Incorporating reference ranges from
healthy individuals in joint
longitudinal and time-to-event
modelling
Markus Elze, LSHTM / Warwick
Markus Elze
Some slides had to be removed from the online
version of this presentation due to
confidentiality, copyright or agreements with
partners.
If you want any more information, I would love
to have a discussion with you!
markus.elze@lshtm.ac.uk
www.markus-elze.eu
Markus Elze
Structure
1. Biological motivation
2. Joint modelling
3. Use of exogenous information for joint
modelling
Markus Elze
Markus Elze
Markus Elze
‘Bone Marrow Transplantation’
for high-risk haematological malignancies
Stem cell
collection
Donor
Transplantation
High-dose
chemotherapy
Normal
leukocyte
Immune
reconstitution
High mortality
up to 50%
Leukaemia
cell
3 months
High-risk patient
This „cartoon“ example is simplified. Time frames are for children and are longer in adults.
Markus Elze
1-3 years
Early intervention may allow use of
gentler interventions and reduce side effects
Complication
Possible intervention
Relapse
Donor lymph infusion
Chemotherapy
Graft-versus-Host Disease
Immunosuppressives
Graft failure
Stem cell boost
Additional transplant
Opportunistic infection
Targeted treatment
(e.g. antibiotics)
This list is simplified and serves only to motivate the method presented in this presentation.
Markus Elze
Joint modelling
• Model time-to-event for adverse events
• Incorporate longitudinal immune data
– Allow for immune system reconstitution over time
– Update predictions based on full history, not just current
measurement
• Link time-to-event and longitudinal submodel
sensibly to achieve good numerical behaviour
Markus Elze
Joint modelling
/exp
′
R packages JM, JoineR
Henderson, R., et al. Joint modelling of longitudinal measurements and event time data.
Biostatistics 1(4), 465-480, Jun 2000. doi: 10.1093/biostatistics/1.4.465
Markus Elze
Joint modelling
/exp
R packages JM, JoineR
Henderson, R., et al. Joint modelling of longitudinal measurements and event time data.
Biostatistics 1(4), 465-480, Jun 2000. doi: 10.1093/biostatistics/1.4.465
Markus Elze
′
Low patient numbers complicate
modelling even for linear models
• Convergence failure
• Insignificant
association
• Undue influence of
individual patients
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We would like to model even more
– Initial value
– Recovery speed
– Final value
• But data already
insufficient for modelling
• Can we get free data?
Immune measurements (arbitrary units)
0.0
0.2
0.4
0.6
0.8
1.0
• Complex reconstitution should be modelled as
precisely as possible:
0
Markus Elze
100
200
Time in days
300
Dynamic complication prediction incorporating
reference ranges from healthy individuals
1. Create reference ranges for healthy individuals
2. Use these to assess patient status post HSCT
3. Jointly model immune recovery and complications
Markus Elze
Reference ranges
Assess & convert
Joint modelling
“Healthy” values depend on age
• Many immune subpopulations known to be
age- (and sex-)dependent
• Published age-group
means and variances
not ideal
Comans-Bitter, W.M., et al. Immunophenotyping of blood lymphocytes in childhood. Reference values for lymphocyte
subpopulations. J Pediatr 130(3), 388-393, Mar 1997. doi: 10.1016/S0022-3476(97)70200-2
Markus Elze
Reference ranges
Assess & convert
Joint modelling
The LMS method
• Create age- and sex-dependent percentiles based
on Box-Cox transformation to normality
•
/
⋅
(or
!"#
/
for $
0)
• Make $, ', ( cubic splines of age (and sex) and fit
using penalized maximum likelihood
• Create reference centiles using resulting z-scores
Cole, T. J. and Green, P. J. Smoothing reference centile curves: the LMS method and penalized likelihood. Statistics in
medicine 11, 1305-1319, Jul 1992.
Markus Elze
Reference ranges
Assess & convert
Joint modelling
Reference ranges for 100 healthy children
Heinze, A., et al. Age-matched dendritic cell subpopulation reference values in childhood. Scan J of Immunol.
Markus Elze
Reference ranges
Assess & convert
Joint modelling
Patients slowly recover to normal levels
Markus Elze
Reference ranges
Assess & convert
Joint modelling
Patients slowly recover to normal levels
Markus Elze
Reference ranges
Assess & convert
Joint modelling
Using z-scores for the longitudinal submodel
• Replace the immune measurement with the ageand sex-dependent z-score cut-off at 3 and -5
• )
≔ max min /
, 3 , 15 , where
8#9: ,;9 : 1 1
/' 345 , 657
/
$ 345 , 657 ⋅ ( 345 , 657
Markus Elze
Reference ranges
Assess & convert
Joint modelling
Convert raw measurements to z-scores
Elze MC, et al. Dendritic cell reconstitution predicts relapse-free survival in children after allogeneic stem cell
transplantation. Bone Marrow Transplantation.
Markus Elze
Conclusions
• Measurements from healthy children can provide
“free” information for joint modelling of immune
data and adverse events
• Publications should consider skewness and provide
sufficient data to create age- and sex-dependent
centiles without grouping data
Markus Elze
Open questions
•
•
•
•
How do we assess performance of joint models?
Are LMS models the best way to get percentiles?
How do we best integrate z-scores in the model?
How do we model other aspects of immune
reconstitution?
Markus Elze
Acknowledgements
The Köhl group
Prof. J L Hutton
Chancellor's
Scholarship
Cell and Gene Therapy
Markus Elze