6. Time-to-Event Regression

  1. Bee Choo Tai1 and
  2. David Machin2

Published Online: 11 OCT 2013

DOI: 10.1002/9781118721957.ch6

Regression Methods for Medical Research

Regression Methods for Medical Research

How to Cite

Tai, B. C. and Machin, D. (2013) Time-to-Event Regression, in Regression Methods for Medical Research, John Wiley & Sons Ltd, Oxford. doi: 10.1002/9781118721957.ch6

Author Information

  1. 1

    Saw Swee Hock School of Public Health, National University of Singapore and National University Health System; Yong Loo Lin School of Medicine, National University of Singapore and National University Health System, Singapore

  2. 2

    Medical Statistics Unit, School of Health and Related Sciences, University of Sheffield; Cancer Studies, Faculty of Medicine, University of Leicester, Leicester, UK

Publication History

  1. Published Online: 11 OCT 2013
  2. Published Print: 29 NOV 2013

ISBN Information

Print ISBN: 9781444331448

Online ISBN: 9781118721957



  • Cox regression model;
  • hazard ratio (HR);
  • Kaplan-Meier method;
  • proportional hazards (PH);
  • time-to-event regression


When the interval between two happenings, say date-of-birth to date-of-weaning of breast fed infants is recorded, the resulting ‘time-to-event’ data often require special regression techniques for their analysis, although time itself is measured on a continuous scale. This chapter describes how censored observations arise, essentially when the second happening or endpoint event has not occurred, although the initiation event has. It is these censored observations that cause the required technical changes to the statistical methods to be made. The chapter describes the Kaplan-Meier method of summarizing in graphical form time-to-event data, which includes censored observations. The hazard ratio (HR) and the Cox regression model are introduced to enable comparison between two groups. The Cox model is then extended to allow for comparison of more groups, and also to take account of relevant covariates. Graphical and test-based methods for checking the proportional hazards (PH) assumption of the Cox model are described.