Competing Risks
A brief non-technical summary of the cand. scient. thesis
and some of the applied methods' applications
The thesis compares estimators for transitions in a competing risks model by using
Monte Carlo simulation. Monte Carlo simulation is a standard tool in many areas of
quantitative analysis. For information on some of its applications to nance confer the
overview-section of the Wikipedia article Monte Carlo methods in nance.
The competing risks model considers the probability of transition from a state (also
called event) to one out of many other states (events) among the subjects (which often
are persons, but may be companies or other entities). A competing risks model consists
of three or more states generalizing the survival analysis model which consists of two
states only. The states of a competing risks model are said to compete since the
possible transitions are said to compete. By the methodology presented in the thesis,
we may model how the probability of a transition depends on dierent variables (often
called risk factors, explanatory variables, drivers or characteristics) and do analysis (for
example hypothesis testing) on the variables' inuence on the transitions.
The model and its corresponding methodology presented and applied in the thesis have
many applications
in nance, banking, insurance and medicine. Consider
the following example of survival analysis. Banks want to measure the probability
1,2
of borrowers defaulting
. The borrowers may be in one of two states Non-default
and Default, and the probability of default is the probability of the transition Non-
default →Default. Examples of risk factors are age, sex, marital status, income and
type of loan. Additional applications include the following. In life insurance, it is used
to model the time to death among members of pension schemes. It is used in modeling time to accident (incident) in non-life insurance. The method is used in modeling
costumer time to churn.
Chapter 1 of the thesis gives a non-technical introduction. Basic concepts of survival
analysis are introduced in Chapter 2, one of these being Cox regression. Cox regression
(also called the proportional hazards model) is a widely used method for analyzing
time to event data (survival analysis or competing risks). If no transition from an
event (state) to another event (state) has occurred, the method uses that information
too. The topics of Chapters 3 and 4 are more advanced methods and extensions of the
concepts in Chapter 2. This allows data analysis on several more practical situations.
The concepts are
illustrated by data analysis on a real dataset
on time to lung
cancer. Chapter 5 describes the Monte Carlo simulation setup by which the estimators
of risk are compared. The precision of the estimators are shown in plots and tables.
We nd and describe some situations where the risk-estimators' precision deviates
considerably. Chapter 6 summarizes our ndings and some related tables are shown in
Appendix A.
A lot of programming
(done using R) is required for all parts of the
thesis. Appendix B shows the R-code for Chapter 5.
1 Confer the Wikipedia article on credit risk.
2 Confer http://www.idescat.cat/sort/sort331/33.1.1.cao-etal.pdf