Advanced Topics in Survival Analysis
Presenter(s): Oliver Perra
Survival analysis is a statistical approach used to investigate the occurrence and the timing of events. The specific nature and characteristics of the outcome of interest (whether and when an event takes place) mean that more widely regression methods (e.g. logistic regression) cannot be applied in similar cases. When event occurrence is measured using discrete time metrics (e.g., school years), methods have been developed that rely on conditional probability of events. For resources on these methods, please refer to Dr Perra’s “Introduction to Survival Analysis”. However, when event occurrence is measured using a continuous-time metric (e.g. days, hours, etc.), there are additional challenges in modelling. Some of these challenges have been addressed by the Kaplan-Meier method, which capitalises on the observed timing of events, without imposing arbitrary time intervals on the data. This approach is also appealing insofar it has maximum likely properties.
A further advancement in survival analysis has been provided by Cox’s regression model named after him (also known as the proportional hazards model): the model allows to investigate the effects of predictors on event occurrence when the timing of events is measured on a continuous time scale. The Cox regression model is semi-parametric, offering great flexibility and efficiency: it estimates the effects of predictors without requiring assumptions about the shape of the baseline hazard function. The model however makes some key assumption, including assuming the effect of each predictor on the hazard is proportional and constant over time (the proportional hazards assumption). However, the latter assumption can be tested and relaxed to allow time-varying effects of predictors. For these reasons, many authors prefer to avoid calling model the proportional hazards model. Thanks to the semi-parametric characteristics and the possibility of relaxing assumptions, the Cox regression model has become one of the most used methods in epidemiology and medical sciences. These resources will provide the means to develop a solid understanding of the model.
The Kaplan-Meier Method For Analysing Time Continuous Events
The presentation will firstly focus on the challenges in investigating event occurrence when the timing of events is measured using a continuous time metric. The Kaplan-Meier method of estimating the continuous time survivor function will be then introduced, referring to a specific example of data from a study of cancer patients. The presentation will also illustrate how the Kaplan-Meier allows to estimate other statistics such as the cumulative hazard function. The topics will be foundational for an understanding of methods used to investigate effects of predictors on event occurrence. Scripts of data analyses run in the statistical software R are provided alongside the presentation.
The Cox Regression Model
The presentation will build from the topics covered in the previous presentation to develop intuition regarding the Cox regression model and its key assumptions.
Further Applications of the Cox Regression Model
The presentation will provide a worked example of Cox regression model to illustrate its outputs and their interpretation. The presentation will also illustrate key applications of the model, focusing in particular on the estimation of individual participants’ relative Risk Scores, and how these can be used to recover a baseline function, as well as functions of “prototypical” individuals, i.e., individuals that represent groups with meaningful combinations of predictors’ values. Finally, the presentation will provide an example of how the proportional hazards assumption can be relaxed to allow time-varying effects of predictors. All the examples provided will be available in R statistical software scripts included with the resources.
> Download exercise files, questions and solutions.
About the author
Dr Oliver Perra is a lecturer at the School of Nursing and Midwifery, Queen’s University Belfast. His research revolves around the early experiences that explain differences in children’s adaptation and socio-cognitive abilities. He explores these issues by applying a transactional approach: this allows to investigate how interactions between children's characteristics and modifiable environmental factors can affect children's developmental pathways.
- Published on: 13 October 2025
- Event hosted by: Queen’s University Belfast
- Keywords: Longitudinal Research | Cohort study | Regression Methods | Survival analysis | Hazard analysis | Time Series Analysis | quantitative method |
- To cite this resource:
Oliver Perra. (2025). Advanced Topics in Survival Analysis. National Centre for Research Methods online learning resource. Available at https://www.ncrm.ac.uk/resources/online/all/?id=20860 [accessed: 18 October 2025]
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