Visiting PhD student project: On the development of new flexible and interpretable parametric distributions and their use in survival analysis

This is a project for the visit of Dani Granzotto, a PhD student at the University of Sao Paolo, Brazil as part of her PhD sandwich program. She will be working under my supervision and the project was written jointly my and Dani. The project is funded by the "Science without borders" program of the The Brazilian National Council for Scientific and Technological Development (CNPq) and it does pays fees to the University of Bath.

Project details

In recent years there has been a surge of new probability distributions
to be used in many areas of science including survival analysis. With
the advent of high performance computing there seems to be no need for
new distributions per-se but need for more understanding of how to find
distributions (new or otherwise) that have the following key properties

1. Simple (Small number of parameters)
2. Flexible (fit well for a broad range of data patters)
3. Interpretable (Keep the interpretation of key parameters)

In many practical applications, interest is focused is only a few key
population quantities. Examples are population means, quantiles or
regression parameters such rate ratios. In a regression seeting, it is
common that the choice of the probability distribution of the response
variable is not the primary matter and is of key methodological interest
to understand when a particular choice of response distribution has no
impact on inference about the parameters of interest(robustness).
Equivalently,the investigator would like to know about response
distributions for which there is a large impact on inference.

The main focus of the work that D. Granzotto will perform during her
visit to Bath is on the the sensitivity of the statistical inferences
to different choices of the response distributions in a survival
analysis regression setting. The work will focus equally on both
methodological/analytical aspects as well as the comptational ones so
that the main end is to provide the final user with a set of modelling
tools together with a comprehensible user guide. The study will be
sample driven and will be illustrated with a set of real survival
datasets as well as simulations.


The programme to be develop during her twelve months visit to the
university of Bath is as follows:

Months 1-2. Literature review
Months 3-4. Analysis of toy models and simulations
Months 5-7. Analysis of real datasets
Months 8-9. Formal software Implementation in R
Months 10-12. Writing up