On Portfolio Selection: Improved Covariance Matrix Estimation for Swedish
Handledare: Jan Holst
Centre for Mathematical Sciences
Lund Institute of Technology,
When treating cancer it can be considered important to estimate the growth
rate of the tumour. Of basic interest in this context is to estimate the
time for the DNA synthesis, i.e. the time it takes for the DNA in the nucleus
of the cell to duplicate, Ts.
Using a bromodeoxyuridine (BrdUrd)-DNA flowcytometry (FCM)-method it is possible
to measure the relative DNA content in the cell and separate the cells in
the DNA synthesis phase at time zero from the rest of the population. The
DNA distributions for these cells can then be followed through the cell cycle.
An established way to describe the movement through the DNA synthesis phase
is the relative movement curve (RM). When all BrdUrd-labelled DNA is replicated
the RM value should theoretically reach one and then remain there. Since
this is not normally the case in practice, the interpretation of Ts is the
time when the RM curve reaches its maximum and local polynomial kernel regression
is used to estimate the derivative of the curve.
A simple Markov model approach to the estimation of Ts is also suggested.
A state in the Markov model corresponds to an interval of DNA content. Divided
BrdUrd-labelled cells are moved back to the last state and an absorbing state
is created. The intensity matrix will contain the estimated rates of the
DNA replication and when an initial DNA distribution is estimated the time
to absorption and a distribution for that time are estimated. Ts will be
the estimated mean time to absorption.