School of Mathematics and Statistics (SoMaS)

MAS6012 Sampling, Design, Medical Statistics

This unit looks at the particular application area of Medical Statistics, and also considers efficient designs for the collection of data through samples, surveys and experiments. In Clinical Trials students meet some variants on mainstream theory designed to accommodate ethical constraints arising from experimenting on humans. Comparing survival patterns (of patients or industrial components) is often necessary and Survival Analysis introduces appropriate methods which handle censored data. Implementation of techniques in standard statistical packages forms an important aspect of the unit. Sampling Theory introduces methods for obtaining samples from finite populations and conducting surveys. The impact of using different experimental designs on the statistical properties of the results will also be studied. Some standard designs will be introduced, as well as the theory required to tailor-make designs that fully satisfy the requirements of the investigations where they would be used.

There are no prerequisites for this module.
No other modules have this module as a prerequisite.

Outline syllabus

• Semester 1: Medical Statistics
  • Clinical Trials
    • Basic concepts and designs:
      controlled and uncontrolled clinical trials; historical controls; protocol; placebo; randomisation; blind and double blind trials; ethical issues; protocol deviations.
    • Size of trials.
    • Multiplicity and meta-analysis:
      interim analyses; multi-centre trials; combining trials.
    • Cross-over trials.
    • Binary response data:
      logistic regression modelling; McNemar's test, relative risks, odds ratios.
  • Survival Data Analysis
    • Basic concepts:
      survivor function; hazard function; censoring.
    • Single sample methods:
      lifetables; Kaplan-Meier survival curve; parametric models.
    • Two sample methods:
      log-rank test; parametric comparisons.
    • Regression models:
      inclusion of covariates; Cox's proportional hazards model; parametric and accelerated failure time regression models.
• Semester 2: Sampling Theory and Design of Experiments
  • Sampling Theory
    • Basic concepts:
      The importance and practical use of sample surveys; comparison of sample and census.
    • Simple random sampling:
      estimation of a population mean and proportion; choice of sample size.
    • Stratified random sampling:
      estimation, criteria for good stratification, allocation of sample strata sizes, when to stratify.
    • Other sampling methods:
      Questionnaire design and survey methods, preparation and organisation of a survey.
  • Design of Experiments
    • Notation:
      Design region. Variation and blocking. Stages in experimental research. Randomisation.
    • Criteria for a good experiment:
      Optimality criteria.
    • General theory of block designs
    • Factorial designs:
      Estimability. Blocking. Confounding. Screening.
    • Response surface designs
      
    • Optimum Design theory:
      General Equivalence Theorem. Experiments with constraints. Design construction.
    • Statistical methods for computer experiments:
      Uncertainty and variance-based sensitivity analysis

Aims

• To introduce distinctive methodologies specifically related to sample surveys, design of physical and computer experiments, clinical trials and analysis of survival data, building on students' existing knowledge of simple sampling and linear modelling methods.
• To develop enough of the theory to allow a proper understanding of what these methods can achieve, while showing how and when these methods (sometimes in combination) are applied to data arising in practical contexts.
• To illustrate applications of statistics within the medical field.

Learning outcomes

• have some appreciation of the ethical constraints involved in experimentation on human subjects;
• understand aspects of the nature and design of clinical trials; and be able to offer advice on the design and size of clinical trials;
• have some expertise in the handling of binary response data through logistic modelling; and be able to construct lifetables and survival curves;
• be able to compare survival patterns between different treatments and between different risks; and be familiar with proportional hazard models;
• be familiar with computer implementation of the statistical techniques used in medical statistics; and be able to tackle an extended statistical analysis of a practical medical problem.
• recognise the possible pitfalls in published survey data; and understand the need for randomness and the desirability of stratification in sampling;
• understand the main stages in experimental research and know the desirable properties and the criteria of optimality of experimental designs;
• understand the main features of block designs, factorial and fractional factorial designs and know simple methods for their construction;
• understand the result of the General Equivalence Theorem and apply it to obtain optimal experimental designs;
• understand how to conduct an uncertainty and variance-based sensitivity analysis for a computer model output.

Teaching methods

Lectures, with a complete set of printed notes, plus task and exercise sheets. Some outside reading is also expected.

Assessment

Project (15%) on Medical Statistics, coursework (15%) on Design Sampling and a three-hour combined examination (70%).

Full syllabus

Clinical Trials

• Basic concepts and designs:
  controlled and uncontrolled clinical trials; historical controls; protocol; placebo; randomisation; blind and double blind trials; ethical issues; protocol deviations. (4 sessions)
• Size of trials:
  (1 session)
• Multiplicity and meta-analysis:
  interim analyses; multi-centre trials; combining trials. (2 sessions)
• Cross-over trials:
  (1 session)
• Binary response data:
  logistic regression modelling; McNemar's test, relative risks, odds ratios. (2 sessions)

• Basic concepts:
  survivor function; hazard function; censoring. (1 session)
• Single sample methods:
  lifetables; Kaplan-Meier survival curve; parametric models. (4 sessions)
• Two sample methods:
  log-rank test; parametric comparisons. (1 session)
• Regression models:
  inclusion of covariates; Cox's proportional hazards model; parametric and accelerated failure time regression models. (4 sessions)

• Basic concepts:
  The importance and practical use of sample surveys; comparison of sample and census. (1 session)
• Simple random sampling:
  estimation of a population mean and proportion; choice of sample size. (2 sessions)
• Stratified random sampling:
  estimation, criteria for good stratification, allocation of sample strata sizes, when to stratify. (2 sessions)
• Other sampling methods:
  Questionnaire design and survey methods, preparation and organisation of a survey (1 session)

• Notation:
  Design region. Variation and blocking. Stages in experimental research. Randomisation. (2 sessions)
• Criteria for a good experiment:
  Optimality criteria. (1 session)
• General theory of block designs:
  (3 sessions)
• Factorial designs:
  Estimability. Blocking. Confounding. Screening. (3 sessions)
• Statistical methods for computer experiments:
  (2 sessions)
• Optimum Design theory:
  General Equivalence Theorem. Experiments with constraints. Design construction. (3 sessions)

Reading list