Predicting Motor Outcomes following STN DBS for Parkinson’s disease: A probabilistic approach
Paul Silberstein1, Nicole White2, Peter Silburn3, Terry Coyne4, Raymond Cook1, Lyndsey Jones1,
Daniel Wasson1,George Fraachia1, Helen Johnson2 and Kerrie Mengersen2
1 North Shore Private Hospital, Sydney, Australia
2 Queensland University of Technology, Brisbane, Australia
3 University of Queensland Centre for Clinical Research, Brisbane, Australia
4 St. Andrew’s War Memorial Hospital, Brisbane, Australia
Introduction
Previous studies examining motor outcome
following STN DBS for Parkinson’s disease have
focussed on comparing patient subgroups defined
by deterministic criteria. In light of the variable and
overlapping phenotypes observed in Parkinson’s
disease, a probabilistic approach to clinical
subgroup characterisation may yield better
predictors of patient outcome following surgery.
Here we consider the use of a novel, probabilistic
algorithm to subgroup identification in Parkinson’s
disease and determine the relationship between
phenotypic presentation and motor outcome in a
consecutive cohort of 50 patients with PD
undergoing STN DBS.
The shortcomings of deterministic
classification
Clinical subgroup definitions in PD such as Hoehn
and Yahr (HY) staging [1] and Tremor-PIGD
dominance [2] are based on deterministic criteria. In
other words, based on a single or few strict criteria,
patients are assigned to a single subgroup with
certainty, taken to be characteristic of their disease.
These systems have much value in describing
principle aspects of PD such as overall severity.
However, the major shortcoming of deterministic
systems of classification is their inability to
adequately describe large numbers of different
symptom profiles, as is witnessed in PD. This is
largely due to the constraint that each patient can
belong to one subgroup only, based on their
symptom profile. As a result, departures from
deterministic criteria are ignored, and may only be
accounted for by increasing the number of patient
subgroups. A hypothetical case where this
approach may not be appropriate is described in the
following example.
Subgroup definitions:
This scenario is representative of the variation in
symptom profiles observed in PD. The inability to
account this variation may have implications for the
comparison of patient outcomes, which in turn may
affect the determination of predictive factors of
individual outcome. This study considers an
alternative strategy to patient classification, in an
effort to develop more flexible subgroup criteria, for
purposes of determining predictors of patient
outcome following STN DBS.
Probabilistic classification
Probabilistic classification relaxes the need for strict
criteria to describe and assign patients to subgroups.
In this work, we consider finite mixture modelling, a
popular tool for probabilistic classification, to identify
clinical subgroups in PD based on responses to items
in UPDRS-III. These proposed subtypes are then
applied to a consecutive series of 50 PD patients
treated using STN DBS, in an effort to disseminate
postoperative outcomes.
A finite mixture model assumes that within a study
population, a fixed number of subgroups (K) exist,
each representative of a feature of the data. Each
subgroup describes a proportion (ηk) of the
population. A feature of the data, represented
mathematically by a probability density f (yi |θk), is
taken to describe patients with similar symptom
profiles, yi,. The choice of f (yi |θk) is flexible,
depending on the type of data under study.
Combined, these parameters specify the finite
mixture model,
The probabilistic component of this approach relates
to the assignment of patients to subgroups on the
basis of their unique symptom profile. If we let zi
model a patient i ’s true subgroup membership, then
the probability of belonging to each subgroup
k=1,…K is calculated as
Subgroup 1: Male patients, 60+ years of age
Subgroup 2: Female patients, <60 years of age
Patient data & Classification:
Patient
Gender
Age
Subgroup
1
Male
60+
1
2
Male
< 60
??
3
Female
< 60
2
4
Female
60+
??
The above example models the simplest case where
patients are assigned to subgroups given responses
on two criteria. For patients unable to be uniquely
classified (Patients 2 & 4), the only way to account
for these extra profiles is to increase the total
number of defined subgroups. Hence, it can be
seen that as the number of criteria increases, the
number of subgroups required to capture all
combinations increases significantly, sometimes to
impractical levels.
Alternatively, one could complete the classification
by assigning these patients randomly to a single
subgroup. However, the fundamental flaw of this
approach is that assignment is performed with a
high degree of uncertainty, with misclassification
likely to occur. This has major implications for the
comparison of subgroups, as this uncertainty in
classification propagates to comparing postoperative
and other outcomes.
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The inclusion of the normalising factor ensures that
each patient’s set of probabilities adds to 1. For each
patient, their most likely subgroup membership
corresponds to their highest probability.
All mentioned parameters in the above model are
estimated using Gibbs sampling, a Bayesian iterative
algorithm [3]. Beginning with initial estimates for all
model parameters, the sample proposes a patient
classification based on these estimates and Equation
(2). This process is then repeated in an iterative
fashion until convergence of parameters is achieved,
illustrated below
Update
Classify
The benefits of this approach to classification in
terms of describing symptom variability are threefold. Firstly, by replacing deterministic with
probabilistic assignment, each subgroup is no longer
defined by a single symptom profile. Instead, each
subgroup may be characterised in terms of common
elements of included symptom profiles. This allows
us to account for more variability in profiles without
increasing the number of desired subgroups.
Secondly, patients are allowed to have features of
more than one subgroup without being assigned to
one with certainty. For these patients, their
probabilities will be close together.
Finally, on the point of estimation, patients with
elements of more than one subgroup may change
classifications throughout the course of the iterative
process. This provides us with an intuitive solution
compared to deterministic schemes that assign the
same patients to a single subgroup with a degree of
uncertainty.
Subgroup 3:Low to midrange Tremor, Midrange
Bradykinesia/Rigidity, Midrange Akinesia/Postural
disturbance
Outcome
Subgroup
Mean(95% CI)
In this work, we take further advantage of the
iterative approach for calculating and comparing
postoperative outcomes. Whenever a new
classification is proposed, we can summarise each
subgroup in terms of means and 95% credible
intervals. Subgroups may be compared by
percentages differences. As a result, outcomes for
patients with multiple memberships are included in
calculations for each relevant subgroup. This has
significant implications for better disseminating
patient outcomes in light of complex symptom
patterns observed, compared to the once-off, static
approach deterministic schemes provide.
Relative
change in
LD
equivalent
dose
Relative
benefit of
simulation
minus
medication
Relative
benefit of
stimulation
and
medication
combined
Effect of
stimulation
vs. effect of
medication
1
2
3
79.8(65.5, 95.9)
77.8(64.0, 91.5)
78.0(64.4, 92.3)
1
2
3
50.3(41.1, 59.4)
54.6(43.6, 64.4)
54.7(45.6, 65.0)
1
2
3
70.5(55.5, 86.2)
70.2(56.0, 83.7)
70.5(58.3, 82.8)
1
2
3
84.0(64.5, 111.0)
88.8(66.2, 108.4)
89.4(73.8, 107.0)
Data description
Data used in this work consisted of two patient
cohorts; one for model estimation and the other for
prospective prediction. The first dataset consisted of
261 patients with idiopathic PD, collected as part of
the Queensland Parkinson’s Project (QPP) [4].
Exclusion criteria included previous surgical
treatment for PD and a HY stage less than 2. These
criteria were chosen to provide a reasonable
representation of PD patients suitable for first-time
treatment by STN DBS. The second dataset was a
consecutive series of 50 patients treated for PD by
STN DBS.
For each dataset, patient information was collected
using items 20-31 of the UPDRS. To create
symptom profiles for each patient, variables
describing the following symptoms were created:
Tremor
(items 20 and 21)
0=0-4
1=5-9
2 = 10+
Bradykinesia/Rigidity
(items 22 to 26)
0 = 0 - 14
1 = 15 - 29
2 = 30+
Akinesia/Postural disturbance
(items 27 to 31)
0=0-5
1 = 6 - 11
2 = 12+
STN DBS dataset:
•Relative change in LD equivalent dose was on
average 3-3.5% higher in Subgroup 1
•Comparison of postoperative outcomes revealed
that Subgroups 2 & 3 experienced the greatest
improvements.
•Relative benefit of stimulation minus medication:
On average, Subgroup 1’s improvement was 7%
lower than Subgroups 3 and 2.
•Effect of stimulation vs. effect of medication: On
average, Subgroup 1’s response was 4-5% lower
than that for Subgroups 2 and 3.
These variables were used to identify an appropriate
number of subgroups, using finite mixture modelling,
similar to the work of White et. al [5].
For the analysis of the STN DBS dataset, the
following postoperative measures were compared
between formulated subgroups:
Relative change in LD equivalent dose
Relative benefit of stimulation minus medication
Relative benefit of stimulation and medication
combined
Effect of stimulation versus effect of medication
Results
Baseline dataset
•The finite mixture model proposed three subgroups
as the best fit to the data (chosen using suitable
model fit criterion)
Subgroup 1: Low responses for all three symptom
groups
Subgroup 2: Low Tremor, Midrange to high
Bradykinesia/Rigidity, High Akenesia/Postural
disturbance
References
[1] Hoehn, M. & Yahr, M. (1967), Parkinsonism: onset, progression and
mortality, Neurology, 17, 427-42
[2] Jankovic, J. (1990), Variable expression of Parkinson's disease: a
base-line analysis of the DATATOP cohort. The Parkinson Study Group,
Neurology, 40, 1529-1534
[3] Frühwirth-Schnatter, S. (2006), Finite mixture and Markov switching
models, Springer, New York
[4] Correspondence to George D. Mellick, Eskitis Institute for Cell and
Molecular Therapies, School of Biomolecular and Physical Sciences,
Griffith University, Nathan, QLD 4111, Australia
[5] White, NM, Johnson, HL, Mengersen, KL, Silburn, PA, Mellick, G
and Dissanayaka, N, Finite mixture models for exploring complex
disease: An application to Parkinson’s disease subgroup identification
and characterisation, submitted to Biometrics, March 2009.