The BSU is an internationally recognised research unit specialising in
statistical modelling with application to medical, biological or public
health sciences. Details of the work carried out in the Unit appear on the
website www.mrc-bsu.cam.ac.uk . The Unit has 3 MRC PhD studentships to start
from October 2007. Awards cover Cambridge University fees and a stipend of
at least 12,000 pounds for a period of 3 years. Applicants must have or
expect to get a first or high 2.1 honours degree in mathematics, statistics
or a related discipline. A masters degree is desirable but not essential.
Examples of some of the projects available for PhD study are given below. We
will also consider suitable projects as suggested by prospective candidates.
Full research council funding can be awarded to UK citizens and applicants
who satisfy UK residency criteria, fees only are payable for citizens of EU
countries. It is not possible to award studentships to citizens of countries
outside Europe. Non-UK citizens with their own source of funding are
encouraged to apply.
Applicants should send CV, letter and contact details of 2 academic referees
to the Postgraduate Administrator at the Biostatistics Unit by 29th February
2007. E-mail applications are acceptable to [log in to unmask]
PROJECTS
Causal inference for longitudinal data
Joint Supervisors: Vern Farewell and Brian Tom
As a cause must always precede its effect, it is perhaps natural to consider
causal dependence in a longitudinal data setting. For example, interest may
lie on how the occurrence of one event influences the occurrence of another
or how a change in one stochastic process (e.g. continuous measurement
process) leads to a change in another (e.g. survival event process) in a
causal manner. In these situations, explicit incorporation of time in the
statistical modelling is essential. The recent uses of dynamic models for
multivariate survival data (Aalen et al. 2004; Biometrics 60, 764-773) and
dynamic linear models for the expected increments of some constructed
variable (Diggle et al. 2007; Applied Statistics, 56 1-31) suggest a useful
strategy for investigating causality in a longitudinal setting. This PhD
project will build on recent methodological work in causal inference and in
joint modelling to develop statistical approaches for answering causal
questions in a longitudinal setting.
The effect of non-compliance in randomized trials with survival outcomes
Joint Supervisors: Ian White and Krista Fischer
In many randomized clinical trials, the main outcome is time to a certain
event (the observations being censored for individuals not experiencing the
event of interest during follow-up time). To analyze such data, classical
survival analysis methods can be used.
When not all patients comply with the treatment and the compliance data is
available, it is of interest to estimate the treatment effects, adjusted for
compliance levels. Since compliance is a (possibly time-dependent)
post-randomization variable, classical regression methods cannot be directly
applied. The existing methods to estimate the effects of compliance on
time-to-event outcomes are restricted to certain special classes of models
and are not so easy to implement in practice.
The tasks of this project include:
- review existing methodology and derive easily-implemented estimating
algorithms to estimate the effect of compliance for survival outcomes
- work towards developing structural modelling methodology for fitting a
broad and flexible class of proportional hazards models for the effects of
compliance
- apply the methodology in the analysis of randomized trials
Various data sets are available for this project, including the Estonian
trial on Postmenopausal Hormone Therapy (EPHT). The results of EPHT were
inconclusive with respect to most of the main outcomes, defined as time to a
diagnosis of a certain disease. One of the reasons for such results is
believed to be the low treatment adherence in the hormone therapy (HT) arms.
Thus it would be of interest to estimate the effects of adherence to HT on
various outcomes of interest.
Uncertainty in economic models
Joint supervisors: Linda Sharples and Christopher Jackson
Statistical input into the estimation of costs and benefits of new
treatments has become more common in recent years, due to the increased use
of cost-effectiveness modelling in determining health service policy.
Traditionally point estimates of costs and benefits were calculated
deterministically but more sophisticated modelling approaches have attempted
to fully incorporate the stochastic nature in which costs and benefits
arise. Typically Markov models are set up to describe patient movement
between a series of health states. Variation arises from a number of sources
including: uncertainty surrounding the structure of the Markov model; the
nature of covariate effects on different transitions between health states;
choice of different model inputs; missing data and extrapolation of the
model beyond the observation period. This project will categorise and
explore sources of variation in long-term economic models. A clinical trial
comparing different diagnostic strategies for diagnosis of coronary artery
disease, augmented by long-term event rates from published studies, will be
used as a case study.
Cognitive change modelling for individuals in the presence of missing data
Supervisor: Fiona Matthews
The investigation of cognitive decline has often been conducted by
examination of change in cognitive abilities at the marginal level, that is,
by aggregating data across individuals over time. However, the process has
been identified to be too complex to be described at this level and models
at the person level are needed to gain full understanding of the loss of
cognitive abilities in old age. A problem faced by researchers when
investigating cognitive decline in old age is that attrition plays a
fundamental role in the occurrence of missing observations as individuals
die or drop out of the study. Unless considered in the models in an adequate
way, estimates of change will not reflect this situation. In these potential
projects, data from two population based longitudinal studies of ageing will
be used to motivate examples and test models.
Two large population based studies the Medical Research Council Cognitive
Function and Ageing Study (CFAS) and the Cambridge City over 75 Cohort Study
are rich resources of longitudinal data on the health of the older
population. The MRC Biostatistics Unit is working with the Department of
Public Health and Primary Care at the University of Cambridge on the
statistical analysis of these data, with the CFAS data archive held within
the Unit.
The aims of the potential project are to assist with the modelling of
cognitive change that can provide individual trajectories, either singularly
or as part of groups with common shapes. Potential investigations include:
* Investigation of penalised splines with random coefficients models
within a Bayesian framework .
* The jointly modelling of person specific curves in this context with
models for the description of possible informative missing data processes
* Functional data analysis area will be considered to compare modelling
flexibilities across modelling frameworks.
* Investigation of classes of individuals with similar decline over time
has identified groups of individuals who experience decline at similar rates
over time.
* Informing the process of class formation may be disproportionally
driven by the missing data. The aims of this project include an initial
extension of previous models for the estimation of random effects models
with a mixture of distribution for the random effects, the fit of missing
data models allowing for non monotone missing data.
* Identifying individuals who have reached the beginning of the terminal
process may identify more realistic treatment options and potential for
support. Terminal decline is not a simple process and the impact of
individuals who do not die during the time of the study or who have
accidental deaths are likely to be important processes to model.
The work will involve
* development of suitable statistical models
* fitting these models in two population based epidemiological studies
* simulation studies to explore the properties of the methods
* interpretation of results in an epidemiological context
These projects will be supervised by Fiona Matthews. The student will gain
both a methodological insight and experience of applied studies as the data
is collected from a wider collaboration within the ageing programme of the
University Department of Public Health and Primary Care.
The measurement of healthy life
In many disease areas the focus of research has been to concentrate on
reducing mortality from the disease. Now as the population ages the focus is
changing to concentrate on living a longer healthier life. Two projects are
proposed within the methodology of measuring healthy life.
Benchmarking measurements of healthy life
Supervisor: Fiona Matthews
Many methods have been proposed to estimate healthy life. The project
proposed here will use large cohort studies from the UK and US to
investigate the different methods of measuring healthy life. Initial
investigation will use the current methodologies to include methodological
work on how the different methods interrelate, study design and sample size
considerations and how missing data impacts on the estimates obtained. These
methodologies will then be extended to generate new methods for better
estimation in the future. The methods proposed have been formulated based on
different types of longitudinal studies. Some formulations may be more
methodologically sound for different study designs. Missing data may well
differentially impact on some types of study designs. Information for
researchers is required for help on analysis, but more importantly
information on the precision using different study designs.
This project will be supervised by Fiona Matthews, with input from Prof
Carol Jagger University of Leicester. The student will gain both a
methodological insight and experience of applied studies as the data is
collected from a wider collaboration within the ageing programme of the
University Department of Public Health and Primary Care, Cambridge and
within the Epidemiology Department of Leicester.
Measuring healthy life relaxing the Markov assumption
Joint Supervisors: Fiona Matthews and Ardo van den Hout
The aim of the project is to contribute to the development of longitudinal
data analysis and multi-state modelling. An assumption that is often used in
multi-state models is the first order Markov assumption which states that
the transition to the next state only depends on the current state, i.e.,
the history of the process is not taken into account. This assumption makes
the estimation of life expectancies in various states straight forward given
a fitted multi-state model. Often, however, the first order Markov
assumption does not hold. For example, if an individual is in state 1, the
probability of a transition to state 2 might depend on whether the
individual has been in state 2 before. In this project, multi-state models
will be investigated that are not first order Markovian. The start will be
the literature on semi-Markov models where part of the history of the
process is captured by time-dependent covariates. Estimation of life
expectancies using semi-Markov models can then be undertaken by simulating
individual trajectories given a specification of, e.g., age and sex. This
extension has not been used for the estimation of life expectancies. The
methods will be applied using data from the UK Medical Research Council
Cognitive Function and Ageing Study (1991-2005). In studies of the older
population the measurement of cognitive ability is essential as it is an
important predictor of health, survival, and need for care.
This project will be supervised by Fiona Matthews and Ardo van den Hout.
The student will gain both a methodological insight and with a direct
applicability to applied statistics as the data is collected from a wider
collaboration within the ageing programme of the University Department of
Public Health and Primary Care, Cambridge.
Sequential methods for meta-analysis
Supervisor: Dr Julian Higgins
Meta-analyses are statistical analyses that integrate the findings of
multiple studies. They are commonly encountered as part of retrospective,
systematic reviews of existing research. However, they are increasingly
being considered in prospective contexts. For example, if a particular
epidemiological association is identified as potentially important, data
collections from multiple epidemiological studies can be interrogated as
part of a prospective meta-analysis. This approach is now common in the
field of human genome epidemiology in particular, where interesting findings
are confirmed or refuted by attempting to replicate them systematically in
other data sets. Similar theoretical issues arise when meta-analyses are
regularly updated, such as those in the Cochrane Database of Systematic Reviews.
If meta-analyses are repeated using conventional statistical methods then
the risk of false-positive findings increases. Sequential methods for
meta-analysis are required that mirror established sequential methods for
clinical trials. The ability to incorporate random effects across studies,
and to examine study-level effect modifiers, are important aspects of
meta-analysis methodology. There is limited methodology for tackling these
in the context of a sequential meta-analysis.
This project will examine Bayesian and classical methods for sequential
meta-analysis, with applications in clinical trials and epidemiology,
particularly human genome epidemiology. The work will build on collaborative
work previously undertaken by Dr Higgins and Prof Anne Whitehead (Lancaster
University), and may involve collaboration with the Molecular Epidemiology
Unit at the University of Cambridge on applications to genetics of coronary
heart disease.
Combining information across multiple genetic markers
Joint Supervisors Julian Higgins and Frank Dudbridge
Genetic association studies seek to identify genetic variants that are
predictive of disease outcomes. Studies typically examine multiple genetic
markers, which can vary from variants in a handful of candidate genes up to
several hundreds of thousands of markers in a genome-wide association study.
It is rare for there to be only a single study, and combining evidence
across multiple studies is important both to enhance power and to form
succinct summaries of the current knowledge base. Multiple studies of the
same disease may find associations with different markers in the same gene,
may genotype different markers, and have different degrees of multiplicity.
The markers investigated tend not to directly cause disease, but may be
physically close to the causal loci.
The project will consider how to combine evidence across multiple genetic
association studies dealing with multiple genetic markers. Methods will
allow increased power to detect an untyped causal locus, and will be
applicable to genome-wide association studies as well as candidate gene
studies. They are also relevant to field-wide summaries of evidence on
genetic predisposition to particular diseases, as are being developed by the
Human Genome Epidemiology Network (www.cdc.gov/genomics/hugenet).
|
