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1 Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: FME - School of Mathematics and Statistics UB - (ENG)Universitat de Barcelona MASTER'S DEGREE IN STATISTICS AND OPERATIONS RESEARCH (Syllabus 2013). (Teaching unit Optional) 5 Teaching languages: Spanish Teaching staff Coordinator: Others: JOSEP LLUÍS CARRASCO JORDAN JOSEP LLUÍS CARRASCO JORDAN - A JORDI OCAÑA REBULL - A Requirements - It is necessary that students have basic knowledge of R. In the following link the materials from a course to introduction to R are available - It is recommended that students have taken a course in Design of Experiments or have basic knowledge on this subject. In particular it is recommended that students know the methodology outlined in chapters 12 and 13 included in Montgomery, DC (2001). Design and analysis of experiments, 5th edition. John Wiley & sons. Degree competences to which the subject contributes Specific: 5. CE-1. Ability to design and manage the collection of information and coding, handling, storing and processing it. 6. CE-2. Ability to master the proper terminology in a field that is necessary to apply statistical or operations research models and methods to solve real problems. 7. CE-3. Ability to formulate, analyze and validate models applicable to practical problems. Ability to select the method and / or statistical or operations research technique more appropriate to apply this model to the situation or problem. 8. CE-4. Ability to use different inference procedures to answer questions, identifying the properties of different estimation methods and their advantages and disadvantages, tailored to a specific situation and a specific context. 9. CE-5. Ability to formulate and solve real problems of decision-making in different application areas being able to choose the statistical method and the optimization algorithm more suitable in every occasion. Translate to english 10. CE-6. Ability to use appropriate software to perform the necessary calculations in solving a problem. 11. CE-7. Ability to understand statistical and operations research papers of an advanced level. Know the research procedures for both the production of new knowledge and its transmission. 12. CE-8. Ability to discuss the validity, scope and relevance of these solutions and be able to present and defend their conclusions. 13. CE-9. Ability to implement statistical and operations research algorithms. Transversal: 1. ENTREPRENEURSHIP AND INNOVATION: Being aware of and understanding how companies are organised and the principles that govern their activity, and being able to understand employment regulations and the relationships between planning, industrial and commercial strategies, quality and profit. 1 / 5

2 2. SUSTAINABILITY AND SOCIAL COMMITMENT: Being aware of and understanding the complexity of the economic and social phenomena typical of a welfare society, and being able to relate social welfare to globalisation and sustainability and to use technique, technology, economics and sustainability in a balanced and compatible manner. 3. TEAMWORK: Being able to work in an interdisciplinary team, whether as a member or as a leader, with the aim of contributing to projects pragmatically and responsibly and making commitments in view of the resources that are available. 4. EFFECTIVE USE OF INFORMATION RESOURCES: Managing the acquisition, structuring, analysis and display of data and information in the chosen area of specialisation and critically assessing the results obtained. Teaching methodology The in-person lessons consist of sessions in the classroom where the theoretical concepts are introduced with practical examples by means of slides that will be available for students. Furthermore, the appropriate software to carry out the analyses and procedures will be also introduced by solving real data examples. Learning objectives of the subject To face concrete situation, the student have to know how identifying the appropriate designs, properly carry out the experimentation and analyzing the results. To obtain theoretical and practical knowledge of some critical designs in Biostatistics. To know the regulatory that rules the approval of generic drugs and formulations. To know to differentiate between a situation that requires an analysis of differences from an analysis of equivalence. To provide the concepts and approaches to carry out an analysis of bioequivalences and equivalence in general. To provide the concepts and approaches to carry out an analysis of concordance among measurements. To know differentiating an analysis of concordance from an association or parameter comparison analysis. To identify the sources of disagreement. To provide the skill of discriminating among approaches depending of the type of data and objectives. Study load Total learning time: 125h Hours large group: 30h 24.00% Hours medium group: 0h 0.00% Hours small group: 15h 12.00% Guided activities: 0h 0.00% Self study: 80h 64.00% 2 / 5

3 Content BLOCK 1. SOME EXPERIMENTAL DESIGNS 1.1. BALANCED INCOMPLETE BLOCK DESIGN (BIB) Concept of BIB. Existence of BIB. Fisher's inequality. Symmetrical BIB BIB data analysis. Linear model. ANOVA table. Examples CROSSOVER DESIGNS Concept of crossover design. Crossover design 2 2 (or AB/BA). ANOVA in designs 2 2. Linear model and analysis of several effects Superior order crossover design and its analysis. BLOCK 2. BIOEQUIVALENCE AND Y EQUIVALENCE 2.1. INTRODUCTION TO BIOEQUIVALENCE (BE) Bioavailability. Concept of bioequivalence among drugs. Regulatory standards TOST analysis. Confidence intervals inclusion principle. Confidence intervals for BE. Bayesian approach. Non-parametric approach Residual effect problem (carryover). TOST power and high variability drugs. 3 / 5

4 2.2. FURTHER BIOEQUIVALENCE APPROACHES AND RELATED CONCEPTS Individual and populational bioequivalence Multivariate bioequivalence Non inferiority 2.3. EQUIVALENCE TESTS General concept of equivalence test Main applications: goodness-of-fit, homogeneity of variances, additivity in linear models, equivalence of proportions Complements: equivalence tests and statistics based on distances; application in bioinformatics. BLOCK 3. ASSESSMENT OF THE DATA QUALITY: RELIABILITY AND CONCORNDANCE OF MEASUREMENTS 3.1. INTRODUCTION Model of measurement. Types of measurement errors Concepts: validity, accuracy, reliability and calibration Classification of the approaches to evaluate agreement ANALYSIS WITH QUALITATIVE DATA 4 / 5

5 Components of discordance: bias and association. Comparison of paired proportions. Evaluation of linear association in contingency tables Concordance index: kappa index and weighted kappa y kappa. Kappa index extended to k observers ANALYSIS WITH CONTINUOUS DATA Components of discordance: bias, association and heteroscedasticity Coefficient of concordance: definition and generalization Intraclass correlation coefficient: reliability, consistency and concordance Procedures based on probability criteria: tolerance intervals and total deviation index. Bland-Altman approach. Other approaches to assess concordance Assessment of individual bioequivalence as a concordance among measurements issue. Qualification system Overall mark will be obtained as an average of: 1) Proposed exercises (50%) 2) Test about theoretical concepts treated along the course (50%) Bibliography Basic: Vonesh, E.F., Chinchilli, V.M. Linear and nonlinear models for the analysis of repeated measurements. Marcel Dekker, ISBN Chow, S-C., Liu, J-P. Design and analysis of bioavalability and bioequivalence studies. 3th ed. CRC, ISBN Shoukri, M.M. Measures of interobserver agreement. Chapman & Hall/CRC, Agresti, A. Categorical data analysis. 2nd ed. John Wiley & Sons, Inc., Fleiss, J.L. Design and analysis of clinical experiments. John Wiley & Sons, Inc., Complementary: Raghavarao, D.; Padgett, L.V. Block designs. analysis, combinatorics and applications. World Scientific. Series on Applied Mathematics, vol. 17., ISBN Senn, S. Cross-over trials in clinical research. 2nd ed. John Wiley & Sons, Inc., Patterson, S., Jones, B. Bioequivalence and Statistics in Clinical Pharmacology. Chapman & Hall/CRC, ISBN Wellek, S. Testing statistical hypotheses of equivalence. Chapman & Hall/CRC, ISBN Dunn, G. Design and analysis of reliability studies. Oxford University Press, / 5

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