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CLINICAL TRIALS

Organisation and Planning: Protocol, patient selection, response Justification of  method for randomisation: Uncontrolled trials, blind trials, Placebo’s, ethical issues. The size of a clinical trial: Maintaining trials progress: Forms and data management, protocol deviations. Methods of data analysis: Binary responses, cross-over trials, survival data prognostic factors. Testing Hypothesis, Statistical Models: Inferential statistics-creating statistical hypothesis, the Z-test; designing a single variable experiment; errors in statistical decision making.  Power of test used in clinical trials/maximizing tests power. Significance testing:  t-test. Conducting two-way experiments and trials. Interpreting  overall results of Clinical Trials. Nonparametric Procedures/Tests & Ranked Data: , Mann-Whitney U test, Kruskal-Willis, Friedman.

 

 

Course Code: 
STA 809
No. of Credits: 
3
Level: 
Level 800
Course Semester: 
First Semester
Pre-requisite: 
STA 303
Select Programme(s): 
Statistics

TIME SERIES ANALYSIS

Stationary and non-stationary series: removal of trend and seasonality by differencing. Moments and auto-correlation. Models: simple AR and MA models (mainly AR(1), MA(1)): moments and auto-correlations; the conditions of stationarity: invertibility. Mixed (ARMA) models, and the AR representation of MA and ARMA models. Yule-Walker equations and partial auto-correlations (showing forms for simple AR, MA models). Examples showing simulated series from such processes, and sample auto-correlations and partial auto-correlations.  (Other models, e.g., trend and seasonal). Model identification: Elementary ideas of identification of models based on simple acf and pacf showing difficulties with real series. Estimation of parameter: initial estimate based on sample acf and pacf only (least squares estimates by iterative method). Result for standard error of sample acf, pacf and estimators. Forecasting: use of the AR representation for forecasting. Minimum mean square error forecasts. Updating.

 

Course Code: 
STA 815
No. of Credits: 
3
Level: 
Level 800
Course Semester: 
First Semester
Pre-requisite: 
STA 406
Select Programme(s): 
Statistics

ADVANCED TOPICS IN OPERATIONS RESEARCH

Formulating Linear Programming Models:  Goal programming, Transportation problem, Case study.  Mathematical Programming: Project planning and control, Dynamic programming,

Integer programming.  Probabilistic Models: Application of queuing theory, Forecasting and simulation, Decision analysis (making hard decisions), Multi-criteria decision making.

 

Course Code: 
STA 807
No. of Credits: 
3
Level: 
Level 800
Course Semester: 
First Semester
Pre-requisite: 
MAT409
Select Programme(s): 
Statistics

MULTIVARIATE METHODS

Multivariate data summary and graphical displays. Multivariate normal distributions: Estimation of mean and covariance, one- and two-sample problems, analysis of variance.

Reduction of dimensionality: principal components and factor analyses. Discrimination and classification. Correlation; partial, multiple and canonical. Non-metric problems: clustering and scaling.

 

 

Course Code: 
STA 806
No. of Credits: 
3
Level: 
Level 800
Course Semester: 
Second Semester
Pre-requisite: 
STA 405
Select Programme(s): 
Statistics

STATISTICAL INFERENCE AND BAYESIAN METHODS

Criteria of choice, and optimality consideration, in respect of point estimation, hypothesis tests and confidence intervals.  Likelihood methods with special consideration of maximum likelihood estimates (m.l.e.) and likelihood ratio tests including multiparameter problems (and linearisation methods).  Specific techniques will include:  Hypothesis Testing:

Pure significance tests, simulation tests, Neyman Pearson Lemma, UMP test.  Point Estimations: Efficiency, consistency, minimum variance bound estimators.  Determination of m.l.e’s including linearisation and asymptotic properties, maximum likelihood ratio tests and large-sample equivalents, asymptotic           optimality. Score tests.  Jackknifing, bootstrapping. Prior distributions: Representation of prior information via a prior distribution, substantial information, vague priors and ignorance, empirical Bayes ideas. Normal Models: Theory for  unknown), prior-posterior-predictive, normal regression model. Comparisons: Comparisons of classical, Bayesian, decision-theory approaches and conclusions via specific examples.

 

 

Course Code: 
STA 805
No. of Credits: 
3
Level: 
Level 800
Course Semester: 
First Semester
Pre-requisite: 
STA 402
Select Programme(s): 
Statistics

SAMPLING TECHNIQUES AND SURVEY METHODS

The necessity and practical use of sample surveys: sample versus census, presentation and organisation of a survey. Methods of sampling. Simple random samples: techniques, estimation, choice of sample size. Ratio and regression estimators. Stratified random sampling: criteria for good stratification before or after sampling. Quota sampling.  One-stage and two-stage cluster sampling. Systematic sampling. Comparison and choice of estimators. Estimation of treatment contrasts and their precision. 

Course Code: 
STA 804
No. of Credits: 
3
Level: 
Level 800
Course Semester: 
Second Semester
Pre-requisite: 
STA 302
Select Programme(s): 
Statistics

ADVANCED STATISTICAL METHODS

Exploratory Data Analysis: Data display, histograms, stem-and-leaf plots, box plots, data summary and   description. Elementary Methods: Single-and two-sample problems, standard normal-theory tests and estimators,       departures from assumptions, Poisson, Binomial and multinomial models, dispersion tests, goodness-of-fit, two-way contingency table. Regression Methods: Linear, multi-linear and polynomial regression, estimation of parameters, examination of residual, model checking.  Analysis of variance: One- and two-way analyses of variance. Examination of residuals. Unbalanced case.

Course Code: 
STA 803
No. of Credits: 
3
Level: 
Level 800
Course Semester: 
First Semester
Pre-requisite: 
STA 403
Select Programme(s): 
Statistics

PROBABILITY AND STOCHASTIC PROCESSES

Random point processes in time and space: Poisson process, inhomogeneous, compound and spatial generalizations. Review of transient and stability of random phenomena: the use of discrete time renewal theory, including the renewal theorem (without proof) with examples. Population models: discrete branching process, birth-and-death process, simple queuing models. Discrete time Markov chain: transition probabilities, classification of stages, equilibrium and absorption probabilities.

Course Code: 
STA 802
No. of Credits: 
3
Level: 
Level 800
Course Semester: 
Second Semester
Pre-requisite: 
STA 404
Select Programme(s): 
Statistics

DATA ANALYSIS

In this course the student will be cast in the role of a practicing statistician and become involved in projects within many fields of applications. Each of the selected projects has to be written in a report, some of which will be presented orally at seminars.  Some presentations may be done jointly with other students.  These are important aspects in the training of a practicing statistician, who must be able to present findings in a concise, but lucid manner, which can be, understood even by non-statisticians.  The reports are continuously assessed, each project being graded and returned quickly. Some of the projects are designed to illustrate basic statistical techniques from various courses and methods and to introduce the use of the statistical packages MINITAB, GLIM, PLUM, GENSTAT AND SPSS.  Others may be more open-ended or require more specialist techniques. The course opens with one or two non-assessed exercises designed to make the student familiar with the computing facilities. 

Course Code: 
STA 816
No. of Credits: 
3
Level: 
Level 800
Course Semester: 
Second Semester
Pre-requisite: 
STA 304 & STA 401
Select Programme(s): 
Statistics

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