In this thesis we develop methods for dealing with missing data in a univariate response variable when estimating regression parameters. Missing outcome data is a problem in a number of applications, one of which is follow-up studies. In follow-up studies data is collected at two (or more) occasions, and it is common that only some of the initial participants return at the second occasion. This is the case in Paper II, where we investigate predictors of decline in self reported health in older populations in Sweden, the Netherlands and Italy. In that study, around 50% of the study participants drop out. It is common that researchers rely on the assumption that the missingness is independent of the outcome given some observed covariates. This assumption is called data missing at random (MAR) or ignorable missingness mechanism. However, MAR cannot be tested from the data, and if it does not hold, the estimators based on this assumption are biased. In the study of Paper II, we suspect that some of the individuals drop out due to bad health. If this is the case the data is not MAR. One alternative to MAR, which we pursue, is to incorporate the uncertainty due to missing data into interval estimates instead of point estimates and uncertainty intervals instead of confidence intervals. An uncertainty interval is the analog of a confidence interval but wider due to a relaxation of assumptions on the missing data. These intervals can be used to visualize the consequences deviations from MAR have on the conclusions of the study. That is, they can be used to perform a sensitivity analysis of MAR. The thesis covers different types of linear regression. In Paper I and III we have a continuous outcome, in Paper II a binary outcome, and in Paper IV we allow for mixed effects with a continuous outcome. In Paper III we estimate the effect of a treatment, which can be seen as an example of missing outcome data.

Pharmaceutical drug development is a costly and time consuming process. Reportedly, it takes about 10-15 years and ~900 million dollars of investment to launch a new drug in the world market. Any measure that increases the power and also decreases uncertainty about that power also increases drug net present value. For some time now, it has been argued that judicious utilization of available data might lead to more efficient use of resources during drug development. Conventionally, assessment of effectiveness has been based on comparing change from baseline at some pre-specified time for the control and test treatment (SPA). The last observation carry forward (LOCF) is a widely used technique if the data are missing due to any reason. Although, LOCF is known to introduce bias, the direction and magnitude is debatable.The primary aim of the proposed simulation experiments was to assess the properties of the random effects model (REM) and mixed model repeated measures (MMRM) methods that utilize all the data collected during pivotal trials. A total of 43 scenarios based on disease progression, magnitude of drug effect, between and within subject variability and patient drop-outs were analyzed. Three analysis methods, viz. SPA, REM and MMRM, were investigated. For the SPA method, the missing data were imputed with four different methods, such as LOCF, mean imputation, population and individual regression. The false-positive, false-negative inferences and bias in estimating the effect size for each method was assessed.The most important finding of this report is that the REM and MMRM methods are efficient alternatives to the SPA methods with ~50% savings on sample size. These methods are based on sound scientific principles and provide stronger evidence against the null hypothesis. The choice of the REM versus MMRM method is dependent on the purpose of the analysis and data gathered from the experimental design. The results support the use of likelihood-based MMRM methods for regulatory decision making. The REM methods are useful in understanding the time course of the disease and drug effect, making predictions based on the data and gaining insights into time to steady state effect for rational decision making. The SPA methods are less powerful across all the scenarios. The SPA-LOCF yielded anticonservative results in some cases with type-1 error rate exceeding 15% if data were missing due to toxicity. On the other hand, the drug effect was consistently underestimated (~40%), if data were missing due to lack of effectiveness. The results demonstrate that the SPA-LOCF methods make it practically impossible to establish effectiveness in these areas with a reasonable sample size.

La découverte d’un nouveau bassin, Regourdou 1, offre l’occasion de discuter de l’implication fonctionnelle de la morphologie pelvienne néandertalienne. Dans un premier temps, ce spécimen est décrit, ce qui permet de vérifier son appartenance aux Néandertaliens et mettre en évidence certains traits spécifiques à cette population. Bien qu’aucun ne soit autapomorphique, la combinaison de ces caractères caractérise la ceinture pelvienne néandertalienne. Le bassin Regourdou 1 est ensuite reconstruit à l’aide d’une estimation desdonnées manquantes, par thin-plate spline à partir de Kebara 2. Les dimensions du canal pelvien de Regourdou 1sont comparées à celles de deux autres spécimens néandertaliens (Tabun C1 et Kebara 2) et d’une populationmoderne (n=151). L’analyse de la morphologie des détroits obstétricaux néandertaliens (par morphométrie géométrique), et de la relation céphalo-pelvienne, met en évidence la présence de caractéristiques associées chez l’Homme anatomiquement moderne à la naissance rotationnelle. Notre travail confirme l’existence de mécaniques obstétricales néandertaliennes de type moderne. Cette interprétation permet d’enrichir notre connaissance biologique et culturelle de cette population. / The discovery of a new Neandertal pelvis, Regourdou 1, allows discussing the functional implications of Neandertal pelvic morphology. First, the specimen is described, which offers to proveits affiliation to the Neandertal population and to highlight specific Neandertal features. Even if none of these are autapomorphic, the combinaison of these traits characterize the Neandertal pelvic belt. The pelvis Regourdou 1 is reconstructed, by an estimation of missing-data, thanks to the thin-plate splines method, applied on Kebara 2. The dimensions of Regourdou 1 birth canal are compared with those of two others Neandertal individuals (Tabun C1 and Kebara 2) as well as a modern population (n=151).The analysis of the obstetrical planes morphology (by geometric morphometrics) and the cephalo-pelvic relation highlights the presence of traits associated with rotational birth in modern Human. Our work attests the existence of modern type obstetrical mechanics, in Neandertal. This interpretation allows enriching our biological and cultural knowledge of this population.

In this work we model the historical development of best performances in men's 100, 200, 400 and 800m running events. We suppose that the years best performances are independent random variables with generalized extreme value distribution for minima and that there is a decreasing trend in location. Parameters of the models are estimated by using maximum likelihood techniques. The data of years best performances are missing for some years, we treat them as right censored data that are censored by value of world record valid at that time. Graphic tools used for models diagnostics are adjusted to the censoring. The models we get are used to estimate the ultimate records and to predict new records in next years. At the end of the work we estimate several models describing historical development of years best performances for more events at one time.

Le traitement des données manquantes est un sujet en pleine expansion en épidémiologie. La méthode la plus souvent utilisée restreint les analyses aux sujets ayant des données complètes pour les variables d’intérêt, ce qui peut réduire lapuissance et la précision et induire des biais dans les estimations. L’objectif de ce travail a été d’investiguer et d’appliquer une méthode d’imputation multiple à des données transversales d’enquêtes épidémiologiques et de systèmes de surveillance de maladies infectieuses. Nous avons présenté l’application d’une méthode d’imputation multiple à des études de schémas différents : une analyse de risque de transmission du VIH par transfusion, une étude cas-témoins sur les facteurs de risque de l’infection à Campylobacter et une étude capture-recapture estimant le nombre de nouveaux diagnostics VIH chez les enfants. A partir d’une base de données de surveillance de l’hépatite C chronique (VHC), nous avons réalisé une imputation des données manquantes afind’identifier les facteurs de risque de complications hépatiques graves chez des usagers de drogue. A partir des mêmes données, nous avons proposé des critères d’application d’une analyse de sensibilité aux hypothèses sous-jacentes àl’imputation multiple. Enfin, nous avons décrit l’élaboration d’un processus d’imputation pérenne appliqué aux données du système de surveillance du VIH et son évolution au cours du temps, ainsi que les procédures d’évaluation et devalidation.Les applications pratiques présentées nous ont permis d’élaborer une stratégie de traitement des données manquantes, incluant l’examen approfondi de la base de données incomplète, la construction du modèle d’imputation multiple, ainsi queles étapes de validation des modèles et de vérification des hypothèses. / The management of missing values is a common and widespread problem in epidemiology. The most common technique used restricts the data analysis to subjects with complete information on variables of interest, which can reducesubstantially statistical power and precision and may also result in biased estimates.This thesis investigates the application of multiple imputation methods to manage missing values in epidemiological studies and surveillance systems for infectious diseases. Study designs to which multiple imputation was applied were diverse: a risk analysis of HIV transmission through blood transfusion, a case-control study on risk factors for ampylobacter infection, and a capture-recapture study to estimate the number of new HIV diagnoses among children. We then performed multiple imputation analysis on data of a surveillance system for chronic hepatitis C (HCV) to assess risk factors of severe liver disease among HCV infected patients who reported drug use. Within this study on HCV, we proposedguidelines to apply a sensitivity analysis in order to test the multiple imputation underlying hypotheses. Finally, we describe how we elaborated and applied an ongoing multiple imputation process of the French national HIV surveillance database, evaluated and attempted to validate multiple imputation procedures.Based on these practical applications, we worked out a strategy to handle missing data in surveillance data base, including the thorough examination of the incomplete database, the building of the imputation model, and the procedure to validate imputation models and examine underlying multiple imputation hypotheses.

Les études sur les couples traités par fécondation in vitro (FIV) ont jusqu’à présent porté essentiellement sur l’évaluation du succès en FIV. Très peu de données sont disponibles sur le devenir à long terme de couples traités par FIV. L’objectif de ce travail était d’estimer la fréquence de réalisation du projet parental à long terme, et d’étudier les facteurs associés aux interruptions précoces des traitements et aux naissances naturelles.L’enquête DAIFI-2009 a inclus 6 507 couples ayant débuté un programme de FIV en 2000-2002 dans l’un des 8 centres de FIV participant à l’étude. Les données médicales des couples et leur parcours dans le centre ont été obtenus à partir des dossiers médicaux des centres de FIV pour tous les couples. L’information sur le devenir des couples après le départ du centre a été obtenue par questionnaire postal auprès des couples en 2008-2009 (38% de participation 7 à 9 ans après l’initiation des FIV). L’étude des facteurs associés à la participation à l’enquête postale suggérait que la fréquence de réalisation du projet parental estimée sur les répondants seulement pourrait être biaisée. Les différentes méthodes mises en œuvre pour corriger la non réponse (pondération, imputation multiple) n’ont pas modifié l’estimation de la fréquence de réalisation du projet parental. Au total, 7 à 9 ans après l’initiation des FIV, 60% des couples ont réalisé leur projet parental de façon biologique, suite à un traitement ou suite à une conception naturelle. Lorsque les adoptions sont aussi prises en compte, 71% des couples ont réalisé leur projet parental. Après l’échec d’une première tentative de FIV, un couple sur 4 (26%) a interrompu les FIV dans le centre d’inclusion. Globalement, les couples avec de mauvais facteurs pronostiques ont un plus grand risque d’interrompre les FIV. Cependant, la proportion plus importante d’interruption parmi les couples avec une origine inexpliquée de l’infécondité pourrait s’expliquer par la survenue plus fréquente de naissance naturelle dans ce sous-groupe de couples. Parmi les couples n’ayant pas eu d’enfant suite aux traitements, 24% ont ensuite conçu naturellement en médiane 28 mois après l’initiation des FIV. Parmi les couples ayant eu un enfant suite aux traitements, 17% ont ensuite conçu naturellement en médiane 33 mois après la naissance de l’enfant conçu par AMP. Les facteurs associés aux naissances naturelles sont des indicateurs d’un meilleur pronostic de fertilité, particulièrement chez les couples sans enfant AMP.L’enquête DAIFI-2009 a permis d’apporter des informations sur le parcours à long terme des couples traités par FIV qui n’avait jusqu’à présent été que peu étudié, souvent sur de faibles effectifs et avec un suivi plus court. Ces résultats doivent apporter de l’espoir aux couples inféconds, puisque la majorité d’entre eux ont finalement réalisé leur projet parental, même si cela peut prendre de nombreuses années. / Until now, most studies of couples treated by in vitro fertilization (IVF) have been centered on IVF success. Very few data are available on the long-term outcome of these couples, including spontaneous conception and adoptions. This work aimed to estimate the long-term cumulative parenthood rate, and to study factors associated with early IVF discontinuation and with spontaneous live births.The DAIFI study is a retrospective cohort including 6,507 couples who began IVF in 2000-2002 in one of the eight participating French IVF centres. Medical data on all couples were obtained from centre databases. Information on long-term outcome after leaving the IVF center was collected by postal questionnaire sent to couples in 2008-2010 (7 to 9 years after IVF initiation, participation rate 38%). Study of factors associated with participation in the postal survey suggested that the cumulative parenthood rate estimated only in participants might be biased. The different methods used to correct for non-response bias (inverse probability weighting, multiple imputation) did not modify the estimation of the cumulative parenthood rate obtained with the complete case approach. Finally, 7 to 9 years after IVF initiation, the cumulative parenthood rate was estimated at 60%, including live births following IVF, other treatment or spontaneous conception. When adoptions were also considered, the cumulative parenthood rate reached 71%. After a first failed IVF cycle, just over one couple out of four (26%) discontinued IVF treatment. Globally, couples with poor prognostic factors had a higher risk of early discontinuation of IVF treatment. However, the higher proportion of early discontinuation observed among couples with unexplained infertility could be linked to a higher chance of spontaneous pregnancy in this subpopulation. Among couples who remained childless after treatment, 24% later had a spontaneous live birth (SLB), at a median of 28 months after the first IVF attempt. Among couples who had had a child during medical treatment, 17% later had an SLB, at a median of 33 months after the birth following medical treatment. Regarding factors associated with SLB, they can be viewed as indicators of a better fertility prognosis, especially among unsuccessfully treated couples.The DAIFI study has provided information on the long-term outcome of couples treated by IVF, which has until now been little studied, often on small samples and with a shorter duration of follow-up. These results should give hope to infertile couples as nearly three couples out of four finally became parents, even if it may take many years.

Missing data continues to be an issue not only the field of statistics but in any field, that deals with data. This is due to the fact that almost all the widely accepted and standard statistical software and methods assume complete data for all the variables included in the analysis. As a result, in most studies, statistical power is weakened and parameter estimates are biased, leading to weak conclusions and generalizations. Many studies have established that multiple imputation methods are effective ways of handling missing data. This paper examines three different imputation methods (predictive mean matching, Bayesian linear regression and linear regression, non Bayesian) in the MICE package in the statistical software, R, to ascertain which of the three imputation methods imputes data that yields parameter estimates closest to the parameter estimates of a complete data given different percentages of missingness. In comparing the parameter estimates of the complete data and the imputed data, the parameter estimates in each model were evaluated and compared. The paper extends the analysis by generating a pseudo data of the original data to establish how the imputation methods perform under varying conditions.

<p>The Bayesian approach to cluster analysis is presented. We assume that all data stem from a finite mixture model, where each component corresponds to one cluster and is given by a multivariate normal distribution with unknown mean and variance. The method produces posterior distributions of all cluster parameters and proportions as well as associated cluster probabilities for all objects. We extend this method in several directions to some common but non-standard situations. The first extension covers the case with a few deviant observations not belonging to one of the normal clusters. An extra component/cluster is created for them, which has a larger variance or a different distribution, e.g. is uniform over the whole range. The second extension is clustering of longitudinal data. All units are clustered at all time points separately and the movements between time points are modeled by Markov transition matrices. This means that the clustering at one time point will be affected by what happens at the neighbouring time points. The third extension handles datasets with missing data, e.g. item non-response. We impute the missing values iteratively in an extra step of the Gibbs sampler estimation algorithm. The Bayesian inference of mixture models has many advantages over the classical approach. However, it is not without computational difficulties. A software package, written in Matlab for Bayesian inference of mixture models is introduced. The programs of the package handle the basic cases of clustering data that are assumed to arise from mixture models of multivariate normal distributions, as well as the non-standard situations.</p>

We present distribution independent bounds on the generalization misclassification performance of a family of kernel classifiers with margin. Support Vector Machine classifiers (SVM) stem out of this class of machines. The bounds are derived through computations of the $V_gamma$ dimension of a family of loss functions where the SVM one belongs to. Bounds that use functions of margin distributions (i.e. functions of the slack variables of SVM) are derived.

This thesis investigates the impact of fragmentation in the ownership of complementary patents or patent thickets on firms' market value. This question is motivated by the increase in the patent ownership fragmentation following the pro-patent shifts in the US since 1982. The first chapter uses panel data on patenting US manufacturing firms from 1979 to 1996, and estimates the impact of patent thickets on firms' market value. I find that patent thickets lower firms' market value, and firms with a large patent portfolio size experience a smaller negative effect from their thickets. Moreover, no systematic difference exists in the impact of patent thickets on firms' market value over time. The second chapter extends this analysis to account for the indirect impacts of patent thickets on firms' market value. These indirect effects arise through the effects of patent thickets on firms' R\&D and patenting activities. Using panel data on US manufacturing firms from 1979 to 1996, I estimate the impact of patent thickets on market value, R\&D, and patenting as well as the impacts of R\&D and patenting on market value. Employing these estimates, I determine the direct, indirect, and total impacts of patent thickets on market value. I find that patent thickets decrease firms' market value, while I hold the firms’ R\&D and patenting activities constant. I find no evidence of a change in R\&D due to patent thickets. However, there is evidence of defensive patenting (an increase in patenting attributed to thickets), which helps to reduce the direct negative impact of patent thickets on market value. The data sets used in Chapters 1 and 2 have a number of missing observations on regressors. The commonly used methods to manage missing observations are the listwise deletion (complete case) and the indicator methods. Studies on the statistical properties of these methods suggest a smaller bias using the listwise deletion method. Employing Monte Carlo simulations, Chapter 3 examines the properties of these methods, and finds that in some cases the listwise deletion estimates have larger biases than indicator estimates. This finding suggests that interpreting estimates arrived at with either approach requires caution.