Supplementary File 1
Markov Model
Continuos-time Markov models were fitted to the data in order to model the natural course of MDS and
simultaneously estimate the effect of allo-SCT on overall survival. While discrete-time Markov processes are
simpler and more commonly used as decision models, a continuous-time model gives a more realistic
representation of a disease process, particularly in the case of chronic diseases, in which model states may have a
natural interpretation in terms of staged progression. This is because in a continuous time Markov model
transitions between states are allowed to take place at any point in time, and not just at the start of a discrete
cycle (such as a month or year).
A commonly-used model is characterised by a series of successively more severe disease stages, and an
‘absorbing’ state (i.e. a state in which transitions to other states are not allowed), often death. The patient may
advance into or recover from adjacent disease stages, or die at any disease stage. Observations of the state S n(t)
are made on a number of individuals n at arbitrary times t, which may vary between individuals.
The stages of disease may be modelled as a homogeneous continuous-time Markov process governed by a matrix
Q of transition intensities qij representing the instantaneous risk of progression from the ith to the jth state.
Under this model, the time spent in state i has an exponential distribution with mean -1/qii and the probability
that the next state is j is -qij/qii. Multi-state Markov models may be fitted to the data which have irregular
observation times using freely-available software [Jackson, 2011]. The multi-state Markov model implemented
for MDS is illustrated below. IPSS-R risk scores were adopted as time-dependent indicators of the natural course
of the disease. Only transitions to higher risk scores are allowed (i.e. no possibility of a recovery). Allo-SCT is
modeled as a time-dependent categorical covariate. At any point in time it may assume 3 possible values: no
transplantation performed so far; transplantation preformed less than three months before; transplantation
performed more than three months before. The 3-month threshold was established to allow for excess of
mortality due to transplant-related causes soon after transplantation. The effect of allo-SCT on survival in each
disease state is then estimated as a hazard ratio with respect to the “no transplantation” category in the same
disease state.
q34
intermediate
IPSS-R
high
IPSS-R
3
4
q23
r137
r237
q37
low
IPSS-R
2
q47
r147
q45
r247
very high
IPSS-R
5
q57
r227
r157
r127
q67
very low
IPSS-R
1
AML
Death
q17
7
r167
r267
qi i+1
qi7
r1i7
r2i7
=
=
=
=
q56
r257
q27
q12
transition intensity from ith state to the next; i=1,…,6 (disease progression)
mortality rate in state i when not transplanted
hazard ratio of death in state i up to 3 months after allo-SCT vs. qi7
hazard ratio of death in state i from 3 months after allo-SCT onwards vs. qi7
6
Supplementary Table 1 Summary of fitted continuous-time Markov model for IPSS-R. For each state, the
maximum likelihood and 95% CI of the expected length of stay (conditional upon surviving to that state) are
reported, along with the transition intensity to a higher risk score and to death. As to transition intensities, their
absolute value is of little practical use, being an instantaneous risk of transition. The comparison of transition
intensities between different states, however, may be interpreted as a relative risk of transition. For example, the
transition intensity to death (instantaneous risk of death) in the high IPSS-R risk category is 2.3-fold the intensity
in the low IPSS-R risk.
IPSS-R model: expected survival in each state and transition intensities
Expected years in state
(given survival to state)
IPSS-R State
Point estimate
very low
Low
intermediate
High
very high
AML
2.30
3.66
2.36
1.58
1.12
0.44
95% CI
1.74
3.05
1.99
1.33
0.91
0.35
Transition intensity to next state
Point estimate
3.04
4.39
2.81
1.89
1.37
0.56
q12=0.43
q23=0.019
q34=0.030
q45=0.044
q56=0.066
95% CI
0.33
0.016
0.025
0.037
0.053
0.58
0.023
0.036
0.053
0.081
Transition intensity to death
Point estimate
q17=0.00035
q27=0.038
q37=0.040
q47=0.088
q57=0.016
q67=2.27
IPSS-R model: Hazard ratio for death in each state, according to time elapsed since transplantation
Up to 3 months
IPSS-R State
low
intermediate
high
very high
Point estimate
r127=44.91
r137=42.24
r147=28.41
r157=876.28
After 3 months
95% CI
15.29
13.73
10.38
4.38
131.88
129.96
77.72
17X104
Point estimate
r227=7.17
r237=5.74
r247=5.03
r257=188.06
95% CI
2.64
1.94
1.88
0.94
19.51
17.02
13.49
37x103
95% CI
0.0000
0.022
0.021
0.048
0.0005
1.79
1.25
0.064
0.077
0.16
0.43
2.89
Supplementary Table 2. Prognostic factors on posttransplantation outcome (overall survival) by explorative
multivariate analysis. Clinical and demographic variables were evaluated at the time of transplant in patients
receiving allo-SCT upfront, and before remission-induction chemotherapy in patients receiving treatment before
transplant.
OS
Clinical variables
HR
P
Recipient sex
1.12
.23
Recipient age
1.49
.02
IPSS-R risk
1.39
<.001
Disease stage at transplantation
1.62
.017
Source of HSC
1.16
.52
Type of donor
1.23
.09
Conditioning Regimen
.94
.53
(<55 vs. 55 years)
(Complete remission vs. active/progressive disease)
(Peripheral blood vs. bone marrow)
(HLA-identical sibling vs. MUD)
(RIC vs. Standard conditioning)