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Japanese Journal of Comprehensive Rehabilitation Science (2020)

Original Article

Comparison of the accuracy of multiple regression analysis using
four methods to predict the functional independence measure atdischarge
Makoto Tokunaga, MD, PhD,1 Hiroaki Yamanaga, MD, PhD1
Department of Rehabilitation Medicine, Kumamoto Kinoh Hospital, Kumamoto, Japan

1

ABSTRACT
Tokunaga M, Yamanaga H. Comparison of the accuracyof multiple regression analysis using four methods
to predict the functional independence measure atdischarge. Jpn J Compr Rehabil Sci 2020; 11: 65-72.
Objective: This study aims to compare the accuracyof four methods of multiple regression analysis inpredicting the motor functional independence measure(mFIM) at discharge.
Methods: The subjects of this study were 1,064 stroke
patients who had been hospitalized in a convalescentrehabilitation hospital. Standard multiple regression
analysis (S prediction) with mFIM at discharge as theobjective variable, multiple regression analysis withreciprocal number of mFIM at admission as one of the
explanatory variables (R prediction), prediction of theeffectiveness of mFIM by multiple regression analysis,
the conversion to mFIM at discharge (E prediction),and the creation of two multiple regression prediction
formulas (S2 prediction) were performed. The absolutevalues of residuals (actual value minus predictedvalue) of mFIM at discharge were compared for thefour methods.
Results: The absolute value of the residuals was
significantly smaller in the R prediction, E prediction,and S2 prediction than that in the S prediction. In
addition, the absolute value was found to besignificantly smaller in the E prediction and S2
prediction than that in the R prediction.
Conclusion: In multiple regression analysis, the useof E prediction or S2 prediction is recommended
because of their high prediction accuracies.
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: April 6, 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.11.65

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Key words: multiple regression analysis, prediction
accuracy, reciprocal number, FIM effectiveness,
multiple prediction formulas
Introduction
Prediction of outcome is important for planning andexecuting treatment plans during rehabilitation.
Multiple regression analysis aims to not only predict
outcomes such as functional independence measure(FIM) [1] at discharge and FIM gain (FIM at dischargeminus FIM at admission) but also identify the factors
affecting the outcome. Many previous reports haveused multiple regression analysis [2‐4].
However, the accuracy of prediction by multiple
regression analysis is not as high as expected. Meyer
et al. [4] studied multiple regression analysis andreported that the coefficient of determination (R2),which means the extent to which the explanatory
variables can explain the objective variable, was anaverage of 0.65 (minimum 0.35 to maximum 0.82) inthe prediction of FIM at discharge. In the prediction of
FIM gain, R2 was found to be an average of 0.22
(minimum 0.08 to maximum 0.4). The reasons for the
low accuracy of prediction by multiple regression
analysis are as follows. 1) Multiple regression analysis
assumes that there is a linear relationship between the
explanatory variables and objective variable, but thisis not always true. 2) Since the FIM gain has a ceiling
effect (meaning that the FIM gain is small for patientswith high FIM scores at admission), the effect offactors on FIM gain is strongly affected by FIM scoresat admission. 3) Multiple regression analysis is amethod of adding the effects of factors. 4) Factors
other than those used for explanatory variables affect
FIM at discharge [5].
To improve the accuracy of prediction of motor
FIM (mFIM) at discharge by multiple regression
analysis, three methods can be used: 1) converting themFIM at admission to a reciprocal number (1/mFIM at
admission) and using it as one of the explanatory
variables [6], 2) predicting the effectiveness of mFIM
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by multiple regression analysis and converting it tomFIM at discharge [7], and 3) creating two prediction
formulas using the data of patients with low and highmFIM at admission [8, 9]. These methods have beenfound to have a higher accuracy than that of standard
multiple regression analysis. However, a comparisonof the accuracy of prediction by these three methods
has not been made.
Wada et al. [10] compared the accuracy of predictionof the standard multiple regression analysis (Sprediction) method, the method of converting the mFIM
at admission to a reciprocal number (R prediction), andthe method of predicting the effectiveness of mFIM by
multiple regression analysis and then converting it to
the mFIM at discharge (E prediction). The absolutevalue of the residuals (actual value minus predictedvalue) of mFIM at discharge was significantly smallerin the R prediction (7.30 ± 6.56) and E prediction(7.56 ± 6.45) than that in the S prediction (9.38 ± 6.62)[10]. However, Wada et al. [10] did not investigate theaccuracy of prediction of the method of creating two
prediction formulas (S2 prediction).
In this study, we performed S prediction, R
prediction, E prediction, and S2 prediction to determine
the method with the highest prediction accuracy bycomparing the absolute values of the residuals of thefour methods.
Subjects and methods
The subjects consisted of stroke patients who had
been discharged from the convalescent rehabilitation
ward in K hospital between April 1, 2013 and March
31, 2019. The following patients were excluded toeliminate the effects of exceptional patients: thosewith subarachnoid hemorrhage, those who had been
admitted within 4 d or more than 60 d after onset,
those who had spent less than 30 d or more than 180 din the hospital, those with mFIM score of 91 points at
admission, and those with mFIM gain of less than 0
point. A total of 1,064 patients were included in thepresent study.
1. S prediction, R prediction, and E prediction
Similar to previous studies [7, 10], age, number ofdays from onset to admission, mFIM at admission,
cognitive FIM at admission, sex, and type of stroke were
defined as the explanatory variables in the S prediction.
Sex and type of stroke were defined as the dummy
variables (male 0, female 1, cerebral hemorrhage 0,
cerebral infarction 1). Multiple regression analysis using
the forced input method was performed. The mFIM
at discharge was defined as the objective variable. In the
R prediction, “1/mFIM at admission” was defined as
one of the explanatory variables instead of mFIM at
admission [6]. In the E prediction, the same explanatory
variables as those in the S prediction were defined, while
mFIM effectiveness was defined as the objective variable

where mFIM effectiveness = mFIM gain/(91 points mFIM score at admission) [11]. Therefore, FIM gain
was expressed by the equation: FIM gain = mFIM
effectiveness × (91 points - mFIM score at admission),and the mFIM at discharge was described by theequation: mFIM at discharge = mFIM gain + mFIM at
admission. Therefore, the predicted value of mFIM atdischarge was obtained using the formula: mFIM atdischarge = predicted value of mFIM effectiveness × (91points - mFIM score at admission) + mFIM score atadmission [7].
2. S2 prediction
The median mFIM gain of stroke patients in theconvalescent rehabilitation ward was found to have aconvex shape with a peak of approximately 40 points
of mFIM at admission [12]. Therefore, mFIM at
admission was divided into two groups: 13‐39 points(low mFIM group) and 40‐90 points (high mFIM
group). Multiple regression analysis was performed in
the S2 prediction, and two prediction formulas werecomputed using the patients’ data of the low mFIM
group and the high mFIM group (S2 prediction).
3. Comparison of absolute values of the residuals
To compare the accuracy of the prediction formulas,
we investigated the absolute values of the residuals of
mFIM at discharge similar to the previous study by
Wada et al. [10]. In the four prediction methods (i.e., S,
R, E, and S2 predictions), the absolute values of theresiduals were obtained not only for all patients but also
for the low and high mFIM groups. The main statistical
tool used was the Kruskal-Wallis test, and when there
was a significant difference, multiple comparisons weremade using the Steel-Dwass method. The significancelevel was found to be less than 5%.
This study complied with the regulations of theClinical Research Ethics Committee of the authors’
hospital (approval number: JMC302-1936). All
personal data were processed in a manner that
protected the anonymity of the subjects. The statisticalsoftware used was 4 Steps Excel Statistics [13].
Results
Table 1 shows the basic attribute data of the 1,064
target patients with 430 patients in the low mFIM at
admission group and 634 patients in the high mFIM at
admission group. The median mFIM effectiveness is0.336 in the low mFIM group and 0.750 in the highmFIM group. The median mFIM gain is 23 points inthe low mFIM group and 18 points in the high mFIM
group, which is smaller than that in the low mFIM
group due to the ceiling effect.
Table 2 shows the prediction formula for the multiple
regression analysis. R2 is 0.813 for R prediction, 0.757
for S prediction, 0.522 for E prediction, and 0.621 forthe low mFIM group and 0.540 for the high mFIM

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group in the S2 prediction. Thus, R2 was the highest in
the R prediction.

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Figure 1 shows the relationship between the measured
and predicted values of mFIM at discharge. The absolute

Table 1. The basic attribute data of the subjects.
Target patients
Number of patients
1,064
Infarction, hemorrhage
400, 664
Sex
Male 618, female 446
Age69.7±13.6 (71)
Number of days from onset to admission 17.8±9.7 (15)
Number of days in hospital
90.0±37.6 (89)Motor FIM score at admission
46.5±24.5 (47)Cognitive FIM score at admission
22.7±8.9 (24)Motor FIM score at discharge
67.4±24.2 (77)Cognitive FIM score at discharge
26.8±8.1 (29)Motor FIM gain
20.9±15.1 (19)Motor FIM effectiveness0.565±0.309 (0.631)

Low mFIM group

High mFIM group

430
213, 217
Male 236, female 194
72.8±13.0 (75)19.2±9.9 (17)112.9±31.4 (116.5)
21.0±8.7 (17)15.6±7.8 (14.5)45.4±22.9 (43.5)
20.9±8.6 (21)24.4±18.7 (23)0.365±0.284 (0.336)

634
187, 447
Male 382, female 252
67.7±13.7 (69)16.8±9.5 (14)74.4±33.1 (68.5)
63.8±14.6 (63)27.5±5.9 (29)82.3±8.8 (85)30.8±4.7 (32)18.5±11.3 (18)0.701±0.244 (0.750)

Abbreviation: FIM, Functional Independence Measure.
Data for this study are expressed as number of patients or mean±standard deviation (median value).
Low mFIM group, mFIM at admission of 13‐39 points; high mFIM group, mFIM at admission of 40‐90 points.
Table 2. The prediction formula for the multiple regression analysis.
Motor FIM score at admission
Number of patients
Explanatory variables
Age
Days from onset to admission
Motor FIM score at admission
1 / motor FIM score at admission
Cognitive FIM score at admission
Sex (male 0, female 1)
Stroke type (hemorrhage 0, infarction 1)
Constants
Coefficient of determination R2

S prediction R prediction E prediction
13‐90 points 13‐90 points 13‐90 points

S2 prediction
13‐39
points40‐90
points

1,064

1,064

1,064

430

634

-0.299-0.233
0.547
―
0.799
-1.551-2.22650.8
0.757-0.322-0.229―-738.354
0.411-1.497-1.800110.2
0.813-0.00664-0.00490
0.00333―
0.01054-0.04798-0.03719
0.765
0.522

-0.619-0.400
0.992
―
0.783
-3.854-0.34367.1
0.621-0.147-0.116
0.331
―
0.233
-1.362-2.00768.6
0.540

Numerical value, partial regression coefficient.
The predicted value for mFIM at discharge in S prediction = -0.299 × age -0.233 × days from onset to admission + 0.547
× mFIM at admission + 0.799 × cognitive FIM at admission -1.551 × (male 0, female 1) -2.226 × (hemorrhage 0,
infarction 1) + 50.8.

Figure 1. Scatter diagram.
Dot, Each patient; horizontal axis, measured value of motor FIM at discharge; vertical axis, predicted value ofmotor FIM at discharge.
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Tokunaga M et al.: Comparison of prediction accuracy of multiple regression analysis

Figure 2. Comparison of residuals between predictions.
Box, 25%tile to 75%tile; horizontal bar, median; ×,
mean.
value of the residuals of mFIM at discharge was 9.4 ± 7.4(median 7.8) for S prediction, 7.8 ± 6.9 (median 6.0) for
R prediction, 7.2 ± 7.1 (median 5.0) for E prediction, and
7.2 ± 7.0 (median 5.0) for S2 prediction, showing asignificant difference among the four methods. Multiple
comparison analysis shows significant differences
between S prediction and R prediction/E prediction/S2
prediction and between R prediction and E prediction/S2
prediction (Figure 2).
Figure 3 shows the relationship between themeasured and the predicted values of mFIM atdischarge, divided into the low mFIM group (13‐39
points) and high mFIM group (40‐90 points). In the
low mFIM group, the absolute value of the residualsof mFIM at discharge is 13.0 ± 8.6 (median 12.0) for
S prediction, 11.5 ± 8.6 (median 9.4) for R prediction,
11.6 ± 8.3 (median 10.2) for E prediction, and 11.2 ±
8.5 (median 9.4) for S2 prediction, showing significant
differences among the four methods. Multiple
comparison analysis shows significant differences
between S prediction and R prediction/S2 prediction(Figure 4a).
In the high mFIM group, the absolute value of theresiduals of mFIM at discharge is 6.9 ± 5.2 (median
5.8) for S prediction, 5.4 ± 4.0 (median 4.6) for R
prediction, 4.2 ± 4.0 (median 2.9) for E prediction, and
4.5 ± 4.0 (median 3.4) for S2 prediction, showing asignificant difference among the four methods.
Multiple comparison analysis shows significant
differences between S prediction and R prediction/E
prediction/S2 prediction and between R prediction andE prediction/S2 prediction (Figure 4b).
Discussion
R2 is often used as an indicator of the accuracy of aprediction equation. However, it cannot be concluded
that the accuracy of prediction is as high as that of theprediction equation with a high R2 described in the
study. This is because 1) the accuracy of prediction is
not always high in groups other than the target groupand 2) R2 is not always the most precise indicator of theaccuracy of prediction. Regarding the former, it isnecessary to evaluate the external validity of theprediction formula [14]. For the latter, R2 is 0.65 on
average when FIM at discharge is the objective variable
and higher than the average of 0.22 when FIM gain is
the objective variable [4]. Since mFIM at discharge =mFIM at admission + mFIM gain, mFIM at discharge
with high R2 was predicted by multiple regression
analysis, and the mFIM at admission was subtracted
from the predicted value of mFIM at discharge to obtain
the predicted value of mFIM gain. The correlation
between the measured and the predicted value of mFIM
gain obtained by this method was the same as that ofwhen the mFIM gain was predicted directly by multiple
regression analysis [15]. That is, when mFIM atdischarge is the objective variable, R2 is large only inappearance, and the prediction accuracy of mFIM atdischarge and the prediction accuracy of mFIM gain are
the same. Furthermore, when mFIM effectiveness was
the objective variable, R2 was 0.54, which was smaller
than the R2 of 0.77 when mFIM at discharge was theobjective variable [7]. Further, when the predicted valueof mFIM at discharge was calculated using the formula:
mFIM at discharge = predicted mFIM effectiveness ×(91 points - mFIM at admission) + mFIM at admission,
the correlation coefficient between the measured value
and the predicted value of mFIM at discharge was ashigh as 0.916, which was higher than the correlation
coefficient of 0.878 when mFIM at discharge waspredicted directly by multiple regression analysis [7].
That is, the accuracy of prediction by multiple regression
analysis using mFIM effectiveness as the objective
variable is higher than that when using mFIM atdischarge as the objective variable. This indicates thatthe accuracy of prediction cannot be evaluated correctly
using R2. Thus, Wada et al. [10] compared the accuracyof the prediction formulas with the absolute value of theresiduals obtained by subtracting the predicted value
from the measured value of the mFIM at discharge. We
used the same method in this study.
The findings of this study indicated that the accuracyof R prediction, E prediction, and S2 prediction was
significantly higher than that of the standard S
prediction, and the accuracy of E prediction and S2
prediction was significantly higher than that of R
prediction. Therefore, we recommend using E
prediction or S2 prediction in multiple regression
analysis for the accurate prediction of mFIM atdischarge.
The accuracy of R prediction and E prediction was
significantly higher than that of the standard S
prediction, which is in good agreement with the

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Figure 3. Scatter diagram divided into the low mFIM group and high mFIM group.
Horizontal axis, Measured value of mFIM at discharge; Vertical axis, Predicted valueof mFIM at discharge.
Low mFIM, mFIM at admission of 13‐39 points; High mFIM, mFIM at admission of
40‐90 points.
findings of Wada et al. [10]. Wada et al. [10] concluded
that the accuracy of R prediction and E prediction was
higher than that of S prediction because the ceiling
effect was corrected in the R prediction and E
prediction methods [10]. The ceiling effect implies
that the mFIM gain is low for patients with a highmFIM at admission. In S2 prediction, the partial
regression coefficient of mFIM at admission is 0.992
in the low mFIM group and 0.331 in the high mFIM
group (Table 2). This is because mFIM gain has aconvex shape with a peak of approximately 40 points
of mFIM at admission [12]. When plotting mFIM at
admission on the horizontal axis and mFIM atdischarge on the vertical axis, if mFIM gain is 0 points
for all patients, the mFIM at discharge is the hypotenuseof a right-angled isosceles triangle. When the mFIM
gain, which has a peak of approximately 40 points of

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mFIM at admission, was added to this hypotenuse, thepartial regression coefficient of mFIM at admission
increased to 0.992 in the low mFIM group. This meansthat mFIM at discharge increases by 0.992 points as
mFIM admission increases by one point. Moreover, inthe high mFIM group, which has a ceiling effect, thepartial regression coefficient of mFIM at admission
was as small as 0.331. In the case of S prediction,
which only computed one prediction formula, thepartial regression coefficient of mFIM at admission
was 0.547, which is an intermediate value between
0.992 and 0.331. In this case, the predicted mFIM atdischarge becomes too large for patients with mFIM
at admission of approximately 90 points in the S
prediction (Figure 3). In R prediction, the reciprocal ofmFIM at admission is close to 0; therefore, thepredicted value of mFIM at discharge in the high69

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Figure 4. Comparison of residuals divided by low and high mFIM groups.
mFIM group does not become too large. The E
prediction uses the formula: mFIM at discharge =predicted value of mFIM effectiveness × (91 points mFIM score at admission) + mFIM score at admission.
In the high mFIM group, 91 points - mFIM score atadmission is close to 0. Therefore, the predicted valueof mFIM at discharge in the high mFIM group does
not become too large in the E prediction.
In this study, unlike the report of Wada et al. [10],the accuracy of E prediction was found to besignificantly higher than that of R prediction. To
investigate this difference in the accuracy of prediction,
we stratified mFIM at admission into a low mFIM
group and a high mFIM group. In the low mFIM
group, there was no significant difference in theaccuracy of R prediction and E prediction, whereas in
the high mFIM group, the accuracy of E prediction
was significantly higher than that of R prediction.
Therefore, when the target patients include many highmFIM patients, a significant difference was detected
between E prediction and R prediction. When thetarget patients included many low mFIM patients,
there was no significant difference between E
prediction and R prediction.
Previous studies have shown that S2 prediction has
higher prediction accuracy than that of the standard S
prediction [8, 9, 15]. However, the previous studies
did not compare the accuracy of S2 prediction, R
prediction, or E prediction. This study revealed that
there was no significant difference between S2
prediction and E prediction, but S2 prediction was
found have a significantly higher accuracy than R
prediction.
The factors that should be stratified when creating
multiple prediction formulas include the mFIM at
admission and the cognitive FIM at admission [15].

Age, modified Rankin Scale before onset, and numberof days from onset to admission can be inputted as
explanatory variables without stratification [15].
Explanatory variables that should be stratified, such as
mFIM at admission, are variables that have a strong
influence on the objective variable and lack a linear
relationship with the objective variable. Anotherreason for creating multiple prediction formulas is thatthe magnitude of the effect of explanatory variables on
mFIM at discharge varies with the patient group. Thisis because rehabilitation inhibitors do not affect all
patients uniformly [16, 17]. However, if too many
prediction formulas are created, the analysis becomescomplicated.
Although we did not examine which factors should
be used as explanatory variables in this study, it isextremely important to select appropriate explanatory
variables to improve the accuracy of prediction bymultiple regression analysis [4, 18].
In most of the previous reports using multiple
regression analysis, the standard method (S prediction)
was selected. Notably, the prediction results obtainedby methods with low accuracy are inevitably
unreliable. Hence, the prediction accuracy of multiple
regression analysis must be improved. Moreover, it isnecessary to identify a method with a high accuracy of
prediction by directly comparing the accuracy of theselected prediction methods.
The limitations of this study are as follows. First,
we excluded patients with a hospital stay of less than
29 days, more than 181 days, and a negative mFIM
gain to eliminate the effects of exceptional patients.
However, this information was not obtained at thetime of admission. A review of multiple regression
analysis predicting FIM improvement in stroke
patients admitted to convalescent rehabilitation wards

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Figure 5. Comparison of residuals in six prediction formulas.
Significant differences were observed between S and R/E/S2/E2, between R and E/S2/R2/E2, and between S2 and E2.
in Japan showed that, in one study, the purpose of
performing multiple regression analysis was tocompute a prediction formula and, in another 18
studies, the purpose was to investigate the influence offactors on FIM improvement [18]. In the first study,
the data obtained at the time of admission were definedas the explanatory variables. In contrast, in the 18
studies, the data defined as the explanatory variables
included the length of hospital stay and nutritional
improvement [18]. The second limitation of this study
is that in R prediction and E prediction, even if two
prediction formulas are computed (R2 prediction andE2 prediction), the accuracy of prediction does not
improve significantly (Figure 5). This indicates that
there are limitations when various methods are
combined to reduce the ceiling effect. The third
important limitation of this study is that although theprediction accuracy was improved by reducing theceiling effect by R prediction, E prediction, and S2
prediction in the high mFIM group, these methods had
no effect on the low mFIM group. Thus, other methods,
such as using appropriate explanatory variables, arenecessary.

References

1. Data management service of the Uniform Data System
for Medical Rehabilitation and the Center for Functional
Assessment Research: Guideline for use of the Uniform
Data Set for Medical Rehabilitation. Version 3.1, State
University of New York at Buffalo, Buffalo, 1990.
2. Heinemann AW, Linacre JM, Wright BD, Hamilton BB,
Granger C. Prediction of rehabilitation outcomes withdisability measures. Arch Phy Med Rehabil 1994; 75:
133‐43.

Jpn J Compr Rehabil Sci Vol 11, 2020

CW6_A4285D02_E.indd

3. Chumney D, Nollinger K, Shesko K, Skop K, Spencer
M, Newton RA. Ability of Functional Independence
Measure to accurately predict functional outcome ofstroke-specific population: systematic review. J Rehabil
Res Dev 2010; 47: 17‐29.
4. Meyer MJ, Pereira S, McClure A, Teasell R, Thind A,
Koval J, et al. A systematic review of studies reporting
multivariable models to predict functional outcomes after
post-stroke inpatient rehabilitation. Disabil Rehabil 2015;
37: 1316‐23.
5. Tokunaga M, Hashimoto Y, Watanabe S, Nakanishi R,
Yamanaga H, Yonemitsu K, et al. Methods for improving
the predictive accuracy using multiple linear regression
analysis to predict the improvement degree of Functional
Independence Measure for stroke patients. Int J Phys Med
Rehabil 2017; 5: 414.
6. Sonoda S, Saitoh E, Nagai S, Okuyama Y, Suzuki T,
Suzuki M. Stroke outcome prediction using reciprocal
number of initial activities of daily living status. J stroke
Cerebrovasc Dis 2005; 14: 8‐11.
7. Tokunaga M, Watanabe S, Sonoda S. A method of
calculating Functional Independence Measure at discharge
from Functional Independence Measure effectivenesspredicted by multiple regression analysis has a highdegree of predictive accuracy. J Stroke Cerebrovasc Dis
2017; 16: 1923‐8.
8. Sonoda S, Saitoh E, Domen K, Chino N. Prognosticationof stroke patients using the Stroke Impairment Assessment
Set and the Functional Independence Measure. In: Chino
N, Melvin JL, eds. Functional Evaluation of Stroke
Patients. 1st ed. Tokyo: Springer-Verlag Tokyo; 1996. p.
103‐14.
9. Tokunaga M, Ikeda Y, Inoue M, Kodama J, Sakamoto
M, Nagatomo M, et al. Multiple regression analysis

71

2020/05/18

10:37:35

72

Tokunaga M et al.: Comparison of prediction accuracy of multiple regression analysis

stratified by age and FIM at admission. J Clin Rehabil
2015; 24: 828‐34. Japanese.
10. Wada Y, Sonoda S, Okamoto S, Watanabe M, Okazaki
H, Okuyama Y. Comparison of prediction accuracy of thetotal score of FIM motor items at discharge in post-stroke
patients in a Kaifukuki rehabilitation ward. Jpn J Compr
Rehabil Sci 2019; 10: 71‐6.
11. Koh GCH, Chen CH, Petrellia R, Thind A. Rehabilitation
impact indices and their independent predictors; asystematic review. BMJ Open 2013: 3(9): e003483.
12
. Tokunaga M, Tokunaga A, Imada Y, Sannomiya K,
Nojiri S, Watanabe S, et al. Deviation value of FIM gain.
J Clin Rehabil 2017; 26: 97‐103. Japanese.
13. Yanai H. Statcel, the useful addin forms on Excel, 4thed. OMS publishing, 2016. p. 1‐309. Japanese.
14. Tokunaga M, Sannomiya K, Nakanishi R, Yonemitsu H.
The external validity of multiple regression analyses
predicting discharge FIM score in patients with stroke
hospitalized in Kaifukuki rehabilitation wards. Jpn J
Compr Rehabil Sci 2015; 6: 14‐20.

15. Tokunaga M, Tori K, Eguchi H, Kado Y, Ikejima Y,
Ushijima M, et al. The stratification of motor FIM andcognitive FIM and the creation of four prediction formulas
to enable higher prediction accuracy of multiple linear
regression analysis with motor FIM gain as the objective
variable. Jpn J Compr Rehabil Sci 2017; 8: 21‐9.
16. Okamoto S, Sonoda S, Watanabe M, Okazaki H, Yagihashi
K, Okuyama Y. Relationship between Functional
Independence Measure (FIM) score on admission andinfluence of inhibitive factors in a comprehensive inpatient
stroke rehabilitation ward. Jpn J Compr Rehabil Sci 2018;
9: 59‐65.
17. Tokunaga M, Taniguchi M, Nakakado K, Mihono T,
Okido A, Ushijima T, et al. Assessment of the effects offactors in stroke rehabilitation using eight multiple
regression analyses. Jpn J Compr Rehabil Sci 2015; 6:
78‐85.
18. Tokunaga M. Review of multiple regression analysis forstroke patients hospitalized in Kaifukuki rehabilitation
wards. J Clin Rehabil (in press). Japanese.

Jpn J Compr Rehabil Sci Vol 11, 2020

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