M7987 Survival analysis I

Faculty of Science
Autumn 2020
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Taught online.
Teacher(s)
doc. PaedDr. RNDr. Stanislav Katina, Ph.D. (lecturer)
Mgr. Markéta Janošová (seminar tutor)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics - Departments - Faculty of Science
Contact Person: doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science
Timetable
Mon 10:00–11:50 M6,01011
  • Timetable of Seminar Groups:
M7987/01: Thu 14:00–15:50 MP1,01014, M. Janošová
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The main goal of the course is to become familiar with some basic nonparametric, semiparametric and parametric probabilistic and statistical models in survival analysis with applications in medicine and life insurance of one and more lives, and multi-state models; to highlight the relationship with survival analysis; to implement these techniques into R language and to be able to apply them to real data.
Learning outcomes
Student will be able:
- to understand principles of likelihood and statistical inference for (un)censored life-time data;
- to select suitable probabilistic and statistical model in statistical inference for (un)censored life-time data;
- to build up and explain suitable simulation study for selected statistical test or confidence for (un)censored life-time data;
- to build up and explain suitable statistical test for (un)censored life-time data;
- to apply statistical inference on real for (un)censored life-time data (life, health and pension insurance of one and two lives);
- to implement methods of statistical inference for (un)censored life-time data in R.
Syllabus
  • Survival characteristics and their actuarial notation — distribution function, survival function, density, risk function, expected value and variance of survival time, mean residual life.
  • Selected models of probability distributions from the generalized gamma family and related distributions — exponential distribution, extreme value distribution, Weibull distribution, log-logistic and lognormal distribution, gamma and generalized gamma distribution.
  • Likelihood functions, point and interval estimates of parameters of selected distributions, statistical inference for uncensored and censored data, goodness of fit tests, selection of appropriate distribution, testing of statistical hypotheses by Wald principle, likelihood ratio and score principle.
  • Parametric regression models in survival analysis for uncensored and censored data (one, two, and multiple samples).
  • Gompertz, Makeham, and generalized Gompertz-Makeham distribution. Mortality tables. Life insurance for one or more lives, present value, mean value, second moment and variance of the present value of life insurance of one and two lives. Implementation of methods in   R and application to real data.
Literature
  • DICKSON, D. C. M., Mary HARDY and H. R. WATERS. Actuarial mathematics for life contingent risks. 2nd ed. Cambridge: Cambridge University Press, 2013. xxi, 597. ISBN 9781107044074. info
  • BOWERS, Newton L. Actuarial mathematics. 2nd ed. Schaumburg, Ill.: Society of Actuaries, 1997. xxvi, 753. ISBN 0938959468. info
  • GERBER, Hans U. Life insurance mathematics. Edited by Samuel H. Cox. 3rd ed. Zurich: Springer, 1997. xvii, 217. ISBN 354062242X. info
Teaching methods
Lectures 2 hours per week.
Practicals 2 hours per week.
On-line using MS Teams or full-time according to the according to the development of the epidemiological situation and the applicable restrictions.
Assessment methods
Homework, oral exam. The conditions may be specified according to the development of the epidemiological situation and the applicable restrictions.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
Teacher's information
The lectures are usually in Czech or in English as needed, and the relevant terminology is always given with English equivalents.

The target skills of the study include the ability to use the English language passively and actively in their own expertise and also in potential areas of application of mathematics.

Assessment in all cases may be in Czech and English, at the student's choice.

The lectures will take place online at MS Teams at the time of the normal lectures according to the schedule. Due to the possible low signal quality, I recommend students not to use the camera. Questions during the lecture will not be possible to ask by voice, but by chat.

The recording from the lecture will be uploaded in the IS sequentially and not in advance, so the recording will be uploaded only after the given lecture and before the next lecture. The recordnig does not have to contain a complete lecture, it is up to a teacher what to share from the record and share it with the students. What is a lecture recording? It can be a PDF of text written by the lecturer on the screen with an electronic pen during the lecture, and this can be supplemented by the voice (or voice and video) of the lecturer. Slides in PDF with TeX-ed text will always be available in the IS and will be shared only after the given lecture and before the next lecture.

Consultations about the lectures will take place through a discussion forum, where the lecturer / instructor moderates this discussion and new discussion forums established by students will not be taken into account. Discussion forums will be based on individual lectures and practicals (if the course has practicals) and about homework. Discussions by e-mail will not take place.

The course is also listed under the following terms Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.
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