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Statistical analysis of time to event outcomes in clinical trials

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  • Full or part time
    Dr Jonathan Bartlett
  • Application Deadline
    No more applications being accepted
  • Competition Funded PhD Project (European/UK Students Only)
    Competition Funded PhD Project (European/UK Students Only)

Project Description


Many clinical trials of new drugs or treatments involve recruiting patients into the trial, randomising them to one of the treatments under study, and measuring how long until each patient experiences an adverse event of interest, such as cancer progression, heart attack, or death. The statistical analysis of such trials is virtually always performed using Cox’s proportional hazards regression model. Such analyses have recently been the subject of a variety of criticism.

First, some have claimed that the resulting effect estimates (hazard ratios) do not have a valid interpretation as a so called causal effect, even when the model assumptions hold (1). Second, in some therapy areas, in particular cancer trials of immunotherapies, the key assumption of this model is increasingly found not to hold, rendering the validity and interpretation of the results difficult (2).

This PhD will involve evaluating existing alternative methods of analysis to the Cox model and developing new methods of analysis where appropriate. This will consist of a combination of analytical work, simulation studies, and analysis of real clinical trial datasets. The outputs will include recommendations for what methods of analysis should be used in trials with time to event outcomes, which will have the potential to influence the analysis of future clinical trials in many disease areas. A further possible output is open source software and tutorials to enable those conducting clinical trials to readily adopt the methods that the research advocates.

After the PhD, the student will be extremely well placed for their next career step, particularly in further academic biostatistics research or in the pharmaceutical industry.


The student will have a number of training opportunities during the PhD, including participating in the Academy for PhD Training in Statistics (APTS) programme, short courses at other institutions (for example on causal inference methods), and relevant statistical units run at the University of Bath. The project will be closely linked to the SAMBa Centre for Doctoral Training (CDT) at Bath and run as an aligned studentship. The student will be able to participate in various activities as part of this, including the flagship Integrative Think Tanks (ITTs).


Applicants should hold, or expect to receive, a First Class or high Upper Second Class UK Honours degree (or the equivalent qualification gained outside the UK) in a relevant subject. A master’s level qualification would also be advantageous.


Informal enquiries are welcomed and should be directed to Dr Jonathan Bartlett, [Email Address Removed]

Formal applications should be made via the University of Bath’s online application form:

Please ensure that you quote the supervisor’s name and project title in the ‘Your research interests’ section.

More information about applying for a PhD at Bath may be found here:

Anticipated start date: 30 September 2019.

Funding Notes

Candidates may be considered for a University Research Studentship which will cover UK/EU tuition fees, a training support fee of £1,000 per annum and a tax-free maintenance allowance at the UKRI Doctoral Stipend rate (£14,777 in 2018-19) for a period of up to 3.5 years.


1. Aalen, O.O., Cook, R.J. and Røysland, K., 2015. Does Cox analysis of a randomized survival study yield a causal treatment effect? Lifetime data analysis, 21(4), pp.579-593.

2. Trinquart, L., Jacot, J., Conner, S.C. and Porcher, R., 2016. Comparison of treatment effects measured by the hazard ratio and by the ratio of restricted mean survival times in oncology randomized controlled trials. Journal of Clinical Oncology, 34(15), pp.1813-1819.

How good is research at University of Bath in Mathematical Sciences?

FTE Category A staff submitted: 44.40

Research output data provided by the Research Excellence Framework (REF)

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