**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:

- Design time to event data
- Model time to event data by the Non-parametric methods
- Test the effects of different interventions on the mean time to event
- Model time to event in relation to covariates
- 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**

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

- Teacher: Dr. Anthony Karanjah

**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:

- Identify a research problem and develop an appropriate research Proposal for their research.
- Evaluate relevant research articles in a particular subject area and develop an analytical literature review
- Evaluate the logical consistency of written material and outcome of a research project
- 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.

- Teacher: Dr. Anthony Karanjah

**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.

- Teacher: Dr. Wycliffe Cheruiyot

linear

- Teacher: Dr. Anthony Karanjah

Multivariate Methods and Analysis

- Teacher: Dr. Anthony Karanjah