Bayesian survival analysis.
In cancer research the efficacy of a new treatment is often assessed by means of
a clinical trial. In such trials the outcome measure of interest is usually time
to death from entry into the study. The time to intermediate events may also
be of interest, for example time to the spread of the disease to other organs
(metastases). Thus, cancer clinical trials can be seen to generate multi-state
data, in which patients may be in anyone of a finite number of states at a
The classical analysis of data from cancer clinical trials uses a survival regression
model. This type of model allows for the fact that patients in the
trial will have been observed for different lengths of time and for some patients
the time to the event of interest will not be observed (censored). The regression
structure means that a measure of treatment effect can be obtained after
allowing for other important factors.
Clinical trials are not conducted in isolation, but are part of an on-going
learning process. In order to assess the current weight of evidence for the use
of a particular treatment a Bayesian approach is necessary. Such an approach
allows for the formal inclusion of prior information, either in the form of clinical
expertise or the results from previous studies, into the statistical analysis.
An initial Bayesian analysis, for a single non-recurrent event, can be performed
using non-temporal models that consider the occurrence of events up to a
specific time from entry into the study. Although these models are conceptually
simple, they do not explicitly allow for censoring or covariates.
In order to address both of these deficiencies a Bayesian fully parametric
multiplicative intensity regression model is developed. The extra complexity of
this model means that approximate integration techniques are required. Asymptotic
Laplace approximations and the more computer intensive Gauss-Hermite
quadrature are shown to perform well and yield virtually identical results.
By adopting counting process notation the multiplicative intensity model is
extended to the multi-state scenario quite easily.
These models are used in the analysis of a cancer clinical trial to assess the
efficacy of neutron therapy compared to standard photon therapy for patients
with cancer of the pelvic region. In this trial there is prior information both
in the form of clinical prior beliefs and results from previous studies. The
usefulness of multi-state models is also demonstrated in the analysis of a pilot
quality of life study.
Bayesian multi-state models are shown to provide a coherent framework for
the analysis of clinical studies, both interventionist and observational, yielding
clinically meaningful summaries about the current state of knowledge concerning
the disease/treatment process.