Introduction of the course.
Statistical analysis and comparisons of events
evolved with time are central to biomedical research,
and they are subjects of intensive investigations
Their underlying stochastic models involve
of events and
of cases at risk,
their hazard functions
and ultimately the construction
A remarkably successful idea of
unifies various statistics
developed for many different statistical methods
in survival analysis.
In this short course
we discuss foundations and properties
of general counting processes and martingale framework.
Then we survey survival analysis in the context of biostatistics,
and examine the application of martingale framework
for longitudinal data,
including Kaplan-Meier estimate for survival functions
and linear rank statistics for comparison of longitudinal data.
I taught this subject as a part of graduate course,
aiming mostly at engineering graduate students
who are not necessarily knowledgeable in the area of
probability theory and statistics.
Lecture is problem-oriented, and our goal is to complete
all the problems presented in the class.
- Stochastic models and their distributions.
(last revised on June 22, 2016).
- Poisson processes and their properties.
- Filtration and martingale in stochastic processes.
- Censorship model for longitudinal data.
- Comparison of two groups in survival analysis: Linear rank statistics.
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