## Stephen Walters

Professor of Medical Statistics and Clinical Trials at the University of Sheffield

Author: What is a Cox model?

Stephen has over 20 years worth of experience of designing, analysing and reporting the results of a variety of studies including randomised controlled trials, observational studies and surveys. He has been an author or co-author on over 200 publications (including 118 in refereed journals and 4 books). His research interests include: design, analysis and interpretation of studies with Health Related Quality of Life (HRQoL) outcome measures; computer intensive methods – the bootstrap; Health Services Research and Technology Assessment; cluster RCTs and clustering by health professional in individually randomised trials and study design and sample size determination.

Stephen has developed several courses on teaching medical statistics to medical and health science students, clinicians and allied health professionals. He has also co-authored four textbooks: ‘Medical Statistics: A Textbook for the Health Sciences’; ‘How to Display Data’; ‘How to Design, Analyse and Report Cluster Randomised Trials in Medicine and Health Related Research’ and ‘Quality of Life Outcomes in Clinical Trials and Health-Care Evaluation’.

Summary: What is a Cox model?

• A Cox model is a statistical technique for exploring the relationship between the survival of a patient and several explanatory variables.
• Survival analysis is concerned with studying the time between entry to a study and a subsequent event (such as death).
• A Cox model provides an estimate of the treatment effect on survival after adjustment for other explanatory variables. In addition, it allows us to estimate the hazard (or risk) of death for an individual, given their prognostic variables.
• A Cox model must be fitted using an appropriate computer program (such as SAS, STATA, SPSS or R). The final model from a Cox regression analysis will yield an equation for the hazard as a function of several explanatory variables.
• Interpreting the Cox model involves examining the coefficients for each explanatory variable. A positive regression coefficient for an explanatory variable means that the hazard is higher and thus the prognosis worse. Conversely, a negative regression coefficient implies a better prognosis for patients with higher values of that variable.

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