Biometrics

Data

Official data in SubjectManager for the following academic year: 2024-2025

Topic

As a first course in statistics it covers the following main blocks: Basic data handling and computer use. Exploring data by graphical and numerical characterization. Basic concepts of probability and statistical inference. The basic methods for statistical inference most frequently used in medicine. These are the traditional goals in all first course in statistics – in all university level of educations.

The second (main) goal of this course (over on the previous ones) to focus on the power of statistical thinking; that is new to students and increasingly important at medical field - not only in the science but also in everyday work at the bedside. So not only as a scientific background but as parts of the everyday work are indispensable the skills and competences which can be laid down and improved by practicing statistics. Most importantly are such the analytical and critical thinking (or: on this field the statistical thinking). Based on this second goal we introduce students to the basics of Medical Decision Making. This is actually the third goal of our course. Because of those second and third goal our course is covering much more than a traditional first statistical class. This course is building also fundamental skills and competences for the daily medical work. An excellent example is the 2020-2021 COVID pandemic. It is attached a ‘COVID-special’ block to every class material now. We study and analyze the data of the pandemic - based on the two new course goals. It demonstrates the power of data analysis to our professional and private life decisions. COVID pandemic – is a real hot issue, isn’t it?

New improvement is the plenty online study material. Another improvement is: there are separated A-level blocks (first of all) for those students

- who are better prepared as to the knowledge and thinking skills (for studying statistics) and / or

- those students who are considering a potential research or university professor career in their future.

Lectures

• 1. Introduction (Statistics in medicine, the 3 main goals of the course, how to learn). Probability and relative frequency. - Pótó László
• 2. Variables, Discrete distributions (binomial and Poisson). - Pótó László
• 3. Continuous variables. Histogram, relative frequency density and probability density function. - Pótó László
• 4. Mean and standard deviation. The normal distribution. - Pótó László
• 5. Distribution of the sample mean, standard error. - Pótó László
• 6. Confidence interval for the expected value. The t distribution - Pótó László
• 7. Principle of hypothesis testing. The one sample and the paired samples t tests. The sign test (preview). - Pótó László
• 8. The confidence interval and the hypothesis testing. Type I and type II errors. MDM basics 1/1. - Pótó László
• 9. The independent samples t test. The F test. - Pótó László
• 10. Linear regression and correlation. - Pótó László
• 11. Contingency tables 1. The chi-squared test. Medical tests. Sensitivity and specificity predictive values. (Contingency tables 2/1). MDM basics 1/2. - Pótó László
• 12. The non-parametric tests (sign test, Wilcoxon and Mann-Whitney tests). - Pótó László
• 13. The principle of the ANOVA. Summary of the hypothesis testing methods. - Pótó László
• 14. Medical tests. Sensitivity and specificity, predictive values. (Contingency tables 2/2). Multivariable methods. MDM basics 2. MDM basics 2. Summary. - Pótó László

Practices

• 1. Probability examples 1. Relative frequency and probability. - Pótó László
• 2. Probability examples 2 - discrete (Binomial and Poisson) distributions. - Pótó László
• 3. Exploring data by graphs. Continuous variables. Histogram. - Pótó László
• 4. Exploring data by numbers - descriptive statistics - Pótó László
• 5. Normal distribution. The distribution of the sample mean. - Pótó László
• 6. Estimations. The confidence interval of the expected value. - Pótó László
• 7. The hypothesis testing - the `five steps`. The one sample (and the paired samples) t tests. The sign test. - Pótó László
• 8. Estimation and hypothesis testing. The Type one and Type two errors. Basics of MDM - Part 1 - Pótó László
• 9. The independent samples t test. - Pótó László
• 10. The linear regression and correlation. - Pótó László
• 11. Contingency tables - the chi-squares test. Basics of MDM - Part 2 - Pótó László
• 12. Nonparametric tests (Sign test, Wilcoxon test, Mann-Whitney test) - Pótó László
• 13. Summary - Part 1: One variable methods - Pótó László
• 14. Summary - Part 2: Two (and more) variables. Integration of MDM basics - Pótó László

Seminars

Reading material

Obligatory literature

1, D.S. Moore: The Basic Practice of Statistics, 7th ed., 2015

Literature developed by the Department

Course material on the Moodle (continuously upgraded and copleted script, video, mp3, basic and advanced level exercises and solutions, ...)
Basic (B) and advanced (A) curriculum units are chosen separately. Level B material and requirements require a very limited weekly study time. Accordingly, however, their long-term usefulness and the skills (scope and level) that can be acquired are also highly limited. In contrast, level A represents a kind of elite training goal. This requires significantly more practice - but it brings significant long-term benefits to the students. Both in terms of their knowledge, skills and attitude. At the same time, the possibility to switch between the two levels is open throughout the course.

Notes

L. Pótó: Biometrics. Workbook for the Practices, Pécs, 2020

Recommended literature

2, D.S. Moore, G.P. McCabe: Introduction to the Practice of Statistics, 5th ed., W.H. Freeman 2005

or:

D. Yates, D.S. Moore, D.S. Starnes: The Practice of Statistics (TI-83/89 Graphing Calculator Enhanced) 2/e, 2003, W.H. Freeman

or

3, W.G. Rees: Essential Statistics, Chapman and Hall, 1992

Conditions for acceptance of the semester

As an optional subject, the exam materials are connected to an optional and non-mandatory exam for the purpose of 'self-test'. Active participation is enough to complete the course. Those who want to check their knowledge and skill development achieved through the course can do so in an optional exam.

Mid-term exams

At least two tests can be completed during the semester, but the same is true for this as for the exam. It is optional, not a condition for completing the subject.

Making up for missed classes

Extra class

Exam topics/questions

On the optional semester exam: A written entry test, one data analysis problem solved by the SPSS and two theory questions from the below list. One of them is out of the MDM questions.

1. The main goals / potential results of learning biometrics/biostatistics

Why should we introduce a ‘new’ way of thinking when working in medicine? What is Statistics (as a field of science) in this context? The main points to learn in a first course of statistics.

Why is this a ‘skill-oriented’ course? What should we develop and how to do it? Give some examples of this 2nd goal (analytical / statistical thinking) from the course, please.

How did we use all these for the 3rd goal (basics of MDM) – explain a few points to this using some examples, please!

What is your own conclusion then: Why was it worth to learn statistics for you – in 2-3 sentences?

(Mainly from the lectures 1, 3, and 6-7-8 and 11-14.)

2. The key feature of the statistical thinking - the probability

Show this term - use a simple example, please. When can it be (and when cannot be) calculated? The relative frequency and probability: How did we proved that the probability can be ‘measured’ (estimated) by the relative frequency? Illustrate how both ways can be used in practical medical situations - by some examples.

(Mainly from the lectures 1, 2, 6-7-8 and 12)

3. The idea of the probability distribution - discrete distributions - 1,

Demonstrate on the example of the binomial distribution how the probability calculations (games of chances case) can be used in real life situations. How can you illustrate a distribution (graphically). Trace its role on the decision making.

(Mainly from the lectures 2, 6-7-8 and 12)

4. The idea of the probability distribution - discrete distributions - 2,

Contrast the binomial and the Poisson distributions: similarities and differences - demonstrated by some examples. Show the importance of discrete distributions trough examples. (Which hypothesis testing methods are based on this approximation?)

(Mainly from the lectures 2, 6-7-8 and 12)

5. The basic principles of statistical thinking - from the data to the decision

The way to the decision - and some pitfalls. (Size of the sample, representativity, lurking variables, probability decision, risk of errors, - and handling them)

(Mainly from the lectures 3 and 6-7-8)

6. Types of the data (variables) and displaying them with graphs

The three most frequent types of data and the methods for summarizing and displaying them.

Applications of some diagrams - strength and weaknesses. What specific info can be observed from a given type of graph? When to choose a given type?

(Mainly from the lecture 3 and 10)

7. The population and the sample

Explain both terms in case of some different types of data. How to characterize (by pictures or numbers) the sample and the population in these examples? Discuss the basic role of both terms in the statistical inference and decision making, please.

(Mainly from the lectures 2, 3, 6-7-8 and 12)

8. Numerical description of continuous data

Contrast the ‘five number’ and ‘three number’ descriptions. When to use one and when the other?

Prove and demonstrate by examples the basic role of the two description while selecting the appropriate decision making (or hypothesis testing) method.

(Mainly from the lectures 4, 6-7-8 and 12)

9. The idea of the probability distribution - continuous distributions

Symmetrical and skewed distributions. How the measures of the sample show (mirror) the shape of the distribution? Demonstrate them on the example of the normal and some skewed distributions. Prove the importance of distinction between them (think to the condition of the decision making methods).

(Mainly from the lectures 4, 6-7-8 and 12)

10. The normal distribution 1

Features. Why is it so frequently used in biology and medicine?

Application examples (reference range, ...).

How does the ?normal approximation? method demonstrate its importance (application examples) ... and how does the conditions of the hypothesis testing methods?

(Mainly from the lectures 4, 5, 6-7-8 and 12)

11. The normal distribution 2

How the ‘distribution of the mean’ shows its importance? Verify the basic role of the ‘distribution of the mean’ while statistical inference and decision making.

(Mainly from the lectures 4, 5, 6-7-8-9-10)

12. Statistical inference

The statistical inference is the main goal (final step) of the statistical thinking. Contrast the point- and the interval estimation from this point of view. Trace both methods (and the use of them) on the example of the confidence interval for the expected value (the p% CI of the expected value).

(Mainly from the lectures 5 and 6)

13. The confidence interval of the population mean

You can find the ?95% CI? on most of the SPSS output (that you learned). What is that and why can you meet it so frequently at statistical analysis? Give examples of results screens (methods): why is it included in the given method - what is the use of it there?

(Mainly from the lectures 5 and 6 - and all the lectures from then)

14. The basic idea of hypothesis testing

Prove the relevance of the ?five steps? method - and demonstrate it on everyday and medical examples. What are the simple given steps of the ?five? and those that are require personal evaluation from case to case? Discuss these later ones on examples.

(Mainly from the lectures 7 - and all the lectures from then)

15. The one sample and the paired t test

At what kind of data (-structure) should you use this method? When hypothesis testing? Relate the two methods to each other. What can be done when the application conditions do not fit? Why not use these later methods at all the situations than?

(Mainly from the lectures 6-7-8-9 and 12)

16. The confidence interval and the hypothesis testing

Contrast the two methods: similarities and differences - strength and weaknesses.

Demonstrate your evaluation on examples.

(Mainly from the lectures 6-7-8)

17. The risk of errors and the power of a test

Discuss the essential feature of the statistical decisions the risk of errors. How can you handle these risks? When should you handle these risks?

Explain on examples: when can you use the value of the risk of a certain error and when to use the power of the test? (Which questions call for this kind of answers?)

(Mainly from the lectures 8 and 9)

18. The two (independent) samples t test

Contrast the paired and independent samples t tests? What are the typical questions which call for the later method? What is the specific requirement (condition) of this method - and how can you handle this with the help of the F test?

(What should we pay for that solution? Why not to use always the solution which has less requirements?)

(Mainly from the lecture 9)

19. Connection between two variables - continuous variables

Contrast the one variable - two samples and the two variables - paired data (one sample) cases. What are the typical questions in the two cases?

Use examples to explain the method of the linear regression and correlation analysis. Stress the steps where there is an obvious role of statistical thinking.

Is this method a hypothesis test?

(Mainly from the lecture 10)

20. Connection between two variables - categorical variables

Relate to each other the two variables methods for continuous and categorical variables - similarities and differences. Which numbers are to be evaluated in the later case?

Which hypothesis testing method(s) are available for that? Explain the five steps on an example. What are the conditions for applying the method(s) and what to do when those conditions are not valid?

(Mainly from the lectures 11 and 12)

21. Evaluation of frequency data - 1.

Why the chi-squares test is not applicable in the medical practice frequently? What to do then? When to use the Fisher’s exact test - out of those cases? What the exact word means in the name?

(Mainly from the lectures 11 and 12)

22. Evaluation of frequency data - 2.

How to qualify a diagnostic test? Which questions can be answered by the sensitivity, specificity and the predictive value(s) of the test? The special features / problems of the predictive values.

The confidence interval for the proportion. Explain (using the previous term) why the chi-squares test gives ?not significant? result at evaluations of medical data frequently.

(Mainly from the lectures 11 and 12)

23. Nonparametric tests - 1.

When to refuse the application of a t test - and when to apply the sign test instead? Demonstrate the ‘five steps’ on an example using the sign test. Contrast this method and the appropriate parametric one? What are the strength and weaknesses of this method?

(Mainly from the lectures 2, 7 and 12)

24. Nonparametric tests - 2.

When to refuse the application of a t test - and when to apply the Wicoxon and the Mann-Whitney test instead? Demonstrate the application of both tests on examples. Contrast these methods and the appropriate parametric ones? What are the strength and weaknesses of these methods?

(Mainly from the lectures 2, 9 and 12)

25. The principle of the ANOVA

Demonstrate the application of the ANOVA method on an example

What is the basic idea of the evaluation? Illustrate it on the case of comparing several group means simultaneously.

What is the strength of this method in contrast to the several t tests for pairs of groups?

(Mainly from the lectures 2, 8, 9 and 13)

MDM-1 Medical Decision Making - basic principles 1

Demonstrate please the application of statistical decision making terms and principles (Ho, Type-1 and 2 error risks, change the alpha decision borderline, the evaluation of medical test results and symptoms; the 4 measures especially the issues of the positive and negative test predictive values in different test situations: at the clinic or screening tests, ...) to a simple medical or any everyday life decision making situation.

Use your calculation exam problem or select your own problem for demonstration.

(Mainly from the lecture 8 and 11-12.)

MDM-2 Medical Decision Making - basic principles 2

Demonstrate please the application of statistical decision making terms and principles (validities of examination results, clinical evidences, probabilities, treatment borderline, further examination options ...) to a simple medical decision making situation.

Use your calculation exam problem or select your own problem for demonstration.

(Mainly from the lectures 11-12 and 14)

Examiners

Instructor / tutor of practices and seminars

• Pótó László