Statistics for Biomedical Engineers

ABOUT THE COURSE: Biostatistics is a discipline that develops and applies methodology for quantitative studies in public health and biomedical research. The methodology learnt using this course will help students to design & analysis of health surveys, clinical trials, prevention trials, intervention studies, longitudinal studies, and laboratory studies. The objective of this course is to provide a comprehensive knowledge on these aspects to the Senior Undergraduate, M.Tech, MS and Ph.D. students, primarily to enhance their analysis and employability skills. The course will provide an introduction of Biostatistics, data representation and analysis. Also will provide Brief insight into probability theory and statistical inference methods. Students will learn various experimental design strategies and statistical methods that can be used to conduct research studies pertaining to health services.INTENDED AUDIENCE: Undergraduate Students, IIIrd/IVth Year students and Masters studentsPREREQUISITES: Preferably Masters/Senior Undergraduate students with engineering/mathematics backgroundINDUSTRY SUPPORT: This is a basic course and will serve as a pre-requeiste for AI/ML courses in medical domain and hence provides value for wider audience in the area of biomedical engineering

Week 1: Introduction to Biostatistics, applications of biostatistics, discussion of few use cases.
Week 2:Introduction to statistics, Need for statistics, Role of probability, Discussion of descriptive statistics
Week 3:Discussion of Mean, Median and mode, Introduction to probability theory, probability distributions, Expectations, Population variance, sample statistics, Inferential statistics
Week 4:Central limit theorem, Confidence intervals, Introduction to Hypothesis testing, Elements of Hypothesis testing, Large sample test, p-values
Week 5:Small sample test, T-distribution, Type I error, Type II error, Power of test, Chi-Square distribution, Hypothesis test using variance, Contingency test, Test of Independence, Probability plots
Week 6:Hypothesis test for two independent population, paired T test, F-distribution, Detailed discussion on ANOVA, Derivation of Mean Squared Treatment and Mean Squared Error in ANOVA, Sample problems
Week 7:Joint distribution, Covariance & Correlation between random variables, Simple Linear Regression, R-squared statistic, Confidence intervals for regression parameters, Multiple Linear Regression, Adjusted R-Squared statistic
Week 8:Logistic Regression, logit function, Derivation of log-likelihood function, Revisit ANOVA using linear regression, Derivation of ANOVA equations, Sample problems
Week 9:Introduction to Blocking, Randomized Complete Block Design, Latin square design, Sample Problems
Week 10:Graeco-Latin Square design, Introduction to factorial design, 22 factorial design, Discussion on interactions
Week 11:23 factorial design, Derivation of relevant equations, Sample problems
Week 12:2-Way ANOVA, Use cases, Derivations, Sample problems