This thesis aimed to apply the causal framework with potential outcomes to examine the causal effect of air temperature on reported violent crimes in Swedish municipalities. The Generalized Estimating Equations method was used on yearly, monthly and also July only data for the time period 2002-2014. One significant causal effect was established but the majority of the results pointed to there being no causal effect between air temperature and reported violent crimes.

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.

In clustered survival data, unobservable cluster effects may exert powerful influences on the outcomes and thus induce correlation among subjects within the same cluster. The ordinary partial likelihood approach does not account for this dependence. Frailty models, as an extension to Cox regression, incorporate multiplicative random effects, called frailties, into the hazard model and have become a very popular way to account for the dependence within clusters. We particularly study the two-level nested lognormal frailty model and propose an estimation approach based on the complete data likelihood with frailty terms integrated out. We adopt B-splines to model the baseline hazards and adaptive Gauss-Hermite quadrature to approximate the integrals efficiently. Furthermore, in finding the maximum likelihood estimators, instead of the Newton-Raphson iterative algorithm, Gauss-Seidel and BFGS methods are used to improve the stability and efficiency of the estimation procedure. We also study competing risks models with missing cause of failure in the context of Cox proportional hazards models. For competing risks data, there exists more than one cause of failure and each observed failure is exclusively linked to one cause. Conceptually, the causes are interpreted as competing risks before the failure is observed. Competing risks models are constructed based on the proportional hazards model specified for each cause of failure respectively, which can be estimated using partial likelihood approach. However, the ordinary partial likelihood is not applicable when the cause of failure could be missing for some reason. We propose a weighted partial likelihood approach based on complete-case data, where weights are computed as the inverse of selection probability and the selection probability is estimated by a logistic regression model. The asymptotic properties of the regression coefficient estimators are investigated by applying counting process and martingale theory. We further develop a double robust approach based on the full data to improve the efficiency as well as the robustness.

Statistical models are often used for the prediction of future random variables. There are two types of prediction, point prediction and probabilistic prediction. The prediction accuracy is quantified by performance measures, which are typically based on loss functions. We study the estimators of these performance measures, the prediction error and performance scores, for point and probabilistic predictors, respectively. The focus of this thesis is to assess the prediction performance of survival models that analyze censored survival times. To accommodate censoring, we extend the inverse probability censoring weighting (IPCW) method, thus arbitrary loss functions can be handled. We also develop confidence interval procedures for these performance measures. We compare model-based, apparent loss based and cross-validation estimators of prediction error under model misspecification and variable selection, for absolute relative error loss (in chapter 3) and misclassification error loss (in chapter 4). Simulation results indicate that cross-validation procedures typically produce reliable point estimates and confidence intervals, whereas model-based estimates are often sensitive to model misspecification. The methods are illustrated for two medical contexts in chapter 5. The apparent loss based and cross-validation estimators of performance scores for probabilistic predictor are discussed and illustrated with an example in chapter 6. We also make connections for performance.

Statistical models are often used for the prediction of future random variables. There are two types of prediction, point prediction and probabilistic prediction. The prediction accuracy is quantified by performance measures, which are typically based on loss functions. We study the estimators of these performance measures, the prediction error and performance scores, for point and probabilistic predictors, respectively. The focus of this thesis is to assess the prediction performance of survival models that analyze censored survival times. To accommodate censoring, we extend the inverse probability censoring weighting (IPCW) method, thus arbitrary loss functions can be handled. We also develop confidence interval procedures for these performance measures. We compare model-based, apparent loss based and cross-validation estimators of prediction error under model misspecification and variable selection, for absolute relative error loss (in chapter 3) and misclassification error loss (in chapter 4). Simulation results indicate that cross-validation procedures typically produce reliable point estimates and confidence intervals, whereas model-based estimates are often sensitive to model misspecification. The methods are illustrated for two medical contexts in chapter 5. The apparent loss based and cross-validation estimators of performance scores for probabilistic predictor are discussed and illustrated with an example in chapter 6. We also make connections for performance.

Many statistical methods for truncated data rely on the assumption that the failure and truncation time are independent, which can be unrealistic in applications. The study cohorts obtained from bone marrow transplant (BMT) registry data are commonly recognized as truncated samples, the time-to-failure is truncated by the transplant time. There are clinical evidences that a longer transplant waiting time is a worse prognosis of survivorship. Therefore, it is reasonable to assume the dependence between transplant and failure time. To better analyze BMT registry data, we utilize a Cox analysis in which the transplant time is both a truncation variable and a predictor of the time-to-failure. An inverse-probability-weighted (IPW) estimator is proposed to estimate the distribution of transplant time. Usefulness of the IPW approach is demonstrated through a simulation study and a real application.

This thesis consists of four papers that are related to commonly used propensity score-based estimators for average causal effects. The first paper starts with the observation that researchers often have access to data containing lots of covariates that are correlated. We therefore study the effect of correlation on the asymptotic variance of an inverse probability weighting and a matching estimator. Under the assumptions of normally distributed covariates, constant causal effect, and potential outcomes and a logit that are linear in the parameters we show that the correlation influences the asymptotic efficiency of the estimators differently, both with regard to direction and magnitude. Further, the strength of the confounding towards the outcome and the treatment plays an important role. The second paper extends the first paper in that the estimators are studied under the more realistic setting of using the estimated propensity score. We also relax several assumptions made in the first paper, and include the doubly robust estimator. Again, the results show that the correlation may increase or decrease the variances of the estimators, but we also observe that several aspects influence how correlation affects the variance of the estimators, such as the choice of estimator, the strength of the confounding towards the outcome and the treatment, and whether constant or non-constant causal effect is present. The third paper concerns estimation of the asymptotic variance of a propensity score matching estimator. Simulations show that large gains can be made for the mean squared error by properly selecting smoothing parameters of the variance estimator and that a residual-based local linear estimator may be a more efficient estimator for the asymptotic variance. The specification of the variance estimator is shown to be crucial when evaluating the effect of right heart catheterisation, i.e. we show either a negative effect on survival or no significant effect depending on the choice of smoothing parameters.   In the fourth paper, we provide an analytic expression for the covariance matrix of logistic regression with normally distributed regressors. This paper is related to the other papers in that logistic regression is commonly used to estimate the propensity score.

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We propose a new method for analyzing longitudinal data which contain responses that are missing at random. This method consists in solving the generalized estimating equation (GEE) of [7] in which the incomplete responses are replaced by values adjusted using the inverse probability weights proposed in [14]. We show that the root estimator is consistent and asymptotically normal, essentially under some conditions on the marginal distribution and the surrogate correlation matrix as those presented in [12] in the case of complete data, and under minimal assumptions on the missingness probabilities. This method is applied to a real-life dataset taken from [10], which examines the incidence of respiratory disease in a sample of 250 pre-school age Indonesian children which were examined every 3 months for 18 months, using as covariates the age, gender, and vitamin A deficiency.

In Chapter 1 of the dissertation, the role of social networks is analyzed as an important determinant in the search behavior of the unemployed. Based on the hypothesis that the unemployed generate information on vacancies through their social network, search theory predicts that individuals with large social networks should experience an increased productivity of informal search, and reduce their search in formal channels. Due to the higher productivity of search, unemployed with a larger network are also expected to have a higher reservation wage than unemployed with a small network. The model-theoretic predictions are tested and confirmed empirically. It is found that the search behavior of unemployed is significantly affected by the presence of social contacts, with larger networks implying a stronger substitution away from formal search channels towards informal channels. The substitution is particularly pronounced for passive formal search methods, i.e., search methods that generate rather non-specific types of job offer information at low relative cost. We also find small but significant positive effects of an increase of the network size on the reservation wage. These results have important implications on the analysis of the job search monitoring or counseling measures that are usually targeted at formal search only. Chapter 2 of the dissertation addresses the labor market effects of vacancy information during the early stages of unemployment. The outcomes considered are the speed of exit from unemployment, the effects on the quality of employment and the short-and medium-term effects on active labor market program (ALMP) participation. It is found that vacancy information significantly increases the speed of entry into employment; at the same time the probability to participate in ALMP is significantly reduced. Whereas the long-term reduction in the ALMP arises in consequence of the earlier exit from unemployment, we also observe a short-run decrease for some labor market groups which suggest that caseworker use high and low intensity activation measures interchangeably which is clearly questionable from an efficiency point of view. For unemployed who find a job through vacancy information we observe a small negative effect on the weekly number of hours worked. In Chapter 3, the long-term effects of participation in ALMP are assessed for unemployed youth under 25 years of age. Complementary to the analysis in Chapter 2, the effects of participation in time- and cost-intensive measures of active labor market policies are examined. In particular we study the effects of job creation schemes, wage subsidies, short-and long-term training measures and measures to promote the participation in vocational training. The outcome variables of interest are the probability to be in regular employment, and participation in further education during the 60 months following program entry. The analysis shows that all programs, except job creation schemes have positive and long-term effects on the employment probability of youth. In the short-run only short-term training measures generate positive effects, as long-term training programs and wage subsidies exhibit significant locking-in'' effects. Measures to promote vocational training are found to increase the probability of attending education and training significantly, whereas all other programs have either no or a negative effect on training participation. Effect heterogeneity with respect to the pre-treatment level education shows that young people with higher pre-treatment educational levels benefit more from participation most programs. However, for longer-term wage subsidies we also find strong positive effects for young people with low initial education levels. The relative benefit of training measures is higher in West than in East Germany. In the evaluation studies of Chapters 2 and 3 semi-parametric balancing methods of Propensity Score Matching (PSM) and Inverse Probability Weighting (IPW) are used to eliminate the effects of counfounding factors that influence both the treatment participation as well as the outcome variable of interest, and to establish a causal relation between program participation and outcome differences. While PSM and IPW are intuitive and methodologically attractive as they do not require parametric assumptions, the practical implementation may become quite challenging due to their sensitivity to various data features. Given the importance of these methods in the evaluation literature, and the vast number of recent methodological contributions in this field, Chapter 4 aims to reduce the knowledge gap between the methodological and applied literature by summarizing new findings of the empirical and statistical literature and practical guidelines for future applied research. In contrast to previous publications this study does not only focus on the estimation of causal effects, but stresses that the balancing challenge can and should be discussed independent of question of causal identification of treatment effects on most empirical applications. Following a brief outline of the practical implementation steps required for PSM and IPW, these steps are presented in detail chronologically, outlining practical advice for each step. Subsequently, the topics of effect estimation, inference, sensitivity analysis and the combination with parametric estimation methods are discussed. Finally, new extensions of the methodology and avenues for future research are presented. / In Kapitel 1 der Dissertation wird die Rolle von sozialen Netzwerken als Determinante im Suchverhalten von Arbeitslosen analysiert. Basierend auf der Hypothese, dass Arbeitslose durch ihr soziales Netzwerk Informationen über Stellenangebote generieren, sollten Personen mit großen sozialen Netzwerken eine erhöhte Produktivität ihrer informellen Suche erfahren, und ihre Suche in formellen Kanälen reduzieren. Durch die höhere Produktivität der Suche sollte für diese Personen zudem der Reservationslohn steigen. Die modelltheoretischen Vorhersagen werden empirisch getestet, wobei die Netzwerkinformationen durch die Anzahl guter Freunde, sowie Kontakthäufigkeit zu früheren Kollegen approximiert wird. Die Ergebnisse zeigen, dass das Suchverhalten der Arbeitslosen durch das Vorhandensein sozialer Kontakte signifikant beeinflusst wird. Insbesondere sinkt mit der Netzwerkgröße formelle Arbeitssuche - die Substitution ist besonders ausgeprägt für passive formelle Suchmethoden, d.h. Informationsquellen die eher unspezifische Arten von Jobangeboten bei niedrigen relativen Kosten erzeugen. Im Einklang mit den Vorhersagen des theoretischen Modells finden sich auch deutlich positive Auswirkungen einer Erhöhung der Netzwerkgröße auf den Reservationslohn. Kapitel 2 befasst sich mit den Arbeitsmarkteffekten von Vermittlungsangeboten (VI) in der frühzeitigen Aktivierungsphase von Arbeitslosen. Die Nutzung von VI könnte dabei eine „doppelte Dividende“ versprechen. Zum einen reduziert die frühe Aktivierung die Dauer der Arbeitslosigkeit, und somit auch die Notwendigkeit späterer Teilnahme in Arbeitsmarktprogrammen (ALMP). Zum anderen ist die Aktivierung durch Information mit geringeren locking-in‘‘ Effekten verbunden als die Teilnahme in ALMP. Ziel der Analyse ist es, die Effekte von frühen VI auf die Eingliederungsgeschwindigkeit, sowie die Teilnahmewahrscheinlichkeit in ALMP zu messen. Zudem werden mögliche Effekte auf die Qualität der Beschäftigung untersucht. Die Ergebnisse zeigen, dass VI die Beschäftigungswahrscheinlichkeit signifikant erhöhen, und dass gleichzeitig die Wahrscheinlichkeit in ALMP teilzunehmen signifikant reduziert wird. Für die meisten betrachteten Subgruppen ergibt sich die langfristige Reduktion der ALMP Teilnahme als Konsequenz der schnelleren Eingliederung. Für einzelne Arbeitsmarktgruppen ergibt sich zudem eine frühe und temporare Reduktion, was darauf hinweist, dass Maßnahmen mit hohen und geringen „locking-in“ Effekten aus Sicht der Sachbearbeiter austauschbar sind, was aus Effizienzgesichtspunkten fragwürdig ist. Es wird ein geringer negativer Effekt auf die wöchentliche Stundenanzahl in der ersten abhängigen Beschäftigung nach Arbeitslosigkeit beobachtet. In Kapitel 3 werden die Langzeiteffekte von ALMP für arbeitslose Jugendliche unter 25 Jahren ermittelt. Die untersuchten ALMP sind ABM-Maßnahmen, Lohnsubventionen, kurz-und langfristige Maßnahmen der beruflichen Bildung sowie Maßnahmen zur Förderung der Teilnahme an Berufsausbildung. Ab Eintritt in die Maßnahme werden Teilnehmer und Nicht-Teilnehmer für einen Zeitraum von sechs Jahren beobachtet. Als Zielvariable wird die Wahrscheinlichkeit regulärer Beschäftigung, sowie die Teilnahme in Ausbildung untersucht. Die Ergebnisse zeigen, dass alle Programme, bis auf ABM, positive und langfristige Effekte auf die Beschäftigungswahrscheinlichkeit von Jugendlichen haben. Kurzfristig finden wir jedoch nur für kurze Trainingsmaßnahmen positive Effekte, da lange Trainingsmaßnahmen und Lohnzuschüsse mit signifikanten locking-in‘‘ Effekten verbunden sind. Maßnahmen zur Förderung der Berufsausbildung erhöhen die Wahrscheinlichkeit der Teilnahme an einer Ausbildung, während alle anderen Programme keinen oder einen negativen Effekt auf die Ausbildungsteilnahme haben. Jugendliche mit höherem Ausbildungsniveau profitieren stärker von der Programmteilnahme. Jedoch zeigen sich für längerfristige Lohnsubventionen ebenfalls starke positive Effekte für Jugendliche mit geringer Vorbildung. Der relative Nutzen von Trainingsmaßnahmen ist höher in West- als in Ostdeutschland. In den Evaluationsstudien der Kapitel 2 und 3 werden die semi-parametrischen Gewichtungsverfahren Propensity Score Matching (PSM) und Inverse Probability Weighting (IPW) verwendet, um den Einfluss verzerrender Faktoren, die sowohl die Maßnahmenteilnahme als auch die Zielvariablen beeinflussen zu beseitigen, und kausale Effekte der Programmteilahme zu ermitteln. Während PSM and IPW intuitiv und methodisch sehr attraktiv sind, stellt die Implementierung der Methoden in der Praxis jedoch oft eine große Herausforderung dar. Das Ziel von Kapitel 4 ist es daher, praktische Hinweise zur Implementierung dieser Methoden zu geben. Zu diesem Zweck werden neue Erkenntnisse der empirischen und statistischen Literatur zusammengefasst und praxisbezogene Richtlinien für die angewandte Forschung abgeleitet. Basierend auf einer theoretischen Motivation und einer Skizzierung der praktischen Implementierungsschritte von PSM und IPW werden diese Schritte chronologisch dargestellt, wobei auch auf praxisrelevante Erkenntnisse aus der methodischen Forschung eingegangen wird. Im Anschluss werden die Themen Effektschätzung, Inferenz, Sensitivitätsanalyse und die Kombination von IPW und PSM mit anderen statistischen Methoden diskutiert. Abschließend werden neue Erweiterungen der Methodik aufgeführt.