RESEARCH ARTICLE
Prediction of Survival With Long-Term Disease Progression in Most
Common Spinocerebellar Ataxia
Alhassane Diallo, MD,
1
*
Heike Jacobi, MD,
2
Arron Cook, MD,
3
Paola Giunti, PhD,
3
Michael H. Parkinson, MBBS,
3
Robyn Labrum, PhD,
4
Alexandra Durr, MD,
5
Alexis Brice, MD,
5
Perrine Charles, MD,
6
Cecilia Marelli, MD,
7
Caterina Mariotti, MD,
8
Lorenzo Nanetti, MD,
8
Marta Panzeri, MD,
8
Anna Castaldo, MSc,
8
Maria Rakowicz, PhD,
9
Rafal Rola, MD,
10
Anna Sulek, PhD,
11
Tanja Schmitz-Hübsch, MD,
2,12
Ludger Schöls, MD,
13,24
Holger Hengel, MD,
13,24
Laszlo Baliko, MD,
14
Bela Melegh, PhD,
14,15
Alessandro Filla, MD,
16
Antonella Antenora, MD,
16
Jon Infante, MD,
17
José Berciano, MD,
17
Bart P. van de Warrenburg, PhD,
18
Dagmar Timmann, MD,
19
Sylvia Boesch, MD,
20
Wolfgang Nachbauer, MD,
20
Massimo Pandolfo, MD,
21
Jörg B. Schulz, MD,
22
Peter Bauer, MD,
23
Kang Jun-Suk, MD,
24
Thomas Klockgether, MD,
2,25
and Sophie Tezenas du Montcel, PhD
1,26
1
INSERM U 1136, Sorbonne Universités, Institut Pierre Louis d’Epidémiologie et de Santé Publique, IPLESP, Paris, France
2
Department of Neurology, University Hospital of Heidelberg, Heidelberg, and German Center for Neurodegenerative Diseases (DZNE),
Bonn, Germany
3
Department of Molecular Neuroscience, UCL, Institute of Neurology, London, United Kingdom
4
Neurogenetics Laboratory, National Hospital of Neurology and Neurosurgery, UCLH, London, United Kingdom
5
Sorbonne Université, Institut du Cerveau et de la Moelle épinière (ICM), AP-HP, Inserm, CNRS, University Hospital Pitié-Salpêtrière, Paris, France
6
Service de Neurologie–CMRR, CHRU Gui de Chauliac, Montpellier, France
7
APHP, Genetics Department, Pitié-Salpêtrière University Hospital Paris, Paris, France
8
Unit of Medical Genetics and Neurogenetics (department), Fondazione IRCCS Istituto Neurologico Carlo Besta, Milan, Italy
9
First Department of Neurology, Institute of Psychiatry and Neurology, Warsaw, Poland
10
Department of Neurology, Military Institute of Aviation Medicine, Warsaw, Poland
11
Department of Genetics, Institute of Psychiatry and Neurology, Warsaw, Poland
12
Charité-Universitätsmedizin Berlin, NeuroCure Clinical Research Center, Clinical Neuroimmunology Group, Berlin, Germany
13
Department of Neurodegeneration and Hertie-Institute for Clinical Brain Research, University of Tübingen and Deutsches Zentrum für
Neurodegenerative Erkrankungen (DZNE), Tübingen, Germany
14
Department of Medical Genetics, and Szentagothai Research Center, University of Pécs, Pécs, Hungary
15
Department of Neurology, Zala County Hospital, Zalaegerszeg, Hungary
16
Department of Neuroscience, and Reproductive and Odontostomatological Sciences, Federico II University Naples, Naples, Italy
17
Service of Neurology, University Hospital Marqués de Valdecilla (IDIVAL), University of Cantabria (UC) and Centro de Investigación
Biomédica en Red de Enfermedades Neurodegenerativas (CIBERNED), Santander, Spain
18
Department of Neurology, Donders Institute for Brain, Cognition and Behaviour, Radboud University Medical Center, Nijmegen, The Netherlands
-----------------------------------------------------------------------------------------------------------------------
*Correspondance to: Dr. Alhassane Diallo, INSERM U1136, Sorbonne
Universités, Institut Pierre Louis d’Epidémiologie et de Santé Publique,
IPLESP, F-75013, Paris, France; E-mail: alhassane.diallo@inserm.fr
Funding agencies: EU FP6 (EUROSCA, grant LSHM-CT-503304),
German Ministry of Education and Research (GeneMove), Polish Ministry of
Scientific Research and Information Technology, EU FP7 (Neuromics, grant
F5-2012-305121), and Fondation pour la Recherche Médicale (FRM, grant
no.: PLP2015103433 4). The sponsors of the study had no role in design,
data collection, data analysis, data interpretation, or writing the report. The
correspo ndin g author had full access to all the data in the study and had
final responsibility for the decision to submit for publication.
Relevant conflicts of interests/financial disclosures: S.T.dM. reports
grants from EU FP6 EUROSCA during the conduct of the study. A.Di.
reports grants from the Fondation pour la Recherche Médicale (FRM), grant
number: PLP20151034334 during the conduct of the study. T.K. reports
grants from EU FP6 EUROSCA during the conduct of the study.
M.P. reports grants from the Friedreich Ataxia Research Alliance, grants
from FNRS (Belgium), grants and personal fees from Biomarin, grants and
personal fees from Voyager Therapeutics, personal fees from Apopharma,
personal fees from Vertex, personal fees from Pfizer, and grants from
Euroataxia outside the submitted work. B.P.vdW. reports grants from
Radboud University Medical Centre, grants from Hersenstichting, grants
from ZonMW, grants from BBMRI-NL, grants from the Gossweiler Founda-
tion, and grants from Bioblast Pharma outside the submitted work.
P.B. reports grants from the European Commission during the conduct of
the study, personal fees from CENTOGENE AG and personal fees from
Actelion Pharmaceuticals outside the submitted work. R.R. reports grant
from Polish Ministry of Scientific Research and Information Technology
(grant no.: 3 PO5B 019 24), during the conduct of the study. M.R. reports
grant from Polish Ministry of Scientific Research and Information Technol-
ogy (grant no.: 3 PO5B 019 24) during the conduct of the study, and grant
Clinical TeleNeuroforma (grant no.: IS-2/230/NCBR/2015), outside the sub-
mitted work. T.S.-H. reports grants from the EU during the conduct of the
study, grants from Bundesministerium für Wirtschaft und Energie, and
grants from Ipsen Pharma outside the submitted work. J.B.S. serves on
scientific advisory boards for Lundbeck Inc, TEVA, Novartis,
ForwardPharma, and Lilly, received funding for travel and speaker hono-
raria from GlaxoSmithKline, Merz Pharmaceuticals, Medical Tribune,
Lundbeck Inc, Pfizer Inc, Boehringer, Bayer, serves as Editor-in-Chief of
the Journal of Neurochemistry, and is Associate Editor for eNeuro. P.G. is
supported by the National Institute for Health Research University College
London Hospitals Biomedical Research Centre. D.T. was funded by the
German Research Foundation (DFB), EU, the Bernd Fink Stiftung, and the
German Heredoataxia-Foundation (DHAG) during the time of the research
(all funding unrelated to the study). S.B reports European Friedreich Ataxia
Consortium for Translational Studies (EFACTS), FP7 Health (HEALTH-F2-
2010-242193), E-Rare-3 “Clinical research for new therapeutic uses of
already existing molecules (repurposing) in rares diseases” (E_Rare-
3JTC2016).
Full financial disclosures and author roles may be found in the online
version of this article.
Received: 25 February 2019; Revised: 29 April 2019; Accepted: 8
May 2019
Published online 00 Month 2019 in Wiley Online Library
(wileyonlinelibrary.com). DOI: 10.1002/mds.27739
Movement Disorders, 2019 1
19
Department of Neurology, Essen University Hospital, University of Duisburg-Essen, Essen, Germany
20
Department of Neurology, Medical University, Innsbruck, Innsbruck, Austria
21
Université Libre de Bruxelles (ULB), Neurology Service–ULB Hôpital Erasme, ULB Laboratory of Experimental Neurology, Brussels, Belgium
22
Department of Neurology, RWTH Aachen University, Aachen, Germany; JARA–Translational Brain Medicine, Aachen-Jülich, Germany
23
Institute of Medical Genetics and Applied Genomics, University of Tübingen, Tübingen, Germany
24
Department of Neurology, University of Frankfurt, Frankfurt, Germany
25
Department of Neurology, University Hospital of Bonn, Bonn, Germany
26
Assistance Publique–Hôpitaux de Paris AP-HP, Hôpitaux Universitaires Pitié-Salpêtrière–Charles Foix, Paris, France
ABSTRACT: Background: Spinocerebellar ataxias are
rare dominantly inherited neurodegenerative diseases
that lead to severe disability and premature death.
Objective: To quantify the impact of disease progression
measured by the Scale for the Assessment and Rating of
Ataxia on survival, and to identify different profiles of dis-
ease progression and survival.
Methods: Four hundred sixty-two spinocerebellar ataxia
patients from the EUROSCA prospective cohort study, suffer-
ing from spinocerebe llar ataxia type 1, spinocerebellar ataxia
type 2, spinocerebellar ataxia type 3, and spinocerebellar
ataxia type 6, and who had at least two measurements of
Scale for the Assessment and Rating of Ataxia score, were
analyzed. Outcomes were change over time in Scale for the
Assessment and Rating of Ataxia score and time to death.
Joint model was used to analyze disease progression and
survival.
Results: Disease progression was the strongest predic-
tor for death i n all genotypes: An increase of 1 standard
deviation in total Scale for the Assessment and Rating of
Ataxia score increased the risk of death by 1.28 times
(95% confidence interval: 1.18–1.38) for patients with spi-
nocerebellar ataxia type 1; 1.19 times (1.12–1.26) for
spinocerebellar ataxia type 2; 1.30 times (1.19–1.42) for
spinocerebellar ataxia type 3; and 1.26 times (1.11–1.43)
for spinocerebellar ataxia type 6. Three subgroups of dis-
ease progression and survival were identified for patients
with spinocerebellar ataxia type 1: “severe” (n = 13; 12%),
“intermediate” (n = 31; 29%), and “moderate” (n = 62;
58%). Patients in the severe group were more severely
affected at baseline with higher Scale for the Assessment
and Rating of Ataxia scores and frequency of nonataxia
signs compared to those in the other groups.
Conclusion: Rapid ataxia progression is associated with
poor survival of the most common spinocerebellar ataxia.
Theses current results have implications for the design
of future interventional studies of spinocerebellar ataxia.
© 2019 International Parkinson and Movement Disorder
Society
Key Words: dynamic predictions; EPOCE; EUROSCA
study; longitudinal data; spinocerebellar ataxia
Spinocerebellar ataxias (SCAs) are rare inherited neu-
rological disorders, clinically characterized by progressive
balance problems and incoordination, that lead to severe
disability and premature death. More than 40 genetically
distinct SCAs have been defined, among which the most
common are SCA1, SCA2, SCA3, and SCA6.
1
They
are caused by abnormal cysteine alanine glycine (CAG)
repeat expansions, encoding elongated polyglutamine
tracts within the proteins associated with each type.
The European prospective cohort study (EUROSCA)
of patients with SCA1, SCA2, SCA3, and SCA6 was initi-
ated in 2005 to study the natural history of ataxia. Longitu-
dinal clinical
2
and survival data
3
from EUROSCA allowed
us to establish genotype-specific progression and survival
rates and identify factors that influence disease course and
survival. These analyses identified SCA1 as the genotype
with the fastest disease progression and shortest survival
among these SCAs.
2,3
Nevertheless, type I autosomal-
dominant cerebellar ataxias are often complex in terms of
clinical manifestations, meaning that it is not self-evident
that severity of ataxia per se is the best predictor of survival.
Simultaneously modeling long-term disease progression
and survival would allow the determination of their correla-
tion, a better understanding of their dependence, and identi-
fication of common prognostic factors and could advance
the design of future clinical trials.
Here, we report data from the EUROSCA study on dis-
ease progression in relation to survival with a long-term
follow-up. We aimed to (1) quantify the effect of disease pro-
gression on the survival of patients with SCA1, SCA2,
SCA3, or SCA6; (2) identify distinct subgroups of disease
progression and survival, as well as factors that influence
these groups; and (3) compute and compare the individual
dynamic prediction of survival based on disease progression.
Methods
Standard Protocol Approvals, Registration,
and Patients Consents
The ethics committees of the participating centers ap-
proved the study. The study is registered with ClinicalTrials.
gov, number NCT02440763. At enrollment, a written con-
sent form was obtained from all study participants.
2 Movement Disorders, 2019
DIALLO ET AL
Study Population
A subsample of 462 SCA patients, with at least two
visits, were analyzed from the 525 SCA patients enrolled
between July 1, 2005 and August 31, 2006 in the multicen-
ter (17 European centers) EUROSCA prospective cohort
study.
4
These patients were diagnosed with progressive,
otherwise unexp lained, ataxia and had a positive molecu-
lar genetic test for SCA1 (n = 107), SCA2 (n = 146), SCA3
(n = 122), or SCA6 (n = 87). Assessments were performed
according to a written study protocol. Patients were seen at
baseline and followed by annual visits for 3 years. After-
ward, study participants entered an extension phase in
which study assessments were performed during routine
visits, resulting in irregular intervals between the visits. The
database was locked on November 3, 2016, after a maxi-
mum observation period of 11 years.
Clinical Outcomes and Genetics Evaluations
Clinical outcomes were disease progression and overall
survival. We avoided survival bias by updating the vital
status from the available electronic EUROSCA patient reg-
istry, interviews of family members, or querying records
from civil registry offices, when feasible, as in the previous
survival study.
3
Disease progression was measured by the
Scale for the Assessment and Rating of Ataxia (SARA).
4
Briefly, the SARA score consists of eight items that yield a
total score of 0 (no ataxia) to 40 (most severe ataxia). All
investigators were experienced in the use of the SARA. We
selected candidate predictors for joint disease progression
and survival modeling, consisting of age at baseline, sex,
age at ataxia onset, repeat lengths of the expanded alleles,
SARA score at baseline, dysphagia, and dystonia, which
have been reported as predictors for survival or disease
progression in our previously published studies.
2,3
We
selected additional candidates, consisting of the inventory
of nonataxia signs (INAS)
5
and its reported abnormali-
ties, such as double vision and cognitive impairment,
physical state (body mass index; BMI), and health-
related quality of life, assessed by the visual analogical
scale (VAS) of the EuroQol five dimensions question-
naire (EQ-5D).
6,7
BMI was calculated using the formula
(weight/height
^2
). Repeat lengths of the expanded and
normal alleles were determined at the Institute of Medi-
cal Genetics and Applied Genomics of the University of
Tubingen (Tubingen, Germany).
Statistical Analysis
Frequencies (percentages) or means (standard devia-
tion; SD) were used to describe the categorical and con-
tinuous variables at baseline. Time from enrollment was
used as the time scale. Survival was calculated from the
date of enrollment to death for any reason. Data for
patients who were alive or lost to follow-up were censored.
We simultaneously modeled time-to-death and disease
progression using the shared random-effects (SRE) model
8
to quantify and capture the best relationship between dis-
ease progression and survival, and the joint latent class
(JLC) model
9
to identify subgroups of homogeneous
patients in terms of survival and disease progression. In
each joint model, the survival model consisted of the
Weibull proportional regression model, adjusted for age at
inclusion, and the longitudinal model consisted of a linear
mixed-effects regression model. We explored several struc-
tural dependencies (Supporting Information Table S1) to
capture the best relationship between disease progression
and survival using the SRE model. Thereafter, we selected
the strongest contributing predictors for survival from a
multivariate regression through a backward procedure
based on the lowest Akaike information criterion (AIC).
The proportion of death for SCA2, SCA3, and SCA6
patients was much smaller than that for SCA1 patients.
Thus, we performed a search for subgroups of partici-
pants sharing the same profiles of disease progression and
risk of death using the JLC model for patients with SCA1
only. We selected the best-fitting model with the optimal
number of latent classes using a compromise between the
lower integrated classification likelihood with Bayesian
information criterion approximation
10
and the nonsignifi-
cant score test for the conditional independence assump-
tion between longitudinal and survival outcomes.
11
Distributions of the baseline variables across these classes
were compared a posteriori using a chi-squared (χ
^2
)test
for categorical variab les and an analysis of variance for
continuous variables with the honestly significant differ-
ence test to account for multiple comparisons.
We assessed the ability of the longitudinal SARA score
to predict death by deriving the individual dynamic pre-
dictions of death from the best-fitting JLC model and the
one-class JLC model, which assumes that the SARA
score is independent of the risk of death. The dynamic
predictions are usually the predicted probabilities that
the death occurs in a window of time [s, s + t] computed
using the baseline candidate predictors and the SARA
score measure collected before time s. Time t is called the
“horizon of prediction” (t ≥ 0) whereas time s is often
called the “time of prediction” or the “landmark time”
(s ≥ 0).
9
These predictions were updated at each new
SARA measurement in a 5-year time horizon using all
SARA measurements collected until the time of predic-
tion s (before 5 years). The choice of a 5-year prediction
horizon was guided by the feasibility and clinical per-
spective of targeting patients at high risk of disease pro-
gression and death who could benefit from future
treatment. We compared the predictive accuracy and dis-
criminative capacity of these predictions using the
expected prognostic observed cross-entropy (EPOCE)
12
and time-dependent area under curve (AUC),
13
as well
as the 95% confidence intervals (CIs) of the differences
in EPOCE and AUC: for the EPOCE, the lower the
value, the better the accuracy and, conversely for the
AUC, the higher the value, the better the prediction.
Movement Disorders, 2019 3
RAPID ATAXIA PROGRESSION IS RELATED TO POOR SURVIVAL
We randomly selected a new patient, not included in
building the model, to illustrate how joint modeling can
be used in practice to perform individual dynamic pre-
dictions. Subsequent analyses were performed sepa-
rately for each genotype, given that survival and disease
progression differed between genotypes.
2,3
All data
analyses were performed using the “JM” and “lcmm”
R packages (R Foundation for Statistical Computing,
Vienna, Austria). Values of P < 0.05 were considered to
be statistically significant, and all tests were two-sided.
Results
Population Characteristics
The 462 patients analyzed here had a total of 2,192
visits, with a median of three visits (interquartile range:
2–4) for each patient. Individual profiles of the SARA evo-
lution show that deceased patients generally had a higher
SARA score at baseline (Supporting Information Fig. S1).
Demographic and clinical data at baseline are shown in
Table 1. During the follow-up, 102 (22%) patients died:
32 (30%) with SCA1, 33 (23%) with SCA2, 26 (21%)
with SCA3, and 11 (13%) with SCA6.
Relationship Between Disease Progression
and Survival
We applied the SRE model to explore the best rela-
tionship between disease progression and survival. For
all genotypes, the current value of the SARA score at a
particular visit t showed the best relationship with the
risk of death at the same visit according to the AIC
(Supporting Information Table S1). In SCA1 patients, a
predictive model obtained from the multivariate joint
model identified higher age at baseline, dysphagia, and
current value of the SARA score as the strongest con-
tributing risk factors for death (Table 2). An increase of
1 SD in the total SARA score was associated with a
28% increase in the risk of death. For SCA2, the
corresponding risk factors for death were higher age at
baseline, longer CAG repeat number, and the current
value of the SARA score. Risk of death increased by
19% for an increase of 1 SD in the SARA score
(Table 2). For SCA3 and SCA6, the only contributing
risk factor for death was the current value of the SARA
score. An increase of 1 SD in the SARA score increased
the risk of death by 30% for SCA3 patients and 26%
for SCA6 patients.
Subgroups of Disease Progression
and Survival for SCA1 Patients
We identified patient subgroups that shared the same
profiles of disease progression and risk of death by esti-
mating the JLC model with one to four latent classes for
patients with SCA1. The model with the optimal number
of classes selected by the compromise criterion included
three classes (Supporting Information Table S3). Class-
specific trajectories and survival function displays showed
a small group (severe group), consisting of 12% (n = 13)
of patients with the fastest progression of the SARA score
(467 [standard error {SE}: 296]) associated with a higher
risk of death than that of the intermediate group (hazard
ratio [HR]: 11.28; 95% CI: 3.75, 33.93; P < 0.0001;
Fig. 1A,B). The other groups, consisting of 29% and
59% of the patients, corresponded to an evolution of the
TABLE 1. Population characteristics at baseline
SCA1 SCA2 SCA3 SCA6
No. (n = 106*) (n = 146) (n = 122) (n = 87)
Sex (n, %male) 66 (62) 68 (47) 61 (50) 48 (55)
Death (n, %yes) 32 (30) 33 (23) 26 (21) 11 (13)
Age (years) 46 (12) 46 (14) 50 (12) 65 (11)
Age at onset
(years)
37 (11) 35 (13) 38 (11) 55 (10)
Disease duration
(years)
9 (5) 11 (6) 12 (6) 10 (6)
Repeat length
expanded allele
49 (6) 40 (4) 71 (4) 22 (1)
Repeat length
normal allele
30 (2) 22 (2) 22 (5) 12 (1)
SARA score 15 (8) 16 (8) 14 (8) 15 (7)
Number of
nonataxia
signs (INAS)
5 (2) 4 (2) 5 (2) 2 (2)
Median follow-up
(years), 95% CI
9.96
(7.2 10.3)
10.25
(10.2 10.3)
10.26
(10.2 10.4)
10.28
(10.2 10.4)
Data are shown as the mean (SD) or number (%).
*One patient (randomly selected) was removed to illustrate how the joint
model can be used to provide individual dynamic predictions.
TABLE 2. Multivariate shared random-effect model (survival
submodel) from the SARA score according to genotype
Parameter Estimate SE HR (95% CI) P Value
SCA1
Age at baseline 0.032 0.015 1.03 (1.00, 1.07) 0.0383
Dysphagia (yes) 2.071 0.951 7.93 (1.20, 52.27) 0.0317
SARA (current value)
a
0.244 0.039 1.28 (118, 138) <0.0001
SCA2
Age at baseline 0.066 0.017 1.07 (1.03, 1.11) 0.0001
CAG (number repeats) 0.217 0.070 1.24 (1.08, 1.43) 0.0019
SARA (current value)
a
0.156 0.029 1.17 (1.10, 1.24) <0.0001
SCA3
Age at baseline 0.213 0.249 1.24 (0.76, 2.02) 0.3937
CAG (number repeats) -0.306 0.221 0.97 (0.63, 1.49) 0.8722
Interaction age and CAG -0.003 0.004 0.99 (0.98, 1.00) 0.3915
SARA (current value)
a
0.263 0.046 1.30 (1.19, 1.42) <0.0001
SCA6
Age at baseline 0.075 0.049 1.08 (0.98, 1.19) 0.1273
SARA (current value)
a
0.229 0.064 1.26 (1.11, 1.43) 0.0004
a
Progression of the SARA score was linear for all genotypes and was
influenced by the expanded repeat CAG for SCA1 patients and age at
onset for SCA2 patients. There were no other predictors for SCA3 or
SCA6 patients. The corresponding longitudi nal submodel is shown in the
Appendix . Bol ded p values were < 0.05, which means the corresponding
factor was significantly associated with death.
4 Movement Disorders, 2019
DIALLO ET AL
SARA score associated with an intermediate and moder-
ate risk of death, respectively. A posteriori classification
showed the patients in the severe group to be significantly
more severely affected at baseline than those in the inter-
mediate and moderate groups (Table 3). Thus, the severe
group was characterized by a lower health-related quality
of life, BMI, and CAG repeat length of the normal allele,
and a longer duration of disease, a higher SARA score
and frequency of number of nonataxia signs, and the
following individual nonataxia signs: dystonia, cognitive
impairment, and dysphagia.
Dynamic Predictions
We derived the individual dynamic prediction of sur-
vival from the one- and three-class JLC model for different
times of prediction s (<5 years) in the window [s, s +5]
years and compared them (Fig. 2). According to the 95%
CIs of the difference in EPOCE and AUC (zero excluded),
the three-class JLC model provided a more accurate esti-
mate (lower EPOCE) and better discriminative capacity to
detect patients with a high risk of death (higher time-
dependent AUC). This ability of the SARA score to dis-
criminate between subjects with a high-risk of death from
those with a lower risk of death exceeded 85% (AUC,
0.852 [SD, 0.062], 0.965 [0.026], 0.974 [0.016], and
0.952 [0.025] for the prediction at the time of visit 1, visit
2, visit 3, and visit 4, respectively). We considered a patient
with SCA1 who was randomly selected and not included
to build the joint model to illustrate the individual
dynamic prediction of survival from the joint model. His
FIG. 1. Class-specific mean trajectories and predicted survival probabilities from the three-class JLC model for longitudinal SARA score in SCA1
patients. (A) Weighted subject-specific predicted SARA trajectories according to the JLC model equation: severe (red line) = 185+47 * time + 027 *
CAG - 007 * interaction between time and repeat CAG; intermediate (green line) = 264 – 094 * time – 016 * CAG + 007 * interaction between time
and repeat CAG; moderate (blue line) = 97 – 1.86 * time – 0006 * CAG + 008 * interaction between time and repeat CAG. (B) Predicted survival
according to the Weibull proportional hazard model equation with the intermediate group as reference (green line): severe (red line) = 027530
2
*
176747
2
* ((027530
2
*time) ^ (176747
2-1
)) * e
2
42274
; moderate (blue line) = 0 27530
2
*176747
2
* ((027530
2
*time) ^ (176747
2-1
)) * e
-3
43041
. [Color figure
can be viewed at wileyonlinelibrary.com]
Movement Disorders, 2019 5
RAPID ATAXIA PROGRESSION IS RELATED TO POOR SURVIVAL
![FIG. 2. Comparison of the predictive accuracy of the two predicted risk of death models within the time window (s, s + 1) when s = [visits before 5-year] and t = 5 years from the JLCM estimated from SCA1 patient data: (A) Cross-validated estimate of EPOCE. (B) Difference in EPOCE and 95% tracking interval (top panel). (C) AUC estimate and 95% point-wise CIs (dashed lines). (D) Difference in AUC (solid line), 95% point-wise CIs (dashed lines) and 95% simultaneous confidence bands (dotted lines). CVPOL is the cross-validated estimate of EPOCE. [Color figure can be viewed at wileyonlinelibrary.com]](/figures/fig-2-comparison-of-the-predictive-accuracy-of-the-two-126cf2bz.webp)
![FIG. 1. Class-specific mean trajectories and predicted survival probabilities from the three-class JLC model for longitudinal SARA score in SCA1 patients. (A) Weighted subject-specific predicted SARA trajectories according to the JLC model equation: severe (red line) = 18 5 + 4 7 * time + 0 27 * CAG - 0 07 * interaction between time and repeat CAG; intermediate (green line) = 26 4 – 0 94 * time – 0 16 * CAG + 0 07 * interaction between time and repeat CAG; moderate (blue line) = 9 7 – 1.86 * time – 0 006 * CAG + 0 08 * interaction between time and repeat CAG. (B) Predicted survival according to the Weibull proportional hazard model equation with the intermediate group as reference (green line): severe (red line) = 0 275302 * 1 767472 * ((0 275302*time) ^(1 767472-1)) * e2 42274; moderate (blue line) = 0 275302 * 1 767472 * ((0 275302*time) ^(1 767472-1)) * e-3 43041. [Color figure can be viewed at wileyonlinelibrary.com]](/figures/fig-1-class-specific-mean-trajectories-and-predicted-p9r8xtvw.webp)
