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Japanese Journal of Comprehensive Rehabilitation Science (2020)

Original Article

Explanatory variables to use in a multiple regression analysis topredict stroke patients’ motor FIM score at discharge fromconvalescent rehabilitation wards: an investigation of patients witha motor FIM score of less than 40 points at admission
Makoto Tokunaga, MD, PhD,1 Katsuhiko Sannomiya, PT2
1
2

Department of Rehabilitation Medicine, Kumamoto Kinoh Hospital, Kumamoto, Japan
Department of Physical Therapy, Kumamoto Kinoh Hospital, Kumamoto, Japan

ABSTRACT
Tokunaga M, Sannomiya K. Explanatory variables to use
in a multiple regression analysis to predict stroke patients’motor FIM score at discharge from convalescentrehabilitation wards: an investigation of patients with amotor FIM score of less than 40 points at admission. Jpn
J Compr Rehabil Sci 2020; 11: 102‐108.

Objective: This study aimed to clarify the
explanatory variables to use in a multiple regression
analysis to predict improvement in the motor
Functional Independence Measure (FIM) during the
hospitalization of patients with severe stroke in aconvalescent rehabilitation ward.
Methods: The subjects of this study were 230
patients with stroke with a motor FIM score of lessthan 40 points at admission. In total, 17 factors werestratified and those with a significant difference inmotor FIM effectiveness between stratified groups
were used as the explanatory variables of a stepwise
regression analysis, which employed the motor FIM
score at discharge as the objective variable.
Results: There were significant differences inmotor FIM effectiveness among the 12 factors. The
10 factors selected through a stepwise regression
analysis were age, cognitive FIM score at admission,
motor FIM score at admission, number of days fromonset to admission, modified Rankin Scale before
onset, Brunnstrom stage of paralyzed lower limb,
body mass index, sitting stability, Japan Coma
Scale, and hemispatial neglect.
Conclusion: It is desirable to use these 10 factors
Correspondence: Makoto Tokunaga, MD, PhD
Department of Rehabilitation Medicine, Kumamoto Kinoh
Hospital, 6-8-1 Yamamuro, Kita-ku, Kumamoto 860-8518,
Japan.
E-mail: tokunaga@juryo.or.jp
Accepted: September 12, 2020.
No benefits in any form have been or will be received fromany commercial party related directly or indirectly to thesubject of this manuscript.
©Kaifukuki Rehabilitation Ward Association 2020
doi.org/10.11336/jjcrs.11.102

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as explanatory variables in multiple regression
analyses.
Key words: stroke, multiple regression analysis,
FIM improvement, set of explanatory variables tobe used, patients with low FIM scores at admission
Introduction

Predicting outcomes is important for planningand executing treatment plans in rehabilitation
medicine. Multiple regression analysis, which isa multivariate analysis, is often used to predict
outcomes such as the Functional Independence
Measure (FIM) [1] at discharge and FIM gain
(FIM at discharge minus FIM at admission).
However, the prediction accuracy of a multiple
regression analysis is not as high as expected. Ina report by Heinemann et al. [2], which reviewed
papers on prediction using multiple regression
analyses, the square of the multiple regression
coefficient (coefficient of determination) was
0.46-0.73. This is a level at which the tendency
of a group can be predicted, but is not sufficientfor predicting individual cases [3].
To improve the accuracy of predicting motor
FIM (mFIM) improvement through a multiple
regression analysis, three methods were reported:
1) conversion of mFIM at admission to areciprocal number (1/mFIM at admission) andusing it as one of the explanatory variables [4], 2)
predicting mFIM improvement rate (mFIM
effectiveness) through a multiple regression
analysis and converting it to mFIM at discharge[5], and 3) creating two prediction formulas using
the data of patients with low and high mFIM at
admission [6]. However, these methods deal withthe problem of the ceiling effect of mFIM gain
(small mFIM gain in patients with high mFIM
score at admission) [7, 8]. These methods
significantly improved prediction accuracy in thehigh mFIM group (patients with an mFIM score
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Tokunaga M et al.: Explanatory variables to use in a multiple regression analysis of strokeat admission of 40-90 points) with the ceiling
effect, but did not improve the prediction accuracy
for the low mFIM group (patients with mFIM
score at admission of 13-39 points) [8]. It is
important to use the appropriate explanatory
variables to improve prediction accuracy in the
low mFIM group.
In a review of 35 papers that predicted FIM
improvement in patients with stroke hospitalizedin convalescent rehabilitation wards in Japan
using a multiple regression analysis (hereafter,
multiple regression analysis predicting FIM
improvement in stroke), explanatory variables
which were used in more than four papers andwere significant in more than half the studies
were only nine factors [9, 10]. These included
mFIM score at admission (significant in 26
papers, used in 29 papers, hereafter written as
26/29), age (23/32), cognitive functions such as
cognitive FIM (cFIM) score at admission (15/15),
length of hospital stay (8/14), number of days
from onset to admission (9/17), modified Rankin
Scale (mRS) before onset (4/5), training time(3/5), body mass index (BMI) (3/5), andBrunnstrom stage (2/4) [9, 10]. The JapaneseSociety of Rehabilitation Medicine recommended
the use of six factors other than those describedabove when conducting clinical research or
surveying stroke [11]. These factors were sex,
stroke type, laterality of the lesion, whether thelesion was above or below the cerebellum tent,
hemispatial neglect, and aphasia [11]. Furthermore,
it was reported that trunk function [12] and theJapan Coma Scale (JCS) [13] are useful for
predicting outcomes in the low mFIM group.
Therefore, the abovementioned 17 factors arepromising candidates for the explanatory variables
that should be used in a multiple regression
analysis to predict mFIM improvement in patientswith stroke. However, no reports have used all 17
factors as explanatory variables. In addition, it is
not clear which factor has a large influence on
mFIM improvement.
In this study, we performed a multiple regression
analysis in patients with stroke, hospitalized in aconvalescent rehabilitation ward, and whose mFIM
score was less than 40 points at admission. The
purpose of this study was to clarify which of theabove 17 explanatory variables had a large
influence on mFIM improvement and to propose
a set of explanatory variables that should be used
in a multiple regression analysis to predict mFIM
improvement.
Subjects and methods

The subjects consisted of patients with stroke
admitted to the convalescent rehabilitation ward
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at K hospital between January 1, 2013 and March
31, 2020, and those with an mFIM score atadmission of 13-39 points. The following patientswere excluded to eliminate the effects of exceptional
patients: those with subarachnoid hemorrhage,
those who had been admitted within 4 days ormore than 60 days after onset, those who had
spent less than 30 days or more than 180 days inthe hospital, those with an mFIM gain of less than
0 points, and bilateral hemiplegia. In total, 230
patients were included in this study.
We retrospectively surveyed the 17 factors
described above, namely sex, age, type of stroke(cerebral infarction or cerebral hemorrhage),paralyzed side (right or left), whether the lesion
was above or below the cerebellum tent, mRS
before onset, number of days from onset toadmission, mFIM score at admission, cFIM scoreat admission, BMI, JCS, Brunnstrom stage ofparalyzed lower limb, presence or absence ofhemispatial neglect, presence or absence ofaphasia, sitting stability, training time, and lengthof hospital stay, as well as mFIM score atdischarge. Training time was the total number ofunits of physical therapy and occupational therapy
per day (1 unit was 20 min of training). For sitting
stability, we classified bedridden and sitting withbackrest leaning as unstable and independent sitting
as stable [14].
1. mFIM effectiveness in the stratified groups

We compared the mFIM effectiveness between
the two groups in terms of sex, stroke type,paralyzed side, above or below the cerebellum
tent, hemispatial neglect, aphasia, and sitting
stability. Age, number of days from onset toadmission, mFIM at admission, cFIM at admission,
training time, and length of hospital stay werecompared for the two groups below and above themedian value. Since no patients had a JCS of
100-300 points, a comparison of the two groupsof 0-3 points and 10-30 points was performed.
BMI was initially divided into three groups: lessthan 18.5 kg/m2 (underweight), 18.5-27.5 kg/m2(normal weight and overweight), and above 27.5kg/m2 (obese) [15]. However, since the obese
group included only 16 cases, two groups werecompared: less than 18.5 kg/m2 and 18.5 kg/m2 or
more. The mRS before onset (0-1, 2-3, 4-5) andBrunnstrom stage (I-II, III-IV, V-VI) of threegroups were compared. mFIM effectiveness wascalculated as mFIM gain/(91 points − mFIM
score at admission) [16]. mFIM gain, which is themFIM improvement score, is strongly affected by
the ceiling effect, whereas mFIM effectiveness,
which is the mFIM improvement rate, is lesslikely to be affected by mFIM score at admission
and is more frequently used in the study of mFIM
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improvement than mFIM gain [16].
A Mann-Whitney U test was used to compare
the two groups. The Kruskal-Wallis test was used
to compare multiple groups, and if there was asignificant difference, multiple comparisons were
performed using the Steel-Dwass method. The
level of significance was <5%.
2. Multiple regression analysis with mFIM score atdischarge as the objective variable

Of the 17 factors in Study 1, 12 factors thatdiffered significantly between the groups wereused as explanatory variables in a stepwise
regression analysis with mFIM score at discharge
as the objective variable. A factor with an F valueof two or more was selected as a valid explanatory
variable. Age, number of days from onset toadmission, mFIM score at admission, cFIM scoreat admission, and training time were input as
numerical values. The mRS before onset (0-5)
and Brunnstrom stage (I-VI) were input as
ordinary scale values. The JCS (0, 1, 2, 3, 10, 20,30) has a large numerical difference between 1
and 2 digits, and so it is not appropriate to input anumerical value. Thus, a dummy variable wascreated [17]. Specifically, JCS 0 point was set to0,0; JCS 1-3 points were set to a 1-digit dummyof 1,0; and JCS 10-30 points were set to a 2-digit
dummy of 0,1. For stroke type, cerebral infarction
was set as 0, and cerebral hemorrhage as 1.

Regarding hemispatial neglect and aphasia,
absent was set as 0 and present as 1. For sitting
stability, unstable was set as 0 and stable as 1.
Since there is no linear relationship between BMI
and mFIM improvement [18], BMI < 18.5 kg/m2
was set as 0 and 18.5 kg/m2 or more as 1. We theninvestigated the standard partial regression
coefficient β, which means the relative strength ofthe explanatory variable to the objective variable.
The statistical software used was four-steps
EXCEL statistics [19].
Results

Table 1 shows the basic attribute data of the
230 target patients. The average mFIM score atadmission was 21.0 points.
Among the 17 factors, mFIM effectivenessdiffered significantly between the stratified groupsof 12 factors, namely age, stroke type, mRS before
onset, number of days from onset to admission,
mFIM at admission, cFIM at admission, BMI, JCS,
Brunnstrom stage of paralyzed lower limb,
hemispatial neglect, sitting stability, and training
time (Table 2). There were no significant differences
between the stratified groups in five factors, namely
sex, paralyzed side, above or below the cerebellum
tent, aphasia, and length of hospital stay.
Among the 12 factors that were significant inStudy 1, there was no correlation coefficient ofTable 1. The basic attribute data of the subjects.
Number of patients
Sex
Age
Type of stroke
Paralyzed side
Above or below the cerebellum tent
Modified Ramkin Scale before onset
Number of days from onset to admission
Motor FIM score at admission
Cognitive FIM score at admission
Body mass index (BMI)
Japan Coma Scale (JCS)
Brunnstrom stage of paralyzed lower limb
Hemispatial neglect
Aphasia
Sitting stability
Training time (units/d)Length of hospital stay
Motor FIM score at discharge
Motor FIM gain
Motor FIM effectiveness

230
Male 127, female 10372.4±13.1 (28-93)
Infarction 109, hemorrhage 121
Right 113, left 117
Above 205, below 25(0) 151, (1) 23, (2) 18, (3) 21, (4) 13, (5) 417.2±8.1 (5-56)
21.0±8.8 (13-39)
15.5±7.8 (5-35)
21.9±3.7 (14.7-36.2)(<18.5) 38, (18.5- 27.4) 176, (≥27.5) 16(0) 43, (1) 52, (2) 40, (3) 74, (10) 16, (20) 2, (30) 3(I) 52, (II) 65, (III) 22, (IV) 32, (V) 42, (VI) 17
Absent 143, present 87
Absent 141, present 89
Unstable 177, stable 53
5.7±0.8 (4-7)
117.9±33.8 (31-179)
46.4±23.8 (13-90)25.4±19.8 (0-70)0.379±0.088 (0-0.982)

Abbreviation: FIM, Functional Independence Measure.
Data for this study are expressed as number of patients or mean±standard deviation (minimum to maximum).
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0.6 or more; thus, there was no multicollinearity.
When a stepwise regression analysis was performed
with the 12 factors as explanatory variables and105

mFIM score at discharge as the objective variable, asignificant prediction formula was obtained (Table3). The coefficient of determination was 0.707

Table 2. Comparison of motor FIM effectivemess in stratified groups.
FactorSex
AgeType of stroke
Paralyzed side
Above or below the
cerebellum tent
Modified Ramkin Scale(mRS) before onset
Number of days fromonset to admission
Motor FIM score atadmission
Cognitive FIM score atadmission
Body mass index (BMI)
Japan Coma Scale (JCS)
Brunnstrom stage (BRS)of paralyzed lower limb
Hemispatial neglect
Aphasia
Sitting stability
Training time
Length of hospital stay

Motor FIM effectivenessp Value

Male 0.391±0.295, female 0.364±0.300<73 yaers old 0.524±0.291, ≧73 years old 0.254±0.241
Infarction 0.326±0.274, hemorrhage 0.426±0.310
Right 0.384±0.308, left 0.374±0.287

0.52＜0.001＜0.05
0.86

Above 0.376±0.294, below 0.404±0.326

0.68

mRS 0-1 0.415±0.301, mRS 2-3 0.281±0.252, mRS 4-5 0.228±0.262 ＜0.01*<13 d 0.482±0.310, ≥13 d 0.337±0.282＜0.01<21 points 0.266±0.275, ≥21 points 0.544±0.247＜0.001<16 points 0.251±0.252, ≥16 points 0.536±0.273＜0.001<18.5 kg/m2 0.213±0.259, ≥18.5 kg/m2 0.411±0.294
JCS 0-3 0.396±0.293，JCS 10-30 0.205±0.291
BRS I-II 0.326±0.294，BRS III-IV 0.428±0.288，BRS V-VI
0.438±0.296
Absent 0.432±0.307, present 0.290±0.258
Absent 0.388±0.295, present 0.364±0.301
Unstable 0.327±0.291, stable 0.552±0.250<6 units/d 0.207±0.226, ≥6 units/d 0.414±0.298<118 d 0.349±0.301, ≧118 d 0.406±0.292＜0.001＜0.01＜0.05**＜0.05
0.57＜0.001＜0.001
0.11

Numerical value, mean±standard deviation of motor FIM effectiveness; p value, comparison between stratified
groups (Mann-Whitney U test or Kruskal-Wallis test); <0.01*, significant between mRS 0-1 and mRS 2-3, between
mRS 0-1 and 4-5; <0.05**, significant between BRS I-II and BRS V-VI.
Table 3. Stepwise regression amalysis with motor FIM score at discharge as the objective variable.

Age
Cognitive FIM at admission
Motor FIM at admission
Number of days from onset to admission
Modified Rankin Scale (mRS) before onset
Brunnstrom stage of paralyzed lower limb
Body mass index (BMI)
Sitting stability
2-digit dummy of Japan Coma Scale (JCS)
Hemispatial neglect

Standard partial
coefficient β

Partialcoefficient B

Standard error

F value-0.3810.298
0.235-0.200-0.135
0.108
0.095
0.089
-0.088-0.058-0.6910.909
0.634-0.591-2.351
1.547
6.085
5.018
-7.228-2.845

0.071
0.146
0.148
0.112
0.692
0.647
2.440
2.475
3.216
1.987

94.5
38.9
18.2
27.7
11.5
5.7
6.2
4.1
5.1
2.0

Constant: 72.0, p value of the prediction formula: <0.001, coefficient of determination R2: 0.707. The explanatory
variables are aranged in descending order of the standard partial regression coefficient β.
The predicted value for motor FIM score at discharge = - 0.691 × age+0.909 × cognitive FIM score at admission +0.634 × motor FIM score at admission - 0.591 × number of days from onset to admission - 2.351 × mRS before
onset + 1.547 × Brunnstrom stage + 6.085 × BMI (<18.5 kg/m2: 0, ≥18.5 kg/m2: 1) + 5.018 × sitting stability(unstable: 0, stable: 1) - 7.228 × two-digit dummy of JCS (0and 1-digit: 0, 2-digit: 1) - 2.845 × hemispatial
neglect (absent: 0, present: 1).
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and coefficient of determination with adjusted
degrees of freedom was 0.694. Of the 12 explanatory
variables, 10 variables, excluding stroke type andtraining time, were selected as valid explanatory
variables.
The absolute value of the standard partial
regression coefficient β was large in the following
order: age, cFIM at admission, mFIM at admission,
number of days from onset to admission, mRS
before onset, Brunnstrom stage of paralyzed
lower limb, BMI, sitting stability, 2-digit dummyof JCS, and hemispatial neglect.
Discussion

This study set 17 factors as candidates for the
explanatory variables: 9 factors frequently usedin multiple regression analyses predicting FIM
improvement in stroke, 6 recommended by theJapanese Society of Rehabilitation Medicine, and2 useful for predicting outcomes for the low
mFIM group. Twelve factors, which differedsignificantly in mFIM effectiveness between thestratified groups, were used as explanatory variablesin the stepwise regression analysis, and 10 wereselected as valid explanatory variables. We
clarified that the order of explanatory variables
with a large standard partial regression coefficientβ was age, cFIM at admission, mFIM at admission,
number of days from onset to admission, mRS
before onset, Brunnstrom stage of paralyzed
lower limb, BMI, sitting stability, 2-digit dummyof JCS, and hemispatial neglect.
The main features of this study were as
follows: 1) it focused on patients with an mFIMof less than 40 points at admission, 2) it objectively
selected explanatory variables that should be
used in a multiple regression analysis, and 3) itrevealed the order of explanatory variables with alarge standard partial regression coefficient β.
These points are discussed below.
1. Reasons for limiting the target to patients withan mFIM score of less than 40 points at admission

The magnitude of the effect of factors on mFIM
improvement varies depending on the patient
population. In other words, the influence of
inhibiting factors is not uniform, but instead differs
according to the degree of activities of daily living(ADL) at admission [12, 20]. Therefore, it isnecessary to stratify patients. Although methods
have been reported to improve prediction
accuracy in the high mFIM group [4-6], thesemethods were not effective in the low mFIM
group [8]. In this study, we aimed to improve theprediction accuracy of the low mFIM group by
using appropriate explanatory variables.

2. Objective selection of explanatory variables thatshould be used in multiple regression analysis

There are many factors which inhibit
rehabilitation. A review by Hasegawa [21]confirmed as many as 60 factors. Kwakkel et al.
[22] reported that valid predictors for functional
recovery after stroke were age, previous stroke,
urinary continence, consciousness at onset,
disorientation in time and place, severity ofparalysis, sitting balance, admission ADL score,level of social support, and metabolic rate of
glucose outside the infarct area in hypertensive
patients. In a multiple regression analysis, thenumber of patients should be more than 10 or 15
times the number of explanatory variables [23].
Therefore, the number of explanatory variables
must be restricted in studies with a limited numberof patients. The factors that the authors considerednecessary were used as explanatory variables;
thus, the explanatory variables differed greatly
depending on the report [9, 10]. This study
proposes ten factors that were objectively selected
as a set of explanatory variables that should be
used in multiple regression analyses predicting
mFIM improvement in stroke.
The 10 explanatory variables to be used may
seem too few. However, a review of 19 reports ofmultiple regression analyses predicting FIM
improvement in stroke indicated that while eachused 4-18 (median 7.5) explanatory variables,
only 1-8 (median 4) were significant [10]. The 10
explanatory variables comprise the basic set, andresearchers are free to add new factors that theywould like to examine.
3. Order of standard partial regression coefficient β

In a review of 16 reports of multiple regression
analyses predicting FIM improvement in stroke,
the standard partial regression coefficient βtended to be larger in mFIM at admission, cFIM
at admission, and age, but the order differed foreach report [9]. In this study, β was the largest in
the order of age, cFIM at admission, and mFIM at
admission. The β of age was the largest, implyingthat age had the largest effect on mFIM improvement.
In a decision tree analysis with mFIM score atdischarge as the objective variable, trunk function
affected outcomes in patients with mFIM scores ofless than 19 points at admission, cognitive function
affected outcomes in those with 31-53 points, andage affected outcomes in those with less than 54
points [12]. Since our study limited patients to
those with an mFIM score of less than 40 points
at admission, the effect of age might be more
pronounced than in previous studies targeting all
patients.

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Frequently used explanatory variables andnecessary explanatory variables

A comparison of the 9 explanatory variables
frequently used in the reviewed 35 reports ofmultiple regression analyses predicting FIM
improvement in stroke [9, 10] and 10 explanatory
variables used in this study shows that 7
variables—age, cFIM at admission, mFIM at
admission, number of days from onset toadmission, mRS before onset, Brunnstrom stageof paralyzed lower limb, and BMI—werecommon.
On the other hand, length of hospital stay andtraining time were only included in the former
reviews [9, 10], and JCS, sitting stability, andhemispatial neglect only in the latter (present
study).
Because patients with a longer hospital staytended to be more severely affected, previous
studies targeting all patients associated a longer
hospital stay with poor mFIM improvement. On
the other hand, there was no difference in mFIM
effectiveness between the two groups divided by
the length of hospital stay in this study, which
focused on the low mFIM group.
Regarding training time, 9 units (3 hours) per
day of rehabilitation is allowed for stroke patients
under the age of 85 years in Kumamoto Prefecture.
However, for patients aged more than 85 years,
the upper limit is 6 units (2 hours). Therefore, thetraining time depends on age. Accordingly, we
conducted an additional study focusing on
patients aged less than 85 years. Training time
was not selected as a valid explanatory variable.
A retrospective study cannot reveal the relationshipbetween training time and mFIM improvement; it
can only reveal the relationship between “whythis patient was prescribed this training time” andmFIM improvement. To accurately evaluate therelationship between training time and mFIM
improvement, it is necessary to conduct a
prospective study in which a training time of 1 to
9 units per day is randomly assigned.
Regarding JCS, sitting stability, and hemispatial
neglect, in a review of 35 reports using multiple
regression analyses predicting FIM improvement
in stroke, hemispatial neglect was used in one
study, but JCS and sitting stability were not used
at all [10]. It is hoped that these three factors will
be frequently used in multiple regression analyses
in the future.
Difficulty in predicting mFIM score at dischargeusing only admission data

FIM may dramatically improve in patients who
have inhibiting factors for rehabilitation such as

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impaired consciousness or total aphasia at thetime of admission and whose symptoms improveafter admission [24]. Therefore, comorbidities
may be a predictor of a low mFIM score atdischarge (poor improvement) and of a highmFIM score at discharge (good improvement).
Since there is a limit to accurately predicting
mFIM score at discharge using only data obtainedat the time of admission, some studies added
mFIM improvement at two weeks [25] or one
month [26] to the explanatory variables, and thus
improved the prediction accuracy of the mFIM
score at discharge.
Conclusion

This study identified 10 explanatory variables
that should be used in multiple regression
analyses to predict mFIM improvement in stroke.
It is hoped that other useful explanatory variables
not studied in this research will be added to thisset in the future to further improve the prediction
accuracy of multiple regression analyses.
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