Advanced topics of the field (NMSA602)

Arnošt Komárek

• Domácí
• Výuka
•  
• BESEDA
• NMST552
•  
• NMSA407
• NMST431
• NMSA602
•  
• NMST432
• NMST440
•  
• Rko
•  
• Diploma theses (CZ)
• Bachelor theses (CZ)

Advanced topics of the field (NMSA602)

Winter semester 2020–21

TOPIC: Analysis of Interval-Censored Data

Language of the lecture is English if and only if there is at least one officially subscribed student who is not enrolled in the Czech study programme.

TIMETABLE

COVID TEACHING

Until standard teaching at MFF UK is allowed by COVID regulations (given incredible inability of a group of people who call themselves as "Government of the Czech Republic" to govern the country, probability of such an event to happen during this winter term is 0.000000000000000000001), distant and mostly fully on-line teaching will be conducted using materials being distributed via e-mail. The on-line teaching will be conducted using the ZOOM platform mostly on Wednesday from 12:30. Each lecture will be recorded and published on stream.cuni.cz (access to the recording will require the SIS login).

OVERVIEW

We deal with interval censoring in situations where a continuous quantity can only be observed in a form of an interval. Standard rounding is a trivial case where, however, interval censoring can usually be ignored. In particular if the rounding is not too coarse. A typical situation leading to interval censoring, which usually can no longer be ignored, is a situation where we want to observe a time to certain event but to determine whether the event occurred, certain examination (laboratory analysis, ...) is necessary. Occasions of such examinations are discrete and it is then only known that the event lies in an interval between two "visits". Despite the fact that a number of methods have been developed for statistical analysis of interval-censored data (especially since the 1990s in connection with HIV / AIDS research), the interval nature of data is often erroneously ignored with subsequent invalid analysis results. We encounter interval-censored data not only in clinical research (and biostatistics), but also in financial and insurance applications. The quantity of primary interest does not always have to be only "time to event".

More common right-censored can be viewed as a special case of interval censoring (where the upper limit of the interval is equal to infinity) and it is therefore no coincidence that a large part of the methods for analyzis of interval-censored data is based on methods for right-censored data. Unfortunately, in the case of interval censoring, theory of counting processes and martingales cannot be used in most theoretical derivations. A significant part of the methods for interval-censored data is then based on the Bayesian approach using MCMC-based inference (or its alternatives).

CONTENT

• Interval censoring (principles), consequences if ignored;
• (Quick) overview of main results and methods for right-censored data;
• Nonparametric maximum-likelihood method (generalization of Kaplan-Meier estimator) to estimate a distribution function;
• Nonparametric two- and K-sample tests (generalizations of the logrank test;
• Regression models (proportional hazards model – PH, accelerated failure time model – AFT): selected frequentist approaches;
• Selected regression models for more complex data structures (dependent observations, double interval-censoring, ...): bayesian approaches.

The lecture will put an emphasis on explanation of main principles of covered methods. The aim is to allow for ability to use those methods with understanding and to apply them at a practical data analyzis. The R software and its selected packages will be exploited as primary software for practical data analyzis.

ENTRY REQUIREMENTS (on top of usual background in probability and statistics)

• Methods for right-censored data (into an extent as covered by the course NMST531: Censored Data Analysis);
• Principles of Bayesian statistics and MCMC methods (into an extent as covered by the course NMST431: Bayesian Methods);
• Linear mixed model (into an extent as covered by the course NMST432: Advanced Regression Models).

LITERATURE