Gelman, King, 及Liu(1998)針對一連串且互相獨立的橫斷面調查提出多重設算程序，且對不同調查的參數以階層模式(hierarchical model)連結。本文為介紹複雜抽樣(分層或群集抽樣)之下，若Q個連續變數有遺漏現象時，如何結合對象之個別特性，各層或各群集的參數，以及連結各層或各群集參數的階層模式，以設算遺漏值及估計模式中之參數。 對遺漏值的處理採用單調資料擴展演算法，只需對破壞單調資料型態的遺漏值進行設算。由於考慮到不同的群集或層往往呈現不同的特性，因而以階層模式連絡各群集或各層的參數，並將Gelman, King, Liu(1998)的推導結果擴展到將個別對象之特性納入考量之上。對各群集而言，他們的共變異數矩陣Ψ及Σ為影響群內其他參數的收斂情形，由模擬獲得的結果，沒有證據顯示應懷疑收斂的問題。 / Gelman, king, and Liu (1998) use multiple imputation for a series of cross section survey, and link the parameter of different survey by hierarchical model. This text introduces a method to impute missing value and estimate the parameters affected by hierarchical model if Q continuous variables has missing value under complex survey. For each cluster, the parameters are influenced by their variance-covariance matrix Ψ and Σ. The result obtained from the simulation have no clear evidence to doubt the convergence of parameters.

Les données manquantes sont fréquentes dans les enquêtes et peuvent entraîner d’importantes erreurs d’estimation de paramètres. Ce mémoire méthodologique en sociologie porte sur l’influence des données manquantes sur l’estimation de l’effet d’un programme de prévention. Les deux premières sections exposent les possibilités de biais engendrées par les données manquantes et présentent les approches théoriques permettant de les décrire. La troisième section porte sur les méthodes de traitement des données manquantes. Les méthodes classiques sont décrites ainsi que trois méthodes récentes. La quatrième section contient une présentation de l’Enquête longitudinale et expérimentale de Montréal (ELEM) et une description des données utilisées. La cinquième expose les analyses effectuées, elle contient : la méthode d’analyse de l’effet d’une intervention à partir de données longitudinales, une description approfondie des données manquantes de l’ELEM ainsi qu’un diagnostic des schémas et du mécanisme. La sixième section contient les résultats de l’estimation de l’effet du programme selon différents postulats concernant le mécanisme des données manquantes et selon quatre méthodes : l’analyse des cas complets, le maximum de vraisemblance, la pondération et l’imputation multiple. Ils indiquent (I) que le postulat sur le type de mécanisme MAR des données manquantes semble influencer l’estimation de l’effet du programme et que (II) les estimations obtenues par différentes méthodes d’estimation mènent à des conclusions similaires sur l’effet de l’intervention. / Missing data are common in empirical research and can lead to significant errors in parameters’ estimation. This dissertation in the field of methodological sociology addresses the influence of missing data on the estimation of the impact of a prevention program. The first two sections outline the potential bias caused by missing data and present the theoretical background to describe them. The third section focuses on methods for handling missing data, conventional methods are exposed as well as three recent ones. The fourth section contains a description of the Montreal Longitudinal Experimental Study (MLES) and of the data used. The fifth section presents the analysis performed, it contains: the method for analysing the effect of an intervention from longitudinal data, a detailed description of the missing data of MLES and a diagnosis of patterns and mechanisms. The sixth section contains the results of estimating the effect of the program under different assumptions about the mechanism of missing data and by four methods: complete case analysis, maximum likelihood, weighting and multiple imputation. They indicate (I) that the assumption on the type of MAR mechanism seems to affect the estimate of the program’s impact and, (II) that the estimates obtained using different estimation methods leads to similar conclusions about the intervention’s effect.

Résumé La technique connue comme l'imputation multiple semble être la technique la plus appropriée pour résoudre le problème de non-réponse. La littérature mentionne des méthodes qui modélisent la nature et la structure des valeurs manquantes. Une des méthodes les plus populaires est l'algorithme « Pan » de (Schafer & Yucel, 2002). Les imputations rapportées par cette méthode sont basées sur un modèle linéaire multivarié à effets mixtes pour la variable réponse. La méthode « BHLC » de (Murua et al, 2005) est une extension de « Pan » dont le modèle est bayésien hiérarchique avec groupes. Le but principal de ce travail est d'étudier le problème de sélection du modèle pour l'imputation multiple en termes d'efficacité et d'exactitude des prédictions des valeurs manquantes. Nous proposons une mesure de performance liée à la prédiction des valeurs manquantes. La mesure est une erreur quadratique moyenne reflétant la variance associée aux imputations multiples et le biais de prédiction. Nous montrons que cette mesure est plus objective que la mesure de variance de Rubin. Notre mesure est calculée en augmentant par une faible proportion le nombre de valeurs manquantes dans les données. La performance du modèle d'imputation est alors évaluée par l'erreur de prédiction associée aux valeurs manquantes. Pour étudier le problème objectivement, nous avons effectué plusieurs simulations. Les données ont été produites selon des modèles explicites différents avec des hypothèses particulières sur la structure des erreurs et la distribution a priori des valeurs manquantes. Notre étude examine si la vraie structure d'erreur des données a un effet sur la performance du choix des différentes hypothèses formulées pour le modèle d'imputation. Nous avons conclu que la réponse est oui. De plus, le choix de la distribution des valeurs manquantes semble être le facteur le plus important pour l'exactitude des prédictions. En général, les choix les plus efficaces pour de bonnes imputations sont une distribution de student avec inégalité des variances dans les groupes pour la structure des erreurs et une loi a priori choisie pour les valeurs manquantes est la loi normale avec moyenne et variance empirique des données observées, ou celle régularisé avec grande variabilité. Finalement, nous avons appliqué nos idées à un cas réel traitant un problème de santé. Mots clés : valeurs manquantes, imputations multiples, modèle linéaire bayésien hiérarchique, modèle à effets mixtes. / Abstract The technique known as multiple imputation seems to be the most suitable technique for solving the problem of non-response. The literature mentions methods that models the nature and structure of missing values. One of the most popular methods is the PAN algorithm of Schafer and Yucel (2002). The imputations yielded by this method are based on a multivariate linear mixed-effects model for the response variable. A Bayesian hierarchical clustered and more flexible extension of PAN is given by the BHLC model of Murua et al. (2005). The main goal of this work is to study the problem of model selection for multiple imputation in terms of efficiency and accuracy of missing-value predictions. We propose a measure of performance linked to the prediction of missing values. The measure is a mean squared error, and hence in addition to the variance associated to the multiple imputations, it includes a measure of bias in the prediction. We show that this measure is more objective than the most common variance measure of Rubin. Our measure is computed by incrementing by a small proportion the number of missing values in the data and supposing that those values are also missing. The performance of the imputation model is then assessed through the prediction error associated to these pseudo missing values. In order to study the problem objectively, we have devised several simulations. Data were generated according to different explicit models that assumed particular error structures. Several missing-value prior distributions as well as error-term distributions are then hypothesized. Our study investigates if the true error structure of the data has an effect on the performance of the different hypothesized choices for the imputation model. We concluded that the answer is yes. Moreover, the choice of missing-value prior distribution seems to be the most important factor for accuracy of predictions. In general, the most effective choices for good imputations are a t-Student distribution with different cluster variances for the error-term, and a missing-value Normal prior with data-driven mean and variance, or a missing-value regularizing Normal prior with large variance (a ridge-regression-like prior). Finally, we have applied our ideas to a real problem dealing with health outcome observations associated to a large number of countries around the world. Keywords: Missing values, multiple imputation, Bayesian hierarchical linear model, mixed effects model. / Les logiciels utilisés sont Splus et R.

本研究旨在了解家庭作業與學習成就的關係。為達研究目的，本研究以階層線性模式分析「國際數學與科學教育成就趨勢調查」2007年4年級學生資料；2007年8年級學生資料；以及2011年8年級學生資料，接著，本研究再以結構方程模式的長期追蹤交叉延宕模式，分析「臺灣教育長期追蹤資料庫」2001年、2003年及2005年追蹤樣本學生資料，本研究主要發現： 一、臺灣4年級學生的學生層次數學家庭作業時間對數學學習成就有顯著負向地影響效果；學生層次科學家庭作業時間對科學學習成就也有顯著負向地影響效果。 二、臺灣4年級學生的班級層次數學家庭作業頻率對數學學習成就沒有顯著地影響效果；班級層次科學家庭作業頻率對科學學習成就也沒有顯著地影響效果。 三、臺灣8年級學生的學生層次數學家庭作業時間對數學學習成就有顯著正向地影響效果；學生層次科學家庭作業時間對科學學習成就也有顯著正向地影響效果。 四、臺灣8年級學生的班級層次數學家庭作業頻率對數學學習成就有顯著正向地影響效果；班級層次科學家庭作業頻率對科學學習成就也有顯著正向地影響效果。 五、臺灣2001年7年級陸續追蹤至2005年11年級的學生，其家庭作業時間與學習成就有顯著正向地相互影響效果。 / This study aimed analyze the relationship between homework and learning achievements. Hierarchical linear modeling was used to analyze the 4th grade of elementary school students from Trends in International Mathematics and Science Study (TIMSS) 2007, 8th grade of junior high school students from TIMSS 2007, and 8th grade of junior high school students from TIMSS 2011. Moreover, structural equation modeling with cross-lagged panel modeling was used to analyze the core panel sample data from Taiwan Education Panel Survey (TEPS) in 2001, 2003, and 2005. The major findings were as follows: 1. Taiwan 4th grade of elementary school students’ student-level mathematic homework time could negative predict the mathematic learning achievements significantly, and student-level science homework time could also negative predict the science learning achievements significantly. 2. Taiwan 4th grade of elementary school students’ class-level mathematic homework frequency could not predict the mathematic learning achievements significantly, and class-level science homework frequency could also not predict the science learning achievements significantly. 3. Taiwan 8th grade of junior high school students’ student-level mathematic homework time could positive predict the mathematic learning achievements significantly, and student-level science homework time could also positive predict the science learning achievements significantly. 4. Taiwan 8th grade of junior high school students’ class-level mathematic homework frequency could positive predict the mathematic learning achievements significantly, and class-level science homework frequency could also positive predict the science learning achievements significantly. 5. Taiwan 7th grade of junior high school students to 11th grade of senior high school students’ homework time could positive predict the subsequent learning achievements significantly, and learning achievements could also positive predict the subsequent homework time significantly.

This thesis is composed of two economic evaluations: one trial-based study and one model-based study. In a recent study published in Clinical Infectious Diseases in 2011, a team of OUCRU investigators found that immediate antiretroviral therapy (ART) was not associated with improved 9-month survival in HIV-associated TBM patients (HR, 1.12; 95% CI, .81 to–1.55; P = .50). An economic evaluation of this clinical trial was conducted to examine the cost-effectiveness of immediate ART (initiate ART within 1 week of study entry) versus deferred ART (initiate ART after 2 months of TB treatment) in HIV-associated TBM patients. Over 9 months, immediate ART was not different from deferred ART in terms of costs and QALYs gained. Late initiation of ART during TB and HIV treatment for HIV-positive TBM patients proved to be the most cost-effective strategy. Increasing resistance of Plasmodium falciparum malaria to artemisinin is posing a major threat to the global effort to eliminate malaria. Artesmisinin combination therapies (ACT) are currently known as the most efficacious first-line therapies to treat uncomplicated malaria. However, resistance to both artemisinin and partner drugs is developing and this could result in increasing morbidity, mortality, and economic costs. One strategy advocated for delaying the development of resistance to the ACTs is the wide-scale deployment of multiple first-line therapies. A previous modeling study examined that the use of multiple first-line therapies (MFT) reduced the long-term treatment failures compared with strategies in which a single first-line ACT was recommended. Motivated by observed results of the published modelling study in the Lancet, the cost-effectiveness of the MFT versus the single first-line therapies was assessed in settings of different transmission intensities, treatment coverages and fitness cost of resistance using a previously developed model of the dynamics of malaria and a literature –based cost estimate of changing antimalarial drug policy at national level. This study demonstrates that the MFT strategies outperform the single first-line strategies in terms of costs and benefits across the wide range of epidemiological and economic scenarios considered. The second analysis of the thesis is not only internationally relevant but also with a focus towards healthcare practice in Vietnam. These two studies add significant new cost-effectiveness evidence in Vietnam. This thesis presents the first trial-based economic evaluation in Vietnam considers patient-health outcome measures as the participants have cognitive limitations (tuberculous meningitis), dealing with missing data along with the potential ways to handle this common problem by the use of multiple imputation, and the issues of censored costs data. Having identified these issues would support the decision makers or stakeholders including the pharmaceutical industry to devise a new guideline on how to implement a well-design trial-based economic evaluation in Vietnam in the future. Another novelty of this thesis is the introduction of the detailed of costing of drug regimens change in which the economic evaluations considering the drug policy change often do not include. This cost could be substantial to the healthcare system for retraining the staff and publishing the new guidelines. This thesis will document the costs incurred by the Vietnamese government by changing the first-line treatment of malaria, from single first-line therapy (ACT) to multiple first-line therapies.

Geralmente, nos experimentos genótipo por ambiente (G × E) é comum observar o comportamento dos genótipos em relação a distintos atributos nos ambientes considerados. A análise deste tipo de experimentos tem sido abordada amplamente para o caso de um único atributo. Nesta tese são apresentadas algumas alternativas de análise considerando genótipos, ambientes e atributos simultaneamente. A primeira, é baseada no método de mistura de máxima verossimilhança de agrupamento - Mixclus e a análise de componentes principais de 3 modos - 3MPCA, que permitem a análise de tabelas de tripla entrada, estes dois métodos têm sido muito usados na área da psicologia e da química, mas pouco na agricultura. A segunda, é uma metodologia que combina, o modelo de efeitos aditivos com interação multiplicativa - AMMI, modelo eficiente para a análise de experimentos (G × E) com um atributo e a análise de procrustes generalizada, que permite comparar configurações de pontos e proporcionar uma medida numérica de quanto elas diferem. Finalmente, é apresentada uma alternativa para realizar imputação de dados nos experimentos (G × E), pois, uma situação muito frequente nestes experimentos, é a presença de dados faltantes. Conclui-se que as metodologias propostas constituem ferramentas úteis para a análise de experimentos (G × E) multiatributo. / Usually, in the experiments genotype by environment (G×E) it is common to observe the behaviour of genotypes in relation to different attributes in the environments considered. The analysis of such experiments have been widely discussed for the case of a single attribute. This thesis presents some alternatives of analysis, considering genotypes, environments and attributes simultaneously. The first, is based on the mixture maximum likelihood method - Mixclus and the three-mode principal component analysis, these two methods have been very used in the psychology and chemistry, but little in agriculture. The second, is a methodology that combines the additive main effects and multiplicative interaction models - AMMI, efficient model for the analysis of experiments (G×E) with one attribute, and the generalised procrustes analysis, which allows compare configurations of points and provide a numerical measure of how much they differ. Finally, an alternative to perform data imputation in the experiments (G×E) is presented, because, a very frequent situation in these experiments, is the presence of missing values. It is concluded that the proposed methodologies are useful tools for the analysis of experiments (G×E) multi-attribute.

Made available in DSpace on 2014-12-17T14:27:07Z (GMT). No. of bitstreams: 1 KeityMFS.pdf: 1141287 bytes, checksum: 00c052907580c678aaf9fa34f505b0fd (MD5) Previous issue date: 2003-08-18 / This legal research aims to demonstrate the prohibition in the Brazilian criminal system of a multiple imputation for the same fact in a simultaneous or successive way. For that it is developed a different idea of the subject. Through comparative, eletronic and bibliographical researches, the dissertation was accomplished in a way to establish the content of the foundations of the criminal procedural emphasizing as fundamental premise the values of the Constitution. In the first section it was demonstrated the limits of the theme and the objective of the research. After that, it was analyzed the basic function of the criminal suit which has the important mission of limiting state's punitive power. In the same way, the criminal procedure corresponds to a warranty of the citizens' freedom. In the same section, it is shown how it is possible to abandon the myth of the real truth in the criminal law system. In the third section of the research, there were pointed elements and definitions about the cognition object, specially the litigious object or "thema decidendum", and also the peculiarities of the judged cases. In the fourth section the subject about origins and evolution of the criminal procedure and its objectives in the legal system is developed to demonstrate its perspectives. Some aspects of the identity's concept of the presupposition of the facts are as well demonstrated in order to relate the theme to the prohibition of multiple imputation. There are also considerations about some other important aspects as the incidence of the legal rules and the possible change on the elements of the penal type. There are several comments about legal procedural in other legal systems comparing them to Brazilian's most elevated Courts. In the end it was systematized the limits to criminal imputation, emphasizing the defende's right as a foundation of the legal system. Is was registered that the ius persequendi can be exercised once / A presente disserta??o tem por objeto o estudo da proibi??o da m?ltipla persecu??o penal, pelo mesmo fato, seja de forma simult?nea ou sucessiva. Para tanto, atrav?s do m?todo dial?tico, foram realizadas pesquisas com o objetivo de estabelecer o conte?do do princ?pio ne bis in idem, em sua vertente processual penal, sempre tendo como premissa fundamental os valores albergados nos princ?pios e regras constitucionais. Assentados, no in?cio da primeira se??o do trabalho, a delimita??o do tema e o objetivo da pesquisa, analisou-se, em seguida, a fun??o basilar do processo penal, o qual, numa vis?o garantista, tem a relevante miss?o de limitar frear - a f?ria do poder punitivo estatal, correspondendo a um efetivo instrumento de garantia da liberdade dos cidad?os, quando subjugados ao ius persequendi. Nessa mesma se??o, restaram destacadas a consagra??o do modelo acusat?rio de processo pela Constitui??o Brasileira de 1988 e a necessidade de abandonar o mito da verdade real, como princ?pio informador do processo penal constitucional. Na segunda se??o da pesquisa, foram apontados os elementos definidores do objeto de cogni??o, especialmente do objeto litigioso ou thema decidendum, havendo, tamb?m, sido abordadas as peculiaridades do instituto da coisa julgada no processo penal. Dando continuidade ? pesquisa, na terceira se??o, discorreu-se sobre a origem e evolu??o do princ?pio ne bis in idem, centrando-se no tema da pesquisa, qual seja, sua manifesta??o no processo penal e a interpreta??o que se deve atribuir aos termos que comp?em sua express?o: rela??o processual com unidade de sujeito e de fato, atrav?s de senten?a definitiva. Deu-se ?nfase, sobretudo, aos aspectos controvertidos do conceito de identidade do fato como pressuposto da proibi??o de m?ltipla persecu??o, abordando-se, dentre outros aspectos, a incid?ncia de concurso aparente de normas e a altera??o dos elementos do tipo penal. Constam, ainda, dessa se??o, lineamentos gerais acerca da aplica??o do princ?pio ne bis in idem processual no direito comparado e nas cortes brasileiras. Por ?ltimo, sistematizou-se o sentido e alcance do princ?pio ne bis in idem, como limite ? persecu??o penal, al?m de terem sido apresentadas sugest?es, inclusive, de lege ferenda, a fim de que seja efetivamente garantido o direito fundamental assegurado ? defesa, no sentido de que, pelo mesmo substrato f?tico, o ius persequendi somente poder? ser exercido uma vez

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No. of bitstreams: 2 Tese - Lucas Lacerda Caldas Zanini Jardim - 2018.pdf: 5066072 bytes, checksum: 4280b5b19a9111a59fea8065049fd5b3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2018-04-27 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Macroecology studies ecological pattern at large geographical and temporal scales. At these scales, information about hundreds or even thousands of studied species. This lack of information may potentially bias studies’ conclusions related with macroecological processes and patterns. In this thesis, we evaluated phylogenetic imputation methods, their uses and effects in macroecological studies. The first chapter evaluated different methods used to deal with missing data, taking into account different scenarios of species trait evolution, as well as percentage and pattern of missing data. We found that dealing with missing data relies on the specific goals and data of the study. Therefore, we suggested caution while using imputed database. In the second chapter, we tested the island rule effect in body mass and brain volume of primates. To do so, we fitted evolutionary models to those traits and then imputed the body mass and brain volume for Homo floresiensis. We concluded that primates do not follow the island rule and even though our models overestimated, on average, brain and body size of Homo floresiensis, its evolution did not deviate from primates’ evolutionary expectation. Lastly, in the third chapter, we tested existence of Bergmann’s rule in mammals using multiple imputation methods, in addition to considering the consequences of ignoring missing data while testing the rule. We found that ignoring missing data can invert (eg. changing from positive to negative effect) the effect of temperature on body mass, but this bias did not turn the effect statistically significant. Therefore, we concluded that mammals do not follow Bergmann’s rule, when evaluated at the class taxonomic level. Finally, this thesis discussed pros, cons and future research avenues in order to make phylogenetic imputation a more robust tool to deal with missing data in macroecology. / A macroecologia estuda padrões ecológicos em grandes escalas geográficas e temporais, em busca de quais processos moldam esses padrões. Nessas escalas de estudo, há raramente informações completas sobre as centenas ou até milhares de espécies estudadas. Essa ausência de informações tem o potencial de enviesar as conclusões dos estudos sobre padrões e processos macroecológicos. Nessa tese, nós avaliamos métodos de imputação filogenética, a sua aplicação e consequências em estudos macroecológicos. Para avaliar potenciais vieses do uso de banco de dados imputados, no primeiro capítulo, nós aplicamos diferentes métodos utilizados para tratar dados faltantes, sob diferentes cenários de evolução dos atributos das espécies, porcentagem e padrão dos dados faltantes. Nós encontramos que a forma de tratar o dado faltante pode ser dependente dos objetivos e dos dados de cada estudo e, portanto, nós sugerimos cautela ao utilizarmos bancos de dados imputados. No segundo capítulo, nós testamos o efeito da regra de ilha na evolução da massa corpórea e do volume cerebral de primatas. A partir dos melhores modelos evolutivos ajustados a esses atributos, nós imputamos a massa corpórea e volume cerebral de Homo floresiensis. Nós concluímos que primatas não seguem regra de ilha e que apesar de nossos modelos superestimarem, em média, o tamanho do corpo e cérebro de Homo floresiensis, a sua evolução não se desvia do esperado pela evolução de primatas. Por fim, no terceiro capítulo testamos a regra de Bergmann em mamíferos, utilizando métodos de imputação múltipla e avaliamos as consequências de desconsiderar os dados faltantes na detecção da regra. Nós encontramos que testar a regra sem considerar os dados faltantes pode inverter o efeito da temperatura na massa do corpo, mas esse viés não tornou o efeito estatisticamente significante. Portanto, concluímos que mamíferos não seguem a regra de Bergmann, quando toda a classe é avaliada. Por fim, essa tese discutiu vantagens, desvantagens e futuras linhas de pesquisa para tornar a imputação filogenética uma ferramenta mais robusta para tratarmos dados faltantes em macroecologia.

Les études cliniques permettent de mesurer de nombreuses variables répétées dans le temps. Lorsque l'objectif est de les relier à un critère clinique d'intérêt, les méthodes de régularisation de type LASSO, généralisées aux Generalized Estimating Equations (GEE) permettent de sélectionner un sous-groupe de variables en tenant compte des corrélations intra-patients. Les bases de données présentent souvent des données non renseignées et des problèmes de mesures ce qui entraîne des données manquantes inévitables. L'objectif de ce travail de thèse est d'intégrer ces données manquantes pour la sélection de variables en présence de données longitudinales. Nous utilisons la méthode d'imputation multiple et proposons une fonction d'imputation pour le cas spécifique des variables soumises à un seuil de détection. Nous proposons une nouvelle méthode de sélection de variables pour données corrélées qui intègre les données manquantes : le Multiple Imputation Penalized Generalized Estimating Equations (MI-PGEE). Notre opérateur utilise la pénalité group-LASSO en considérant l'ensemble des coefficients de régression estimés d'une même variable sur les échantillons imputés comme un groupe. Notre méthode permet une sélection consistante sur l'ensemble des imputations, et minimise un critère de type BIC pour le choix du paramètre de régularisation. Nous présentons une application sur l'arthrose du genoux où notre objectif est de sélectionner le sous-groupe de biomarqueurs qui expliquent le mieux les différences de largeur de l'espace articulaire au cours du temps. / Clinical studies enable us to measure many longitudinales variables. When our goal is to find a link between a response and some covariates, one can use regularisation methods, such as LASSO which have been extended to Generalized Estimating Equations (GEE). They allow us to select a subgroup of variables of interest taking into account intra-patient correlations. Databases often have unfilled data and measurement problems resulting in inevitable missing data. The objective of this thesis is to integrate missing data for variable selection in the presence of longitudinal data. We use mutiple imputation and introduce a new imputation function for the specific case of variables under detection limit. We provide a new variable selection method for correlated data that integrate missing data : the Multiple Imputation Penalized Generalized Estimating Equations (MI-PGEE). Our operator applies the group-LASSO penalty on the group of estimated regression coefficients of the same variable across multiply-imputed datasets. Our method provides a consistent selection across multiply-imputed datasets, where the optimal shrinkage parameter is chosen by minimizing a BIC-like criteria. We then present an application on knee osteoarthritis aiming to select the subset of biomarkers that best explain the differences in joint space width over time.

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