Statistical analysis of replicated spatial point patterns.
The field of pathology provides us with many opportunities for collecting replicated
spatial data. Using an ordinary microscope, for example, we can digitise cell positions
within windows imposed on pieces of tissue. Suppose now that we have some such replicated
spatial data from several groups of individuals, where each point in each window
represents a cell position. We seek to determine whether the spatial arrangement of
cells differs between the groups. We propose and develop a new method which allows
us to answer such questions, and apply it to some spatial neuro-anatomical data.
We introduce point process theory, and extend the existing second order methods to deal
with replicated spatial data. We conclude the first part of the thesis by defining Sudden
Infant Death Syndrome (S.LD.S.) and Intra-Uterine Growth Retardation (LU.G.R.),
and stating why these conditions are neuro-anato,mically interesting.
We develop and validate a method for comparing groups of spatial data, which is motivated
by analysis of variance, and uses a Monte Carlo procedure to attach significance
to between-group differences. Having carried out our initial investigative work looking
exclusively at the one-way set up, we extend the new methods to cope with two and
higher way set ups, and again carry out some validation.
We turn our attention to practical issues which arise in the collection of spatial neuroanatomical
data. How, for example, should we collect the data to ensure the unbiasedness
of any inference we may draw from it? We introduce the field of stereology which
facilitates the unbiased sampling of tissue. We note a recent proposal to assess spatial
distribution of cells using a stereological approach, and compare it with an existing
second order method. We also note the level of structural heterogeneity within the
brain, and consider the best way to design a sampling protocol.
We conclude with a spatial analysis of cell position data, collected using our specified
design, from normal birth-weight non S.LD.S., normal birth-weight S.I.D.S and low
birth-weight S.LD.S cases.