Graphical representation of survival curves in the presence of time-dependent categorical covariates with application to liver transplantation

ABSTRACT

Graphical representation of survival curves is often used to illustrate associations between exposures and time-to-event outcomes. However, when exposures are time-dependent, calculation of survival probabilities is not straightforward. Our aim was to develop a method to estimate time-dependent survival probabilities and represent them graphically. Cox models with time-dependent indicators to represent state changes were fitted, and survival probabilities were plotted using pre-specified times of state changes. Time-varying hazard ratios for the state change were also explored. The method was applied to data from the Adult-to-Adult Living Donor Liver Transplantation Cohort Study (A2ALL). Survival curves showing a ‘split’ at a pre-specified time t allow for the qualitative comparison of survival probabilities between patients with similar baseline covariates who do and do not experience a state change at time t. Time since state change interactions can be visually represented to reflect changing hazard ratios over time. A2ALL study results showed differences in survival probabilities among those who did not receive a transplant, received a living donor transplant, and received a deceased donor transplant. These graphical representations of survival curves with time-dependent indicators improve upon previous methods and allow for clinically meaningful interpretation.

KEYWORDS:

• Cox regression
• graphing
• survival curves
• time-dependent covariate
• time-dependent interaction

Acknowledgements

The data reported here have been supplied by the Hennepin Healthcare Research Institute (HHRI) as the contractor for the Scientific Registry of Transplant Recipients (SRTR). The interpretation and reporting of these data are the responsibility of the author(s) and in no way should be seen as an official policy of or interpretation by the SRTR or the U.S. Government.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Abigail R. Smith http://orcid.org/0000-0001-5496-4460

Jarcy Zee http://orcid.org/0000-0003-0586-1160

Additional information

Funding

Data reported in this publication were provided by the Adult-to-Adult Living Donor Liver Transplantation Cohort Study (A2ALL) study and research was supported by the National Institute of Diabetes & Digestive & Kidney Diseases cooperative agreement [grant number U01-DK62498].