The purpose of this simulation study was to evaluate the relative performance of five missing data treatments (MDTs) for handling missing data in complex sample surveys. The five missing data methods included in this study were listwise deletion (LW), single hot-deck imputation (HS), single regression imputation (RS), hot-deck-based multiple imputation (HM), and regression-based multiple imputation (RM). These MDTs were assessed in the context of regression weight estimates in multiple regression analysis in complex sample data with two data levels. In this study, the multiple regression equation had six regressors without missing data and two regressors with missing data. The four performance measures used in this study were statistical bias, RMSE, CI width, and coverage probability (i.e., 95%) of the confidence interval. The five MDTs were evaluated separately for three types of missingness: MCAR, MAR, and MNAR. For each type of missingness, the studied MDTs were evaluated at four levels of missingness (10%, 30%, 50%, and 70%) along with complete sample conditions as a reference point for interpretation of results. In addition, ICC levels (.0, .25, .50) and high and low density population were also manipulated as studied factors. The study’s findings revealed that the performance of each individual MDT varied across missing data types, but their relative performance was quite similar for all missing data types except for LW’s performance in MNAR. RS produced the most inaccurate estimates considering bias, RMSE, and coverage of confidence interval; RM and HM were the second poorest performers. LW as well as HS procedure outperformed the rest on the measures of accuracy and precision in MCAR; however LW’s measures of precision decreased in MAR and MNAR, and LW’s CI width was the widest in MNAR data. In addition, in all three missing data types, those poor performers were less accurate and less precise on variables with missing data than they were on variables without missing data; and the degree of accuracy and precision of these poor performers depended mostly on the level of data ICC. The proportion of missing data only noticeably affected the performance of HM such that in higher missing data levels, HM yielded worse performance measures. Population density factor had negligible effects on most of the measures produced by all studied MDTs except for RMSE, CI width, and CI coverage produced by LW which were modestly influenced by population density.

Ao modelar-se depósitos minerais é comum enfrentarmos o problema de estimar múltiplos atributos possivelmente correlacionados, onde algumas variáveis são amostradas menos densamente do que outras. A falta de dados impõe um problema que requer atenção antes de qualquer modelagem subsequente. Precisamos, ao final, de modelos que sejam estatisticamente representativos. A maioria dos conjuntos de dados de problemas práticos são amostrados de maneira heterotópica e, para obter resultados coerentes, é preciso entender os motivos pelos quais alguns dados faltam e quais são os mecanismos que influenciaram a ausência de informações. A teoria de dados faltantes relaciona as amostras ausentes com aquelas medidas através de três mecanismos distintos: Faltante Completamente Aleatório (Missing Completely At Random - MCAR), Faltante Aleatório (Missing At Random - MAR) e Faltante Não Aleatório (Missing Not At Random - MNAR). O último mecanismo é extremamente complexo e a literatura recomenda ser tratado inicialmente como um mecanismo MAR. E após uma transformação fixa deve ser aplicada aos valores complementados para que estes se transformem em valores MNAR Embora existam métodos estatísticos clássicos para lidar com dados faltantes, tais abordagens ignoram a correlação espacial, uma característica que ocorre naturalmente em dados geológicos. A metodologia adequada para tratar com a falta de dados geológicos é a atualização bayesiana, em que se inserem valores sob mecanismo MAR considerando a correlação espacial. No presente estudo, a atualização bayesiana foi combinada com transformações fixas para tratar o mecanismo de falta de dados MNAR em dados geológicos. A transformação fixa aqui empregada é baseada no erro de inserção gerado em um cenário MAR no conjunto de dados. Assim, com o conjunto completo resultante foi utilizado em uma simulação sequencial gaussiana dos teores de uma base de dados multivariada, apresentando resultados satisfatórios, superiores aos obtidos por meio da cossimulação sequencial gaussiana, não inserindo qualquer viés no modelo final. / When modeling mineral deposits, it is common to face the problem of estimating multiple attributes possibly correlated where some variables are more densely sampled then others. Missing data imposes a problem that requires attention prior to any subsequent modeling. The later requires estimation models statistically representative. Most practical data sets are often heterotopically sampled, and to obtain coherent results one must understand the reasons why there are missing data and what are the mechanisms that cause the absence of information. The theory of missing data relates the missing samples to those measured through three different mechanisms: Missing Completely At Random (MCAR), Missing At Random (MAR), and Missing Not At Random (MNAR). The last mechanism is quite complex to deal with, and the literature recommends being treated as a MAR mechanism and after a fixed transform should be applied to the imputed values so that these turn into MNAR imputed values. Even though there are classical statistical methods to deal with missing data, such approaches ignore spatial correlation, a feature that occurs naturally in geological data. The adequate methodology to deal with missing geologic data is Bayesian Updating, which approaches the MAR mechanism and accounts for spatial correlation. In the present study, bayesian updating was used combined with fixed transforms to treat MNAR missing data mechanism in geologic data. The fixed transform herein used is based on the error of MAR imputation on the data set. The resulting complete set was then used on a sequential gaussian simulation of the grades on a multivariate data set, presenting satisfactory results, superior to those obtained through sequential gaussian cossimulation, not inserting any biases on the final model.

Ao modelar-se depósitos minerais é comum enfrentarmos o problema de estimar múltiplos atributos possivelmente correlacionados, onde algumas variáveis são amostradas menos densamente do que outras. A falta de dados impõe um problema que requer atenção antes de qualquer modelagem subsequente. Precisamos, ao final, de modelos que sejam estatisticamente representativos. A maioria dos conjuntos de dados de problemas práticos são amostrados de maneira heterotópica e, para obter resultados coerentes, é preciso entender os motivos pelos quais alguns dados faltam e quais são os mecanismos que influenciaram a ausência de informações. A teoria de dados faltantes relaciona as amostras ausentes com aquelas medidas através de três mecanismos distintos: Faltante Completamente Aleatório (Missing Completely At Random - MCAR), Faltante Aleatório (Missing At Random - MAR) e Faltante Não Aleatório (Missing Not At Random - MNAR). O último mecanismo é extremamente complexo e a literatura recomenda ser tratado inicialmente como um mecanismo MAR. E após uma transformação fixa deve ser aplicada aos valores complementados para que estes se transformem em valores MNAR Embora existam métodos estatísticos clássicos para lidar com dados faltantes, tais abordagens ignoram a correlação espacial, uma característica que ocorre naturalmente em dados geológicos. A metodologia adequada para tratar com a falta de dados geológicos é a atualização bayesiana, em que se inserem valores sob mecanismo MAR considerando a correlação espacial. No presente estudo, a atualização bayesiana foi combinada com transformações fixas para tratar o mecanismo de falta de dados MNAR em dados geológicos. A transformação fixa aqui empregada é baseada no erro de inserção gerado em um cenário MAR no conjunto de dados. Assim, com o conjunto completo resultante foi utilizado em uma simulação sequencial gaussiana dos teores de uma base de dados multivariada, apresentando resultados satisfatórios, superiores aos obtidos por meio da cossimulação sequencial gaussiana, não inserindo qualquer viés no modelo final. / When modeling mineral deposits, it is common to face the problem of estimating multiple attributes possibly correlated where some variables are more densely sampled then others. Missing data imposes a problem that requires attention prior to any subsequent modeling. The later requires estimation models statistically representative. Most practical data sets are often heterotopically sampled, and to obtain coherent results one must understand the reasons why there are missing data and what are the mechanisms that cause the absence of information. The theory of missing data relates the missing samples to those measured through three different mechanisms: Missing Completely At Random (MCAR), Missing At Random (MAR), and Missing Not At Random (MNAR). The last mechanism is quite complex to deal with, and the literature recommends being treated as a MAR mechanism and after a fixed transform should be applied to the imputed values so that these turn into MNAR imputed values. Even though there are classical statistical methods to deal with missing data, such approaches ignore spatial correlation, a feature that occurs naturally in geological data. The adequate methodology to deal with missing geologic data is Bayesian Updating, which approaches the MAR mechanism and accounts for spatial correlation. In the present study, bayesian updating was used combined with fixed transforms to treat MNAR missing data mechanism in geologic data. The fixed transform herein used is based on the error of MAR imputation on the data set. The resulting complete set was then used on a sequential gaussian simulation of the grades on a multivariate data set, presenting satisfactory results, superior to those obtained through sequential gaussian cossimulation, not inserting any biases on the final model.

Ao modelar-se depósitos minerais é comum enfrentarmos o problema de estimar múltiplos atributos possivelmente correlacionados, onde algumas variáveis são amostradas menos densamente do que outras. A falta de dados impõe um problema que requer atenção antes de qualquer modelagem subsequente. Precisamos, ao final, de modelos que sejam estatisticamente representativos. A maioria dos conjuntos de dados de problemas práticos são amostrados de maneira heterotópica e, para obter resultados coerentes, é preciso entender os motivos pelos quais alguns dados faltam e quais são os mecanismos que influenciaram a ausência de informações. A teoria de dados faltantes relaciona as amostras ausentes com aquelas medidas através de três mecanismos distintos: Faltante Completamente Aleatório (Missing Completely At Random - MCAR), Faltante Aleatório (Missing At Random - MAR) e Faltante Não Aleatório (Missing Not At Random - MNAR). O último mecanismo é extremamente complexo e a literatura recomenda ser tratado inicialmente como um mecanismo MAR. E após uma transformação fixa deve ser aplicada aos valores complementados para que estes se transformem em valores MNAR Embora existam métodos estatísticos clássicos para lidar com dados faltantes, tais abordagens ignoram a correlação espacial, uma característica que ocorre naturalmente em dados geológicos. A metodologia adequada para tratar com a falta de dados geológicos é a atualização bayesiana, em que se inserem valores sob mecanismo MAR considerando a correlação espacial. No presente estudo, a atualização bayesiana foi combinada com transformações fixas para tratar o mecanismo de falta de dados MNAR em dados geológicos. A transformação fixa aqui empregada é baseada no erro de inserção gerado em um cenário MAR no conjunto de dados. Assim, com o conjunto completo resultante foi utilizado em uma simulação sequencial gaussiana dos teores de uma base de dados multivariada, apresentando resultados satisfatórios, superiores aos obtidos por meio da cossimulação sequencial gaussiana, não inserindo qualquer viés no modelo final. / When modeling mineral deposits, it is common to face the problem of estimating multiple attributes possibly correlated where some variables are more densely sampled then others. Missing data imposes a problem that requires attention prior to any subsequent modeling. The later requires estimation models statistically representative. Most practical data sets are often heterotopically sampled, and to obtain coherent results one must understand the reasons why there are missing data and what are the mechanisms that cause the absence of information. The theory of missing data relates the missing samples to those measured through three different mechanisms: Missing Completely At Random (MCAR), Missing At Random (MAR), and Missing Not At Random (MNAR). The last mechanism is quite complex to deal with, and the literature recommends being treated as a MAR mechanism and after a fixed transform should be applied to the imputed values so that these turn into MNAR imputed values. Even though there are classical statistical methods to deal with missing data, such approaches ignore spatial correlation, a feature that occurs naturally in geological data. The adequate methodology to deal with missing geologic data is Bayesian Updating, which approaches the MAR mechanism and accounts for spatial correlation. In the present study, bayesian updating was used combined with fixed transforms to treat MNAR missing data mechanism in geologic data. The fixed transform herein used is based on the error of MAR imputation on the data set. The resulting complete set was then used on a sequential gaussian simulation of the grades on a multivariate data set, presenting satisfactory results, superior to those obtained through sequential gaussian cossimulation, not inserting any biases on the final model.

Today’s surveys face a growing problem with increasing nonresponse.  The increase in nonresponse rate causes a need for better and more effective ways to reduce the nonresponse bias.  There are three major scientific orientation of today’s research dealing with nonresponse. One is examining the social factors, the second one studies different data collection methods and the third investigating the use of weights to adjust estimators for nonresponse.  We would like to contribute to the third orientation by evaluating estimators which use and adjust weights based on auxiliary variables to balance the survey nonresponse through simulations. For the simulation we use an artificial population consisting of 35455 participants from the Representativity Indicators for Survey Quality project. We model three nonresponse mechanisms (MCAR, MAR and MNAR) with three different coefficient of determination s between our study variable and the auxiliary variables and under three response rates resulting in 63 simulation scenarios. The scenarios are replicated 1000 times to acquire the results. We outline our findings and results for each estimator in all scenarios with the help of bias measures.

No description available.

Neste trabalho aborda-se aspectos teóricos, computacionais e aplicados de análises clássicas de dados categorizados com omissão. Uma revisão da literatura é apresentada enquanto se introduz os mecanismos de omissão, mostrando suas características e implicações nas inferências de interesse por meio de um exemplo considerando duas variáveis respostas dicotômicas e estudos de simulação. Amplia-se a modelagem descrita em Paulino (1991, Brazilian Journal of Probability and Statistics 5, 1-42) da distribuição multinomial para a produto de multinomiais para possibilitar a inclusão de variáveis explicativas na análise. Os resultados são desenvolvidos em formulação matricial adequada para a implementação computacional, que é realizada com a construção de uma biblioteca para o ambiente estatístico R, a qual é disponibilizada para facilitar o traçado das inferências descritas nesta dissertação. A aplicação da teoria é ilustrada por meio de cinco exemplos de características diversas, uma vez que se ajusta modelos estruturais lineares (homogeneidade marginal), log-lineares (independência, razão de chances adjacentes comum) e funcionais lineares (kappa, kappa ponderado, sensibilidade/especificidade, valor preditivo positivo/negativo) para as probabilidades de categorização. Os padrões de omissão também são variados, com omissões em uma ou duas variáveis, confundimento de células vizinhas, sem ou com subpopulações. / We consider theoretical, computational and applied aspects of classical categorical data analyses with missingness. We present a literature review while introducing the missingness mechanisms, highlighting their characteristics and implications in the inferences of interest by means of an example involving two binary responses and simulation studies. We extend the multinomial modeling scenario described in Paulino (1991, Brazilian Journal of Probability and Statistics 5, 1-42) to the product-multinomial setup to allow for the inclusion of explanatory variables. We develop the results in matrix formulation and implement the computational procedures via subroutines written under R statistical environment. We illustrate the application of the theory by means of five examples with different characteristics, fitting structural linear (marginal homogeneity), log-linear (independence, constant adjacent odds ratio) and functional linear models (kappa, weighted kappa, sensitivity/specificity, positive/negative predictive value) for the marginal probabilities. The missingness patterns includes missingness in one or two variables, neighbor cells confounded, with or without explanatory variables.

Neste trabalho aborda-se aspectos teóricos, computacionais e aplicados de análises clássicas de dados categorizados com omissão. Uma revisão da literatura é apresentada enquanto se introduz os mecanismos de omissão, mostrando suas características e implicações nas inferências de interesse por meio de um exemplo considerando duas variáveis respostas dicotômicas e estudos de simulação. Amplia-se a modelagem descrita em Paulino (1991, Brazilian Journal of Probability and Statistics 5, 1-42) da distribuição multinomial para a produto de multinomiais para possibilitar a inclusão de variáveis explicativas na análise. Os resultados são desenvolvidos em formulação matricial adequada para a implementação computacional, que é realizada com a construção de uma biblioteca para o ambiente estatístico R, a qual é disponibilizada para facilitar o traçado das inferências descritas nesta dissertação. A aplicação da teoria é ilustrada por meio de cinco exemplos de características diversas, uma vez que se ajusta modelos estruturais lineares (homogeneidade marginal), log-lineares (independência, razão de chances adjacentes comum) e funcionais lineares (kappa, kappa ponderado, sensibilidade/especificidade, valor preditivo positivo/negativo) para as probabilidades de categorização. Os padrões de omissão também são variados, com omissões em uma ou duas variáveis, confundimento de células vizinhas, sem ou com subpopulações. / We consider theoretical, computational and applied aspects of classical categorical data analyses with missingness. We present a literature review while introducing the missingness mechanisms, highlighting their characteristics and implications in the inferences of interest by means of an example involving two binary responses and simulation studies. We extend the multinomial modeling scenario described in Paulino (1991, Brazilian Journal of Probability and Statistics 5, 1-42) to the product-multinomial setup to allow for the inclusion of explanatory variables. We develop the results in matrix formulation and implement the computational procedures via subroutines written under R statistical environment. We illustrate the application of the theory by means of five examples with different characteristics, fitting structural linear (marginal homogeneity), log-linear (independence, constant adjacent odds ratio) and functional linear models (kappa, weighted kappa, sensitivity/specificity, positive/negative predictive value) for the marginal probabilities. The missingness patterns includes missingness in one or two variables, neighbor cells confounded, with or without explanatory variables.

Ο καρκίνος του παχέος εντέρου αποτελεί ένα από τα συχνότερα κακοήθη νεοπλάσματα παγκοσμίως, προκαλώντας σημαντική νοσηρότητα και θνητότητα. Η συστηματική διερεύνηση της παθογένειας συντελεί σημαντικά στην πρόληψη, έγκαιρη διάγνωση, θεραπεία και πρόγνωση της νόσου. Στην εποχή της μοριακής ιατρικής, η κατανόηση των μοριακών μηχανισμών καρκινογένεσης έχει αναδείξει το ρόλο ενδοκυττάριων σηματοδοτικών μονοπατιών, τα οποία ρυθμίζουν κυτταρικές διαδικασίες, όπως πολλαπλασιασμός, διαφοροποίηση, απόπτωση, αγγειογένεση, διήθηση. Κομβικά συστατικά τέτοιων μοριακών δικτύων αποτελούν οι υποδοχείς αυξητικών παραγόντων, όπως ο Human Εpidermal Receptor-1 (ΗΕR-1/EGFR), ο ρόλος του οποίου έχει τεκμηριωθεί στο αδενοκαρκίνωμα παχέος εντέρου, επιτείνοντας το ενδιαφέρον στη διευκρίνηση του ρόλου γειτονικών υποδοχέων, όπως του Human Εpidermal Receptor-3 (HER-3). O HER-3 συνιστά μεμβρανικό υποδοχέα που συμμετέχει σε μοριακά μονοπάτια ενδοκυτταρικής σηματοδότησης. Επομένως, ποσοτικές μεταβολές στην έκφρασή του αλλά και ποιοτικές αλλαγές στη δομή του, συντελούν δυνητικά στην κυτταρική εξαλλαγή. Τα δεδομένα από τη μελέτη του HER-3 στο αδενοκαρκίνωμα παχέος εντέρου είναι περιορισμένα και ο ρόλος του στην παθογένεια, πρόγνωση και θεραπεία της νόσου παραμένει ασαφής. Αντίστοιχα με τους μεμβρανικούς υποδοχείς, πυρηνικοί υποδοχείς ενέχονται σε διαδικασίες ρύθμισης γονιδιακής έκφρασης. Οι οιστρογονικοί υποδοχείς (ER) α και β διαμεσολαβούν την επίδραση των οιστρογόνων σε κυτταρικό επίπεδο, μεταποιώντας τα επίπεδα των ορμονών σε μεταβολές γονιδιακής έκφρασης. Οι διαφορές στην επίπτωση του καρκίνου του παχέος εντέρου ανάμεσα στα δύο φύλα καθώς και πρόσφατα βιβλιογραφικά δεδομένα έχουν αναδείξει τη σημασία της έκφρασης αυτών των υποδοχέων στην καρκινογένεση του παχέος έντερου. Παράλληλα, η εξειδίκευση της οιστρογονικής δράσης σε επίπεδο ιστού και κυττάρου εξασφαλίζεται μέσω της δράσης συγκεκριμένων συμπαραγόντων (ενεργοποιητών/καταστολέων). Αυτές οι πρωτεΐνες είναι ειδικοί μεταγραφικοί παράγοντες, οι οποίοι συνδεόμενοι με τους οιστρογονικούς αλλά και άλλους υποδοχείς «εξατομικεύουν» την ορμονική επίδραση στο γονιδίωμα. Ο proline-, glutamic acid-, and leucine-rich protein 1 (PELP1), γνωστός και ως modulator of non-genomic activity of ER (MNAR), ο amplified in breast cancer-1 (AIB1) και ο transcriptional intermediary factor-2 (TIF2) είναι σημαντικοί συμπαράγοντες οιστρογονικών υποδοχέων, με συνέπεια η μελέτη τους να αποτελεί αναπόσπαστο μέρος της διερεύνησης οιστρογονο-εξαρτώμενων μηχανισμών. Η συνεχής αλληλεπίδραση HER- και ER-εξαρτώμενων μονοπατιών έχει περιγραφεί σε ποικίλλους ιστούς. Σκοπός της παρούσας μελέτης είναι η διερεύνηση του ρόλου της (υπερ)έκφρασης του μεμβρανικού υποδοχέα HER-3, των οιστρογονικών υποδοχέων (ER) και των συμπαραγόντων PELP1/MNAR, AIB-1 και TIF-2 στον καρκίνο του παχέος εντέρου. Υλικά και μέθοδοι Στην παρούσα μελέτη χρησιμοποιήθηκαν ιστικά δείγματα, μονιμοποιημένα σε φορμόλη και εκλεισμένα σε παραφίνη από 140 ασθενείς με αδενοκαρκίνωμα παχέος εντέρου. Η έκφραση των επιπέδων HER-3 mRNA εκτιμήθηκε με τη μέθοδο της ποσοτικής αλυσιδωτής αντίδρασης πολυμεράσης (RT-PCR) σε 54 αδενοκαρκινώματα και 29 δείγματα φυσιολογικού βλεννογόνου. Η έκφραση των επιπέδων της φωσφορυλιωμένης (pHER-3) και μη φωσφορυλιωμένης HER-3 πρωτείνης εκτιμήθηκε με τη μέθοδο της ανοσοιστοχημείας σε 110 δείγματα φυσιολογικού βλεννογόνου, 24 αδενώματα και 140 αδενοκαρκινώματα. Η έκφραση των επιπέδων του οιστρογονικού υποδοχέα α και β και του PELP1/ΜΝΑR εκτιμήθηκε με τη μέθοδο της ανοσοιστοχημείας σε 113 αδενοκαρκινώματα, 30 αδενώματα και 88 δείγματα φυσιολογικού βλεννογόνου. Αντίστοιχα η έκφραση των επιπέδων του ΑΙΒ1 και TIF-2 εκτιμήθηκε με τη μέθοδο της ανοσοιστοχημείας σε 110 αδενοκαρκινώματα, 30 αδενώματα και 83 δείγματα φυσιολογικού βλεννογόνου. Αποτελέσματα Η πρωτεΐνη HER-3 εκφράζεται στο κυτταρόπλασμα και στον πυρήνα επιθηλιακών κυττάρων παχέος εντέρου σε φυσιολογικό βλεννογόνο, αδενώματα και αδενοκαρκινώματα και φαίνεται να μεταβάλλεται τοπογραφικά (από τον πυρήνα στο κυτταρόπλασμα) κατά τη διαδικασία της καρκινογένεσης. Ωστόσο, η έκφραση της πρωτεΐνης HER-3 σε αδενοκαρκινώματα δε φαίνεται να συσχετίζεται σημαντικά με τις κλινικοπαθολογικές παραμέτρους της νόσου. Η φωσφορυλιωμένη μορφή της πρωτεΐνης HER-3 (pHER-3) εκφράζεται στον πυρήνα και τη μεμβράνη επιθηλιακών και λείων μυικών κυττάρων παχέος εντέρου σε φυσιολογικό βλεννογόνο, αδενώματα και αδενοκαρκινώματα. Η πυρηνική έκφραση pHER-3 δε διαφέρει σημαντικά ανάμεσα σε φυσιολογικό βλεννογόνο, αδενώματα και αδενοκαρκινώματα. Ωστόσο, αυξημένα επίπεδα πυρηνικής έκφρασης pHER-3 συσχετίζονται σημαντικά με μεγαλύτερο στάδιο της νόσου, χωρίς να συσχετίζονται με τα επίπεδα έκφρασης της μη φωσφορυλιωμένης μορφής. Τα επίπεδα έκφρασης του γονιδίου ΗER-3 δε φαίνεται να αυξάνουν σημαντικά κατά την καρκινογένεση. Ωστόσο, αυξημένα επίπεδα HER-3 mRNA στα αδενοκαρκινώματα σχετίζονται με μεγαλύτερη ηλικία των ασθενών, εντόπιση του όγκου στο αριστερό κόλον και το ορθό και με λεμφαδενική διήθηση. Επίσης, συχετίστηκαν με αυξημένη πιθανότητα υποτροπής της νόσου και μειωμένο χρονικό διάστημα ως την υποτροπή. Ο ERα εκφράζεται σπάνια στο παχύ έντερο σε αντίθεση με τον ERβ, ο οποίος εκφράζεται συχνά στον πυρήνα επιθηλιακών αλλά και στρωματικών κυττάρων. Η έκφραση της πρωτεΐνης ERβ καθίσταται πιο έντονη κατά τη διάρκεια της καρκινογένεσης σε άνδρες, και στα αδενοκαρκινώματα συσχετίζεται με την πιθανότητα υποτροπής της νόσου. Ο συμπαράγοντας PELP1/MNAR ανιχνεύεται στον πυρήνα επιθηλιακών αλλά και στρωματικών κυττάρων του παχέος εντέρου και η έκφρασή του αυξάνει κατά την καρκινογένεση και στα αδενοκαρκινώματα συσχετίζεται με την έκφραση του ERβ. Ωστόσο, η υπερέκφραση του PELP1/MNAR στα ERβ θετικά αδενοκαρκινώματα συσχετίζεται με μεγαλύτερη συνολική επιβίωση των ασθενών. Ο AIB1 και ο TIF2 ανιχνεύονται στον πυρήνα επιθηλιακών αλλά και στρωματικών κυττάρων του παχέος εντέρου. Η έκφραση του ΑΙΒ1 αυξάνει κατά την καρκινογένεση και συσχετίζεται με τοπική ανάπτυξη του όγκου. Ωστόσο, στην πολυπαραγοντική ανάλυση ο ΑΙΒ1 αναδεικνύεται ως ανεξάρτητος ευνοϊκός προγνωστικός παράγοντας ως προς τη συνολική επιβίωση. Η έκφραση του ΤΙF2 αυξάνει κατά την καρκινογένεση και στα αδενοκαρκινώματα συσχετίζεται με την έκφραση του AIB1. Ωστόσο, η έκφρασή του στα αδενοκαρκινώματα δε σχετίζεται με κλινικοπαθολογικές παραμέτρους της νόσου. Το πρότυπο έκφρασης των συμπαραγόντων AIB1 και TIF2 δε σχετίζεται σημαντικά με εκείνο του ERβ. Συζήτηση-συμπεράσματα-προοπτικές Η παρούσα μελέτη αναδεικνύει τη σημασία της έκφρασης και φωσφορυλίωσης του ΗΕR3 στην καρκινογένεση του παχέος εντέρου, υποστηρίζοντας τον πιθανό ρόλο τους στην πρόγνωση της νόσου. Τα ευρήματα της μελέτης συμφωνούν με συγκεκριμένα βιβλιογραφικά δεδομένα ως προς τη συχνότητα ανίχνευσης του υποδοχέα στον παχύ έντερο, ενώ είναι η πρώτη η οποία αναδεικνύει τα επίπεδα HER-3 mRNA ως πιθανό προγνωστικό βιοδείκτη. Η διερεύνηση της έκφρασης του οιστρογονικού υποδοχέα β (ERβ1) ανέδειξε αύξηση των επιπέδων του κατά την καρκινογένεση, εύρημα που βρίσκεται σε συμφωνία με μερικά και σε αντιδιαστολή με άλλα βιβλιογραφικά δεδομένα. Η προγνωστική σημασία της έκφρασης των πυρηνικών υποδοχέων εξαρτάται από ποικίλους παράγοντες, όπως τα επίπεδα ειδικών συμπαραγόντων, ομοιοπολικές τροποποιήσεις, την τοπογραφία τους μέσα στο κύτταρο και τα επίπεδα συγκεκριμένων συγκεντρώσεων προσδέτη/ορμόνης. Η αύξηση των επιπέδων των συμπαραγόντων του οιστρογονικού υποδοχέα PELP1/MNAR, ΑΙΒ1 και ΤΙF2 κατά την καρκινογένεση υποδηλώνει πιθανή συμμετοχή τους σε οιστρογονοεξαρτώμενη ογκογόνο σηματοδότηση. Ωστόσο, η απουσία ισχυρής συσχέτισης ανάμεσα στα επίπεδα έκφρασής τους και στα επίπεδα έκφρασης του οιστρογονικού υποδοχέα (ERβ1) υπογραμμίζει την πλειοτροπική τους δράση και τον επιπρόσθετο ρόλο τους σε οιστρογονο-ανεξάρτητη ενδοκυττάρια σηματοδότηση. Περισσότερες μελέτες σε μεγάλο αριθμό ασθενών, κατάλληλα σχεδιασμένες και εκτελεσμένες, με τη χρήση ευαίσθητων και ειδικών πειραματικών τεχνικών καθώς και μεθόδων στατιστικής ανάλυσης απαιτούνται για την επιβεβαίωση των ευρημάτων της παρούσας μελέτης. Στην εποχή της μεταγονιδιωματικής ιατρικής, η αναζήτηση χρήσιμων μοριακών βιοδεικτών δύναται να συντελέσει στη βελτίωση της πρόγνωσης και της ποιότητας ζωής των ασθενών με καρκίνο του παχέος εντέρου. / Colorectal cancer is a major cause of cancer-related morbidity and mortality in the western world and has a significant impact on the health care systems. The deep understanding of molecular mechanisms that underline cellular transformation and tumor progression leads to the identification of key-molecules that are appropriate targets for sophisticated therapy in cancer. One such targeted approach exploits the presence of specific biomarkers that could be considered essential for tumor development. The role of such a biomarker, Human Εpidermal Receptor-1 (ΗΕR-1/EGFR), has been established in the development of colorectal cancer, suggesting the potential involvement of neighboring receptors, such as Human Εpidermal Receptor-3 (HER-3). HER-3 is a membranic receptor implicated in intracellular cell proliferation signaling. Thus, quantitative modifications in its expression and/or qualitative changes in its structure may contribute to cellular malignant transformation. The significance of HER3 expression, localization and phosphorylation remains elusive and data regarding its role in the pathogenesis, diagnosis, prognosis and management of colorectal cancer is limited. Apart from their mebranic counterparts, nuclear receptors are implicated in the regulation of gene transcription. Estrogen receptors (ER) α and β mediate the estrogen actions in the subcellular microenvironment. Differences in the incidence of colorectal cancer in the two genders have underlined the significance of ER expression in colorectal carcinogenesis. The specificity of estrogen activities in various cell types is mediated by the presence of tissue-specific coregulators (coactivators/corepressors). These proteins are specific transcription factors that bind to nuclear receptors, orchestrating their actions on the genome. Frequently, such coregulators are located in the cytoplasm, regulating the non genomic activity of the estrogens. Proline-, glutamic acid-, and leucine-rich protein 1 (PELP1), also known as modulator of non-genomic activity of ER (MNAR), amplified in breast cancer-1 (AIB1) and transcriptional intermediary factor-2 (TIF2) are considered major ER-coregulators. Thus, the investigation of their expression is inherent to the evaluation of estrogen-mediated mechanisms. The dynamic cross-talk between HER- and ER-driven signaling pathways has been described. The aim of this study is the investigation of the role of HER3, ER and coregulators PELP1/MNAR, AIB-1, TIF-2 (over)expression in the pathogenesis and prognosis of colorectal cancer. Material and Methods Sections from formalin-fixed, paraffin-embedded colorectal tissue blocks, derived from 140 patients with colorectal cancer, were used. HER-3 mRNA levels of expression were assessed by quantitative RT-PCR in 54 colorectal adenocarcinomas and 29 normal mucosa specimens. The expression levels of both phosphorylated and unphosphorylated HER-3 protein were assessed by immunohistochemistry in 110 normal mucosa specimens, 24 adenomas and 140 adenocarcinomas. The expression levels of ER α and β, PELP1/ΜΝΑR were assessed by immunohistochemistry in 88 normal mucosa specimens, 30 adenomas and 113 adenocarcinomas. Additionally, the expression levels of ΑΙΒ1 and TIF-2 protein were assessed by immunohistochemistry in 83 normal mucosa specimens, 30 adenomas and 110 adenocarcinomas. Results HER-3 was detected both in the cytoplasm and nucleus, whereas pHER-3 was observed in the nucleus and membrane of cells. A possible switch in HER-3 topography from the nucleus to the cytoplasm during colorectal tumorigenesis is suggested. The expression of pHER-3 did not differ significantly in normal tissue, adenomas and carcinomas, but was related to disease stage. HER-3 mRNA overexpression was significantly associated with decreased time to disease progression. It was also correlated with higher median age, left colon and rectal tumour sites and lymph node involvement. ERα expression was extremely rare in colorectal tissue of our cohort and its expression did not appear to be associated with colorectal carcinogenesis. ERβ and PELP1/MNAR were detected in the nucleus of epithelial, endothelial, inflammatory, smooth muscle cells and myofibroblasts. When intensity of staining was taken into account, the expression of both proteins was significantly increased in epithelial cells of carcinomas compared to normal mucosa. ERβ expression in epithelial cells was correlated with decreased disease progression-free survival. PELP1/MNAR overexpression in epithelial cells was found to be an independent favorable prognostic factor. AIB1 and TIF2 were detected in the nucleus of epithelial, endothelial, inflammatory, smooth muscle cells and myofibroblasts. The expression of both proteins was significantly increased in epithelial cells of carcinomas compared to normal mucosa. In carcinomas, a significant correlation between the levels of expression of AIB1 and TIF2 was noted, but there was no correlation between the expression patterns of these two proteins and ERβ. Although AIB1 overexpression was associated with local tumor invasion, it was also found to correlate independently with prolonged overall survival. TIF2 overxpression did not appear to correlate with clinicopathological parameters. Conclusion/Discussion This study highlights the significance of ΗΕR3 expression and phosphorylation in colorectal carcinogenesis, supporting also its potential prognostic significance. This study supports literature data regarding HER3 expression in colorectal tissue, while is the first to imply a possible prognostic significance of HER-3 mRNA expression levels and to suggest a topographic switch of HER3 protein during colorectal carcinogenesis. ERβ1 protein levels were found to increase during colorectal carcinogenesis, a finding which corresponds only to a small portion of literature data. The prognostic role of nuclear receptors depends on a number of factors, such as coregulator expression levels, chemical modifications, subcellular localization and ligand/hormone levels. The concomitant increase in the expression levels of coregulators PELP1/MNAR, ΑΙΒ1 and ΤΙF2 during colorectal carcinogenesis might imply their potential participation in estrogen-mediated signaling. However, the characteristic absence of strong correlation between their expression pattern and ERβ1 expression pattern underlines their pluripotent role and their possible contribution to estrogen-independent signaling. Further studies with a large number of patients, appropriately designed and conducted using sensitive experimental and statistical methods, are required for the confirmation of our hypothesis generation results. In the post-genomic era, identification of useful molecular biomarkers might contribute to the improvement of the management and prognosis of patients with colorectal cancer.

<p dir="ltr">This dissertation advances the field of causal inference by developing methodologies in the face of assumption violations. Traditional causal inference methodologies hinge on a core set of assumptions, which are often violated in the complex landscape of modern experiments and observational studies. This dissertation proposes novel methodologies designed to address the challenges posed by single or multiple assumption violations. By applying these innovative approaches to real-world datasets, this research uncovers valuable insights that were previously inaccessible with existing methods. </p><p><br></p><p dir="ltr">First, three significant sources of complications in causal inference that are increasingly of interest are interference among individuals, nonadherence of individuals to their assigned treatments, and unintended missing outcomes. Interference exists if the outcome of an individual depends not only on its assigned treatment, but also on the assigned treatments for other units. It commonly arises when limited controls are placed on the interactions of individuals with one another during the course of an experiment. Treatment nonadherence frequently occurs in human subject experiments, as it can be unethical to force an individual to take their assigned treatment. Clinical trials, in particular, typically have subjects that do not adhere to their assigned treatments due to adverse side effects or intercurrent events. Missing values also commonly occur in clinical studies. For example, some patients may drop out of the study due to the side effects of the treatment. Failing to account for these considerations will generally yield unstable and biased inferences on treatment effects even in randomized experiments, but existing methodologies lack the ability to address all these challenges simultaneously. We propose a novel Bayesian methodology to fill this gap. </p><p><br></p><p dir="ltr">My subsequent research further addresses one of the limitations of the first project: a set of assumptions about interference structures that may be too restrictive in some practical settings. We introduce a concept of the ``degree of interference" (DoI), a latent variable capturing the interference structure. This concept allows for handling arbitrary, unknown interference structures to facilitate inference on causal estimands. </p><p><br></p><p dir="ltr">While randomized experiments offer a solid foundation for valid causal analysis, people are also interested in conducting causal inference using observational data due to the cost and difficulty of randomized experiments and the wide availability of observational data. Nonetheless, using observational data to infer causality requires us to rely on additional assumptions. A central assumption is that of \emph{ignorability}, which posits that the treatment is randomly assigned based on the variables (covariates) included in the dataset. While crucial, this assumption is often debatable, especially when treatments are assigned sequentially to optimize future outcomes. For instance, marketers typically adjust subsequent promotions based on responses to earlier ones and speculate on how customers might have reacted to alternative past promotions. This speculative behavior introduces latent confounders, which must be carefully addressed to prevent biased conclusions. </p><p dir="ltr">In the third project, we investigate these issues by studying sequences of promotional emails sent by a US retailer. We develop a novel Bayesian approach for causal inference from longitudinal observational data that accommodates noncompliance and latent sequential confounding. </p><p><br></p><p dir="ltr">Finally, we formulate the causal inference problem for the privatized data. In the era of digital expansion, the secure handling of sensitive data poses an intricate challenge that significantly influences research, policy-making, and technological innovation. As the collection of sensitive data becomes more widespread across academic, governmental, and corporate sectors, addressing the complex balance between making data accessible and safeguarding private information requires the development of sophisticated methods for analysis and reporting, which must include stringent privacy protections. Currently, the gold standard for maintaining this balance is Differential privacy. </p><p dir="ltr">Local differential privacy is a differential privacy paradigm in which individuals first apply a privacy mechanism to their data (often by adding noise) before transmitting the result to a curator. The noise for privacy results in additional bias and variance in their analyses. Thus, it is of great importance for analysts to incorporate the privacy noise into valid inference.</p><p dir="ltr">In this final project, we develop methodologies to infer causal effects from locally privatized data under randomized experiments. We present frequentist and Bayesian approaches and discuss the statistical properties of the estimators, such as consistency and optimality under various privacy scenarios.</p>