Statistical methods for handling non-proportional hazards in clinical trials

Many randomised clinical trials seek to demonstrate that a new treatment lengthens the time before which patients experience some adverse outcome of interest, such as heart attack or recurrence of cancer. The statistical analysis of such trials is almost universally performed using also-called Cox proportional hazards model. This model assumes that the ratio of hazard for failure between the two treatment groups is constant over time. In recent years however it has been increasingly found, particularly in immunoncology, that this assumption is probably violated. In such cases, the Cox model results are difficult to give a valid interpretation to. As such, there is a need to use and where necessary develop new methods of statistical analysis which do not make the proportional hazards assumption.

This research work will broadly consist of evaluating existing methodology alternative to the Cox model and develop new methodology where appropriate to analyse time to event outcomes in clinical trials. The methods to be investigated will include restricted mean survival time, contrasts of survival probabilities at landmark times of interest, weighted log rank tests and derivatives of this. The evaluation of the statistical methods will consist of a combination of analytical work, simulation studies, and application to a small number of real trial datasets exhibiting non-proportional hazards. The evaluation will consider both statistical properties (i.e. power, robustness to violations of assumptions) and interpretability of the resulting effect measures. Particular emphasis will be given to investigating how superiority of different methods may vary according to the type of non-proportional hazards. The research output will give recommendations of which methods of analysis should be used when non-proportional hazards are anticipated in clinical trials. This will potentially have an impact on the future design and analysis of clinical trials.

The supervisory team will consist of Dr. Jonathan Bartlett (80%) as lead supervisor and Prof. Chris Jennison (20%) as secondary supervisor. The project may benefit from existing relationships between the supervisory team (and the student) with the pharmaceutical companies Roche and AstraZeneca, in particular in relation to re-analysis of previously conducted clinical trials.