Noncompliance to treatment allocation is likely to complicate estimation of causal effects in clinical trials. The ubiquitous nonrandom phenomenon of noncompliance renders per-protocol and as- treated analyses or even simple regression adjustments for noncompliance inadequate for causal inference. For survival data, several specialist methods have been developed when noncompliance is related to risk. The Causal Accelerated Life Model (CALM) allows time-dependent departures from randomized treatment in either arm and relates each observed event time to a potential event time that would have been observed if the control treatment had been given throughout the trial. Alternatively, the structural Proportional Hazards (C-Prophet) model accounts for all-or-nothing noncompliance in the treatment arm only while the CHARM estimator allows time-dependent departures from randomized treatment by considering survival outcome as a sequence of binary outcomes to provide an 'approximate' overall hazard ratio estimate which is adjusted for compliance. The problem of efficacy estimation is compounded for two-active treatment trials (additional noncompliance) where the ITT estimate provides a biased estimator for the true hazard ratio even under homogeneous treatment effects assumption. Using plausible arm-specific predictors of compliance, principal stratification methods can be applied to obtain principal effects for each stratum. The present work applies the above methods to data from the Esprit trials study which was conducted to ascertain whether or not unopposed oestrogen (hormone replacement therapy - HRT) reduced the risk of further cardiac events in postmenopausal women who survive a first myocardial infarction. We use statistically designed simulation studies to evaluate the performance of these methods in terms of bias and 95% confidence interval coverage. We also apply a principal stratification method to adjust for noncompliance in two treatment arms trial originally developed for binary data for survival analysis in terms of causal risk ratio. In a Bayesian framework, we apply the method to Esprit data to account for noncompliance in both treatment arms and estimate principal effects. We apply statistically designed simulation studies to evaluate the performance of the method in terms of bias in the causal effect estimates for each stratum. ITT analysis of the Esprit data showed the effects of taking HRT tablets was not statistically significantly different from placebo for both all cause mortality and myocardial reinfarction outcomes. Average compliance rate for HRT treatment was 43% and compliance rate decreased as the study progressed. CHARM and C-Prophet methods produced similar results but CALM performed best for Esprit: suggesting HRT would reduce risk of death by 50%. Simulation studies comparing the methods suggested that while both C-Prophet and CHARM methods performed equally well in terms of bias, the CALM method performed best in terms of both bias and 95% confidence interval coverage albeit with the largest RMSE. The principal stratification method failed for the Esprit study possibly due to the strong distribution assumption implicit in the method and lack of adequate compliance information in the data which produced large 95% credible intervals for the principal effect estimates. For moderate value of sensitivity parameter, principal stratification results suggested compliance with HRT tablets relative to placebo would reduce risk of mortality by 43% among the most compliant. Simulation studies on performance of this method showed narrower corresponding mean 95% credible intervals corresponding to the the causal risk ratio estimates for this subgroup compared to other strata. However, the results were sensitive to the unknown sensitivity parameter.

Les études observationnelles en pharmacoépidémiologie sont souvent mises en place pour évaluer un médicament mis sur le marché récemment ou concurrencé par de nombreuses alternatives thérapeutiques. Cette situation conduit à devoir évaluer l'effet d'un médicament dans une cohorte comprenant peu de sujets traités, c'est à dire une population où l'exposition d'intérêt est rare. Afin de prendre en compte les facteurs de confusion dans cette situation, certains auteurs déconseillent l'utilisation du score de propension au profit du score pronostique, mais cette recommandation ne s'appuie sur aucune étude évaluant spécifiquement les faibles prévalences de l'exposition, et ignore le type d'estimation, conditionnelle ou marginale, fournie par chaque méthode d'utilisation du score pronostique.La première partie de ce travail évalue les méthodes basées sur le score de propension pour l'estimation d'un effet marginal en situation d'exposition rare. La deuxième partie évalue les performances des méthodes basées sur le score pronostique rapportées dans la littérature, introduit de nouvelles méthodes basées sur le score pronostique adaptées à l'estimation d'effets conditionnels ou marginaux, et les compare aux performances des méthodes basées sur le score de propension. La dernière partie traite des estimateurs de la variance des effets du traitement. Nous présentons les conséquences liées à la non prise en compte de l'étape d'estimation du score de propension et du score pronostique dans le calcul de la variance. Nous proposons et évaluons de nouveaux estimateurs tenant compte de cette étape. / Pharmacoepidemiologic observational studies are often conducted to evaluate newly marketed drugs or drugs in competition with many alternatives. In such cohort studies, the exposure of interest is rare. To take into account confounding factors in such settings, some authors advise against the use of the propensity score in favor of the prognostic score, but this recommendation is not supported by any study especially focused on infrequent exposures and ignores the type of estimation provided by each prognostic score-based method.The first part of this work evaluates the use of propensity score-based methods to estimate the marginal effect of a rare exposure. The second part evaluates the performance of the prognostic score based methods already reported in the literature, compares them with the propensity score based methods, and introduces some new prognostic score-based methods intended to estimate conditional or marginal effects. The last part deals with variance estimators of the treatment effect. We present the opposite consequences of ignoring the estimation step of the propensity score and the prognostic score. We show some new variance estimators accounting for this step.

Background: Knee osteoarthritis (OA) is the most common type of OA and is a major cause of pain and thus results in disability for daily activities among persons living in the community. OA currently has no cure. In addition to the conflicting recommendations from clinical guidelines, evidence about the extent to which long-term use of intra-articular injections improves patient outcomes is also lacking. Methods: Using data from the Osteoarthritis Initiative (OAI), marginal structural models (MSMs) applying inverse probability treatment weights (IPTW) were used to examine the effectiveness of intra-articular injections and changes in symptoms over time. The specific aims of this dissertation were to: 1) evaluate longitudinal use of intra-articular injections after treatment initiation among persons with radiographic knee OA; 2) quantify the extent to which intra-articular injection relieves symptoms among persons with radiographic knee OA; and 3) evaluate the performance of missing data techniques under the setting of MSMs. Results: Of those initiating injections, ~19% switched, ~21% continued injection type, and ~60% did not report any additional injections. For participants initiating corticosteroid (CO) injections, greater symptoms post-initial injection rather than changes in symptoms over time were associated with continued use compared to one-time use. Among participants with radiographic evidence of knee OA, initiating treatments with either CO or hyaluronic acid (HA) injections was not associated with reduced symptoms compared to non-users over two years. Compared to inverse probability weighting (IPW), missing data techniques such as multiple imputation (MI) produced less biased marginal causal effects (IPW: -2.33% to 15.74%; -1.88% to 4.24%). For most scenarios, estimates using MI had smaller mean square error (range: 0.013 to 0.024) than IPW (range: 0.027 to 0.22). Conclusions: Among participants with radiographic evidence of knee OA living in the community, the proportion of those switching injection use and one-time users was substantial after treatment initiation. In addition, initiating injection use was not associated with reduced symptoms over time. With respect to issues of missing data, using MI may confer an advantage over IPW in MSMs applications. The results of this work highlight the importance of using comparative effectiveness research with non-experimental data to study these commonly used injections and may help to understand the usefulness of these treatments for patients with knee OA.

U.S. state governments have implemented numerous policies to help mitigate the spread of COVID-19. While there is strong biological evidence supporting the wearing of face masks or coverings in public spaces, the impact of public masking policies remains unclear. We aimed to evaluate how early versus delayed implementation of state-level public masking orders impacted subsequent COVID-19 growth rates. We defined “early” implementation as having a state-level mandate in place before September 1, 2020, the approximate start of the school-year. We defined COVID-19 growth rates as the relative increase in confirmed cases 7, 14, 21, 30, 45, 60-days after September 1. Primary analyses used targeted maximum likelihood estimation (TMLE) with Super Learner and considered a wide range of potential confounders to account for differences between states. In secondary analyses, we took an unadjusted approach and calculated the average COVID-19 growth rate among early-implementing states divided by the average COVID-19 growth rate among late-implementing states. At a national level, the expected growth rate after 14-days was 4%lower with early vs. delayed implementation (aRR: 0.96; 95%CI: 0.95-0.98). Associations did not plateau over time, but instead grew linearly. After 60-days, the expected growth rate was 16% lower with early vs. delayed implementation (aRR:0.84; 95%CI: 0.78-0.91). Unadjusted estimates were exaggerated (e.g. 60-day RR:0.72; 95%CI: 0.60-0.84). Sensitivity analyses varying the timing of the masking order yielded similar results. In both the short and long term, state-level public masking mandates were associated with lower COVID-19 growth rates. Given their low-cost and minimal (if any) impact on the economy, masking policies are promising public health strategies to mitigate further spread of COVID-19.

The use of automated procedures has recently become popular in the causal inference literature. Naive implementations of automatic procedures stand in contrast to the perspective advocated in Imbens and Rubin's Causal Inference. Imbens and Rubin suggest that researchers should make modelling decisions informed by subjective knowledge. We make use of simulated data to compare Imbens and Rubin's approach to naive implementations of two automatic procedures: Genetic Matching and Entropy Balancing. In addition we perform a small Monte Carlo simulation, based on one of the simulated data sets. Using the simulated data sets and the Monte Carlo simulations, we illustrate and explore benefits and drawbacks of the different approaches. We argue that there are benefits to make use of design-decisions grounded in subjective knowledge.

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.

This empirical register study intends to estimate average causal effects of relapse treatment on the risk for acute myocardial infarction (AMI) among patients with Diffuse B-Cell Lymphoma (DLBCL) within the potential outcome framework. The report includes a brief introduction to causal inference and survival anal- ysis and mentions specific causal parameters of interest that will be estimated. A cohort of 2887 Swedish DLBCL patients between 2007 and 2014 were included in the study where 560 patients suffered a relapse. The relapse treatment is hypothesised to be cardiotoxic and induces an increased risk of heart diseases. The identifiability assumptions need to hold to estimate average causal effects and are assessed in this report. The patient cohort is weighted using inverse probability of treatment and censoring weights and potential marginal survival curves are estimated from marginal structural Cox models. The resulting point estimate indicates a protective causal effect of relapse treatment on AMI but estimated bootstrap confidence intervals suggest no significant effect on the 5% significance level.

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