can manipulate a data-generating model and its parameter values. The results indicate that (a) model misspecification for the time-varying predictor or outcome leads to systematic deviation of the estimates from their true values, (b) statistical properties of estimates of the effects are mostly determined by the type of between-person predictors (i.e., observed or latent), and (c) the latent predictor models require nonzero growth factor variances for unbiased estimation, while the observed predictor models need either nonzero or zero variance, depending on the parameter. As concluding remarks, some recommendations for the practitioners are provided.

<p>Population pharmacokinetic-pharmacodynamic (PK-PD) models can be fitted using nonlinear mixed effects modelling (NONMEM). This is an efficient way of learning about drugs and diseases from data collected in clinical trials. Identifying covariates which explain differences between patients is important to discover patient subpopulations at risk of sub-therapeutic or toxic effects and for treatment individualization. Stepwise covariate modelling (SCM) is commonly used to this end. The aim of the current thesis work was to evaluate SCM and to develop alternative approaches. A further aim was to develop a mechanistic PK-PD model describing fasting plasma glucose, fasting insulin, insulin sensitivity and beta-cell mass.</p><p>The lasso is a penalized estimation method performing covariate selection simultaneously to shrinkage estimation. The lasso was implemented within NONMEM as an alternative to SCM and is discussed in comparison with that method. Further, various ways of incorporating information and propagating knowledge from previous studies into an analysis were investigated. In order to compare the different approaches, investigations were made under varying, replicated conditions. In the course of the investigations, more than one million NONMEM analyses were performed on simulated data. Due to selection bias the use of SCM performed poorly when analysing small datasets or rare subgroups. In these situations, the lasso method in NONMEM performed better, was faster, and additionally validated the covariate model. Alternatively, the performance of SCM can be improved by propagating knowledge or incorporating information from previously analysed studies and by population optimal design.</p><p>A model was also developed on a physiological/mechanistic basis to fit data from three phase II/III studies on the investigational drug, tesaglitazar. This model described fasting glucose and insulin levels well, despite heterogeneous patient groups ranging from non-diabetic insulin resistant subjects to patients with advanced diabetes. The model predictions of beta-cell mass and insulin sensitivity were well in agreement with values in the literature.</p>

Population pharmacokinetic-pharmacodynamic (PK-PD) models can be fitted using nonlinear mixed effects modelling (NONMEM). This is an efficient way of learning about drugs and diseases from data collected in clinical trials. Identifying covariates which explain differences between patients is important to discover patient subpopulations at risk of sub-therapeutic or toxic effects and for treatment individualization. Stepwise covariate modelling (SCM) is commonly used to this end. The aim of the current thesis work was to evaluate SCM and to develop alternative approaches. A further aim was to develop a mechanistic PK-PD model describing fasting plasma glucose, fasting insulin, insulin sensitivity and beta-cell mass. The lasso is a penalized estimation method performing covariate selection simultaneously to shrinkage estimation. The lasso was implemented within NONMEM as an alternative to SCM and is discussed in comparison with that method. Further, various ways of incorporating information and propagating knowledge from previous studies into an analysis were investigated. In order to compare the different approaches, investigations were made under varying, replicated conditions. In the course of the investigations, more than one million NONMEM analyses were performed on simulated data. Due to selection bias the use of SCM performed poorly when analysing small datasets or rare subgroups. In these situations, the lasso method in NONMEM performed better, was faster, and additionally validated the covariate model. Alternatively, the performance of SCM can be improved by propagating knowledge or incorporating information from previously analysed studies and by population optimal design. A model was also developed on a physiological/mechanistic basis to fit data from three phase II/III studies on the investigational drug, tesaglitazar. This model described fasting glucose and insulin levels well, despite heterogeneous patient groups ranging from non-diabetic insulin resistant subjects to patients with advanced diabetes. The model predictions of beta-cell mass and insulin sensitivity were well in agreement with values in the literature.