International Biometric Society
MODELLING SURVIVAL FOLLOWING ‘BONE MARROW TRANSPLANTATION’ USING
LONGITUDINAL IMMUNE MEASUREMENTS AT ARBITRARY TIME POINTS
Markus C Elze*1, Oana Ciocarlie2,3, Stephan Klöß2, Annekathrin Heinze4,
Melanie Bremm4, Ulrike Köhl2, Jane L Hutton1
1
University of Warwick, Coventry, United Kingdom
Hannover Medical School, Hannover, Germany
3
Victor Babeş University of Medicine and Pharmacy, Timisoara, Romania
4
Goethe-University Frankfurt, Frankfurt am Main, Germany
2
*E-mail:
m.elze@warwick.ac.uk
Haematopoietic stem cell transplantation (‘bone marrow transplantation’) is a potentially
curative treatment option for different hematologic and oncologic disorders, such as severe
leukaemia. However, it is still associated with high mortality rates due to complications after
transplantation. Early identification of high-risk patients is crucial for successful intervention.
Models that predict patient survival or individual complication risks are needed to assist
clinical decision making and may provide insights into the underlying biological processes.
The speed of immune recovery over time and several patient- and transplantation-related
covariates were shown to be associated with survival and complication risk[1]. We
investigate a dataset of paediatric and young adult patients. Longitudinal measurements of
several immunological subpopulations were taken at arbitrary time points. Measurement
time points and frequency cannot be assumed to be independent of the survival process.
Joint modelling of longitudinal and time-to-event data is a natural approach to data of this
nature[2]. Implementations of joint modelling techniques in R and other languages are
readily available. However, no consensus has been reached yet on how to best assess
goodness of fit and predictive ability of such a model.
For exploratory analyses and for use in clinical practice simpler models may be preferred. A
simple comparison of measurements at a single time point is sometimes found in biological
publications. A cutoff value may be used to group patients into ‘high-risk’ and ‘low-risk’
groups. However, bias may be associated with such an approach. Bias can be reduced by
using appropriate summary measurements, such as the area under the curve[3], and
accelerated failure time models can be fitted. This has the advantage that many measures
of the prognostic ability of survival models are readily available, e.g. explained variation[4].
These simpler models may be used to specify a joint model and joint modelling may in turn
inform the simpler models.
A possible extension of joint modelling is the inclusion of a proportion cured component to
allow for the fact that patients may have a normal life expectancy after a certain period of
relapse-free survival. Furthermore, the incorporation of the measurement frequency as a
variable in the longitudinal modelling may inform on the risk assessment by the clinicians.
References
[1] Koenig M et al. Multivariate analyses of immune reconstitution in children after allo-SCT:
risk-estimation based on age-matched leukocyte sub-populations. Bone Marrow
Transplantation, 45(4):613–621, August 2009.
[2] Henderson R et al. Joint modelling of longitudinal measurements and event time data.
Biostatistics, 1(4):465-480, June 2000.
[3] Matthews JN et al. Analysis of serial measurements in medical research. BMJ, 300:230235, January 1990
[4] Stare J et al. A measure of explained variation for event history data. Biometrics, 67:750–
759, September 2011.
International Biometric Conference, Florence, ITALY, 6 – 11 July 2014