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# BASIC MATHEMATICAL CONCEPTS & BIOSTATISTICS

 Compulsory/Elective Code Semester Lectures Practicals Credits ECTS Compulsory 13Β007 2nd 4 Hrs/Wk 2 Hrs/Wk 5 7.0 Aims: 1. Ability to apply knowledge on mathematical models and biostatistics in the analysis of biomedical data, 2. Analysis of biomedical data using appropriate methods and software, 3. Synthesis, evaluation and interpretation of results from statistical analysis, 4. Critical evaluation of published biomedical research, 5. Autonomous work, 6. Collaborative work, 7. Promotion of free, creative and inductive thinking. Objectives: At the end of the course students should: a) Possess all the necessary mathematical background required for attending other courses of the Department (including the Biostatistics section of this course), as well as for understanding the methods of research applied to Biology and Biomedical Research, b) Know where, when and why Statistics are used in Biomedical Research, c) Be able to present data and apply simple and complex statistical methods, d) Be able to choose the appropriate statistical method depending on the nature of the data and acknowledge the need for further, more complex statistical analysis if required, e) Understand and interpret the results of statistical analysis reported in scientific publications. More specifically, at the end of the course students should possess the following knowledge, skills and abilities: A. Knowledge: a) Knowledge and understanding of basic mathematical concepts, b) Knowledge and understanding of algebraic equations, mathematical functions, differential equations, c) Knowledge and understanding of basic statistical concepts and principles of statistical inference, d) Knowledge and understanding of parametric and non-parametric statistical tests, e) Knowledge and understanding of statistical models, f) Knowledge and understanding of assessment methods of laboratory findings. B. Skills: a) Skills in solving algebraic problems in working life, b) Skills in solving differential and differential equation systems using appropriate software, c) Skills in statistical data management (SPSS), d) Skills in description / presentation of data, e) Skills in statistical analysis of biomedical data, f) Skills in the use of the SPSS statistical package to describe and analyze biomedical data, g) Skills in assessing the accuracy of laboratory findings. C. Abilities: a) Ability of mathematical modeling of biological problems, b) Ability to produce biomedical data presentation reports, c) Ability to select appropriate statistical methods for biomedical analysis, d) Ability to benchmark laboratory findings, e) Ability to understand and critically evaluate statistical methods and their application to published papers. Lectures: Mathematical background: Basic mathematical concepts: Logarithms, Powers, Sequences and Polynomials through simple biological problems. (2 hrs) - Algebraic equations: Categories, Solving Methods, Algebraic Equation Systems, Linear equations and operations between tables. (2 hrs) - Functions of one or more variables: Representation of functions, Limits, Derivatives, Integrals. Basic biological functions (2 hrs) - Multiple Equations of one or more variables: Basic concepts, Linear and homogeneous differential, Methodology for solving simple differential equations, Differential changes in biology. (2 hrs) Biostatistics: Introduction to probability theory (2 hrs) - Basic distributions (Normal, Binomial, Poisson) (2 hrs) - Descriptive Statistics: Quantitative - qualitative variables; Frequency distribution – Plots (2 hrs) - Descriptive Statistics: Central tendency and dispersion measures for quantitative variables; Transformations;Normal limits (2 hrs) - Hypothesis testing; Type I and II errors (2 hrs) - Sample size and power; Confidence Intervals (2 hrs) - t-test for two independent or dependent (pairwise) samples; random errors (2 hrs) - Chi-square tests for association of qualitative variables;Chi-square tests for heterogeneity (2 hrs) - Chi-square tests for paired observations; Goodness-of-fit chi-square tests (2 hrs) - Two-way tables and comparison of proportions; Stratification and Mantel-Haenszel Chi-square test (2 hrs) - Ordinal variables and non-parametric tests (Advantages - disadvantages, Sign test, Wilcoxon test for paired and independent observations, Kruskal-Wallis test, Spearman correlation coefficient) (2 hrs) - Analysis of Variance (2 hrs) - Multiple comparisons (2 hrs) - Parametric correlation coefficient (2 hrs) - Simple linear regression (2 hrs) - Multiple linear regression (3hrs) - Logistic regression (3hrs) - Evaluation of laboratory findings (2 hrs) - Bayes theorem and applications (2 hrs) - Revision and exercises (2 hrs) - Questions and answers (2 hrs) Practicals: 1. Solving algebraic biological problems in worksheets - Computer graphics - Graphical representation of experimental results (2hrs) – 2. Solving differential equations and differential equation systems with available software packages (2hrs) – 3. Methods of mathematical modeling of biological problems: population models and models of cell growth in number and size (2hrs) – 4. Models of intracellular materials and energy flows (2hrs) – 5. Models of enzyme kinetics (2hrs) – 6. Epidemiological models, discrete time models (2hrs) – 7. Introduction to SPSS: import and data management, data description via SPSS (2hrs) – 8. Statistical analysis of data using SPSS: comparison of means, comparison of qualitative data, non-parametric tests, correlation, multivariable models (10 hrs) – 9. Revision/Questions and answers (2 hrs) Instructors: Lectures: G. Touloumi, Professor of Biostatistics (Coordinator) - D. Hatzinikolaou, Associate Professor of Microbial Biotechnology - V. Sypsa, Assistant Professor of Biostatistics - E. Samoli, Assistant Professor of Biostatistics - N. Pantazis, Laboratory Teaching Staff Practicals: D. Hatzinikolaou, Associate Professor of Microbial Biotechnology (Coordinator) - N. Pantazis, Laboratory Teaching Staff Notes: The evaluation process is through a written exam in Greek (there is the possibility for examinations in English for Erasmus students), covering the contents of the course that specifically includes: Written Examination with Extended Response Questions. The assessment criteria for the course are described in the e-Class webpage: https://eclass.uoa.gr/courses/BIOL304 Contact: If you require more information, please contact the Course Coordinator, Prof. G. Touloumi at: Tel. +30 210 746 2089; email: gtouloum[at]med.uoa[dot]gr or the Practicals’ Coordinator, Assoc. Prof. D. Hatzinikolaou, at Tel. 30 210 727 4140; email: dhatzinibiol.uoa.gr