Purpose

To equip students with statistical analysis techniques required for analysis of survival data from observational or experimental studies.

 

Expected Learning Outcomes

At the end of this unit, the students should be able to:

  1. Design time to event data
  2. Model time to event data by the Non-parametric methods
  3. Test the effects of different interventions on the mean time to event
  4. Model time to event in relation to covariates
  5. Analyze survival data using computer software

Course Description

Fundamentals of survival analysis; Survival data, censoring and truncation; Definition and properties of the survival function, hazard and integrated hazard; Inference procedures using likelihood for exponential, Weibull, extreme value distributions; Parametric and nonparametric estimation of survival function and hazard; Explanatory variables: accelerated life models, proportional hazards models, applications, model selection, special case of two groups; Fully parametric statistical models including Weibull and other distributions; Competing risks, time varying explanatory variables, exploratory analyses; Kaplan-Meier estimate of survival function; Model checking using residuals; Non-proportional hazards, sample size determination; Survival analysis: frailty, cure, relative survival, empirical likelihood, counting processes and multiple events; Introduction to multivariate survival models

Core Reading Materials

  1. Klein, J. P. & Moeschberger, M. L. (2013). Survival Analysis: Techniques for Censored and Truncated Data. (2nd Ed.). New York: Springer. ISBN: 978-0387953991
  2. Tableman, M. & Kim, J. S. (2003). Survival Analysis using S: Analysis of Time-to-Event Data. (1st Ed.).  Florida: CRC Press. ISBN: 978-1584884088
  3. Lee, E.T. & Wang, J.W. (2013). Statistical Methods for Survival Data Analysis. (4th Ed.). New Jersey: Wiley Publishing. ISBN: 978-1118095027

Purpose

To enable the students to conduct independent academic research using essential research principles and write a research proposal.

 

Expected Learning Outcomes

At the end of this unit, the students should be able to:

  1. Identify a research problem and develop an appropriate research Proposal for their research.
  2. Evaluate relevant research articles in a particular subject area and develop an analytical literature review
  3. Evaluate the logical consistency of written material and outcome of a research project
  4. Design, defend and evaluate a research proposal for the master’s project.

Course Description

Elements of research: The research process, identification of a research problem, definition of a research gap, Research objectives and questions/ hypothesis, significance of research; Critical review of literature; Research Designs: Qualitative, Quantitative, Casual, Case studies; Designing a research proposal; Writing and presenting a thesis/project report, writing for academic publication; Research Ethics: Principles of academic honesty, accountability, professional courtesy, fairness, conflict of interest,  good stewardship in conduct, publication of research work.

Course Description

Introduction to probability spaces;The theory of measure and integration;Random variablesand limit theorems;Distribution functions, densities and characteristic functions; Convergence of random variables and their distributions; Uniform integrability and the Lebesgue convergence theorems; Weak and strong laws of large numbers, central limit theorem, conditional probabilities and Radon-Nikodym derivatives of measures; Strong and weak convergence of probability measures, measurability and observability.

Prob and Measure Theory Content.docxProb and Measure Theory Content.docx

Multivariate Methods and Analysis