MTech Numerical Methods And Biostatistics syllabus for 1 Sem 2020 scheme 20BBI11

Introduction to statistics and study design:

Introduction to statistics, data, variables, types of data, tabular, graphical and pictorial representation of data. Significance of statistics to biological problems, experimental studies; randomized controlled studies, historically controlled studies, cross over, factorial design, cluster design, randomized; complete, block, stratified design, biases, analysis and interpretation.

Design:

Descriptive statistics and Observational study design: Types of variables, measure of spread, logarithmic transformations, multivariate data. Basics of study design, cohort studies, casecontrol studies, outcomes, odd ratio and relative risks. Principles of statistical inference: Parameter estimation, hypothesis testing. Statistical inference on categorical variables; categorical data, binomial distribution, normal distribution, sample size estimation

Comparison of means:

Test statistics; t-test, F distribution, independent and dependent sample comparison, Wilcoxon Signed Rank Test, Wilcoxon-Mann-Whitney Test, ANOVA. Correlation and simple linear regression: Introduction, Karl Pearson correlation coefficient Spearman Rank correlation coefficient, simple linear regression, regression model fit, inferences from the regression model, ANOVA tables for regression. Multiple linear regression and linear models: Introduction, Multiple linear regression model, ANOVA table for multiple linear regression model, assessing model fit, polynomials and interactions. One-way and Two-way ANOVA tables, F-test. Algorithm and implementation using numerical methods with case studies.

Design and analysis of experiments:

Random block design, multiple sources of variation, correlated data and random effects regression, model fitting. Completely randomized design, stratified design. Biological study designs. Optimization strategies with case studies

Statistics in microarray, genome mapping and bioinformatics:

Types of microarray, objectives of the study, experimental designs for micro array studies, microarray analysis, interpretation, validation and microarray informatics. Genome mapping, discrete sequence matching, programs for mapping sequences with case studies.

Course outcomes:

At the end of the course the student will be able to:

• Demonstrate strong basics in statistics and numerical analysis
• Apply the mathematical principles to solve problems in spheres of bioscience and bioengineering
• Study and design various statistical problems

Question paper pattern:

The SEE question paper will be set for 100 marks and the marks scored will be proportionately reduced to 60.

• The question paper will have ten full questions carrying equal marks.
• Each full question is for 20 marks.
• There will be two full questions (with a maximum of four sub questions) from each module.
• Each full question will have sub question covering all the topics under a module.
• The students will have to answer five full questions, selecting one full question from each module.

Textbook/ Textbooks

1 Biostatistics Alvin E. Lewis McGraw-Hill Professional Publishing 2013

2 Statistics and Numerical Methods in BASIC for Biologists D. Lee and T.D. Lee Van Nostrand Reinhold Company 1982

Reference Books

1 Numerical Methods Wolfgang Boehm and Hartmut Prautzsch CRC Press 1993

2 Numerical Methods of Statistics John F. Monahan Cambridge University Press 2011

3 Numerical Methods for Engineers and Scientists Joe D. Hoffman CRC Press 2001

4 Statistical Methods in Bioinformatics: An Introduction Warren J. Ewens Gregory Grant Springer Science & Business Media 2005