16

Japanese Journal of Comprehensive Rehabilitation Science (2017)

Original Article

Increasing the prediction accuracy of FIM gain by adding FIM
improvement for one month from admission to the explanatory
variables in multiple regression analyses
Makoto Tokunaga, MD, PhD,1 Kenichi Katsura, MD,1 Kaori Tokisato, MD,1 Shoji Honda, MD,1
Toshihito Nakanishi, MD,1 Seiko Takai, MD,2 Yukihiko Nakashima, OT,3 Shinichi Nojiri, PT,4
Susumu Watanabe, MD, PhD1
Department of Rehabilitation, Kumamoto Kinoh Hospital, Kumamoto, Japan
Department of Orthopedic Surgery, Kumamoto Kinoh Hospital, Kumamoto, Japan3
Department of Occupational Therapy, Kumamoto Kinoh Hospital, Kumamoto, Japan
4
Department of Physical Therapy, Seigaen Geriatric Health Facility, Kumamoto, Japan1
2

ABSTRACT
Tokunaga M, Katsura K, Tokisato K, Honda S, Nakanishi
T, Takai S, Nakashima Y, Nojiri S, Watanabe S. Increasing
the prediction accuracy of FIM gain by adding FIM
improvement for one month from admission to the
explanatory variables in multiple regression analyses.
Jpn J Compr Rehabil Sci 2017; 8: 16-20.
Objective: The coefficient of determination in multiple
linear regression analyses using the gain in Functional
Independence Measure (FIM) as objective variables islow. We aimed to improve the prediction accuracy of
FIM gain by adding FIM improvement for one monthfrom admission to the explanatory variables.
Methods: A total of 547 stroke patients admitted to a
Kaifukuki (convalescent stage) rehabilitation ward
were included. In multiple regression analyses using
motor FIM gain as the objective variable, we created a
prediction formula using only data available atadmission (model 1), and a prediction formula adding
FIM improvement for one month from admission(model 2). The coefficient of determination adjusted
for the degrees of freedom R*2 and the residuals
obtained by subtracting the predicted value from themeasured value of motor FIM gain were investigated.
Results: The R*2 of model 1 was 0.364 and that ofmodel 2 was 0.711. The residual of model 1 was 0 ±12.3 and that of model 2 was 0 ± 8.3. In model 2, thestandard deviation of the residual was reduced.
Correspondence: Makoto Tokunaga, MD, PhD
Department of Rehabilitation, Kumamoto Kinoh Hospital,
6-8-1 Yamamuro, Kita-ku, Kumamoto 860-8518, Japan.
E-mail: tokunaga@juryo.or.jp
Accepted: February 9, 2017.
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 2017
doi.org/10.11336/jjcrs.8.16

Conclusion: Adding FIM improvement for one monthto the explanatory variables increased the prediction
accuracy of FIM gain.
Key words: FIM gain, multiple linear regression
analysis, one month from admission, explanatory
variable, stroke
Introduction
Some reports have predicted activities of daily living(ADL) at discharge and ADL gain (discharge ADL admission ADL) using multiple linear regression
analyses based on a patient’s basic attributes and ADL
at admission. In Meyer et al.’s review of such reports[1], the coefficient of determination R2 (how well the
explanatory variables can explain the objective variable)of the prediction formula using Functional Independence
Measure (FIM) at discharge as the objective variable
was on average 0.65 (minimum 0.35 to maximum 0.82),
whereas the R2 of the prediction formula with FIM gainas the objective variable was on average as small as
0.22 (0.08 to 0.4).
Patients admitted to rehabilitation hospitals with an
FIM score of 18 points were divided into patients whose
discharge FIM score remained at 18 points (FIM gain of
0 points) and patients who acquired large FIM gains. In
order to accurately predict this difference, the authors
considered introducing a number of factors influencing
FIM gain into the explanatory variables. In Meyer etal.’s review of 27 reports [1], 126 factors were inputted,of which 63 were significant explanatory variables.
However, we cannot find any reports that use all ofthese 63 factors as explanatory variables. In fact, thenumber of significant factors incorporated into one
prediction formula was on average only 4.1 (standard
deviation 2.5) [1]. Furthermore, the Japanese Guidelines
for the Management of Stroke 2015 state that “even if
Jpn J Compr Rehabil Sci Vol 8, 2017

Tokunaga M et al.: Multiple regression analysis with FIM improvement for one month added to explanatory variables
17

the variables used for prediction are simply increased,
the prediction accuracy does not necessarily rise,indicating the advantages of using as simple prediction
method as possible” [2].
If it is difficult or ineffective to create accurate
prediction formulae by inputting a number of factors
available at the time of admission into the explanatory
variables, then by incorporating into the prediction
formula “the amount of FIM improvement for one
month since admission (FIM improvement for one
month),” which is the result of many of these factors, it
is possible to increase the prediction accuracy of FIM
gain. Indeed, we are improving forecasts at the time ofadmission by using FIM improvement for one month.
In this study, we predicted FIM gain of stroke
patients admitted to a Kaifukuki rehabilitation ward
using multiple linear regression analysis. The aim of
this study was to clarify how the prediction accuracy
will increase by adding FIM improvement for one
month to the explanatory variables rather than using a
prediction formula that uses only data available at thetime of admission as the explanatory variables.
Subjects and Methods
This research was a retrospective study. A total of
770 stroke patients who were admitted to the Kaifukuki
rehabilitation ward in Hospital A between April 1, 2013
and June 17, 2016, after undergoing treatment at acutephase hospitals, were enrolled. The following patientswere excluded: those with traumatic subarachnoid
hemorrhage (3 cases), those aged younger than 40 years
old (29 cases), those who died in the hospital (5 cases),
those whose outcome was not recorded (7 cases), thoseadmitted within 6 days or more than 60 days after onset(45 cases), those who spent less than 31 days in hospital(91 cases), those whose FIM score at admission ordischarge was not recorded (2 cases), those whose FIM
score at one month after admission was not recorded(17 cases), those who were readmitted (12 cases), those
whose total score of the motor items of FIM (mFIM) at
admission was 91 points (4 cases), and those whose
FIM gain was less than 0 point (8 cases). The remaining
547 patients were included in this study.
A multiple regression analysis using mFIM gain as
the objective variable was performed. The four items
of age, number of days from onset to admission,
admission mFIM, and the total score of the cognitive
items of FIM (cFIM) at admission (model 1), or thesix items of mFIM improvement for one month andcFIM improvement for one month, in addition to thepreceding four items (model 2), were selected as
explanatory variables. Regarding the two prediction
equations obtained, the coefficient of determination
adjusted for the degrees of freedom R*2 and the“residuals” obtained by subtracting the predicted value
from the measured value of mFIM gain were
investigated. Many reports have used the coefficient ofdetermination R2, yet by increasing the number of
explanatory variables, even if doing so is not useful, R2
will be a high value. Therefore, the value corrected by
the number of explanatory variables and the amount ofdata so that the value decreases when a meaninglessvariable is used as an explanatory variable is R*2, andthere is the relationship R2 > R*2.
This study was approved by Hospital A’s clinicalresearch ethics committee. All personal information
was converted to data so that individuals could not be
identified. The FIM used was the Japanese version of
the FIM, 3rd edition [3], and the statistical software
used was IBM SPSS Statistics version 23.0.
Results
Table 1 shows the basic attributes of the 547
subjects. Other than a shorter period between onset
and admission, the subjects were very similar to thoserecorded in the national survey of Kaifukuki
rehabilitation wards in Japan [4]. The mFIM gain wasin the range of 0 to 77 points, and the average was 21.2 ±standard deviation of 15.5 points.
R*2 was 0.364 in the prediction formula (model 1)
when four items of the data at the time of admission
were used as explanatory variables (Table 2a). R*2 was
0.711 in the prediction formula (model 2) when six
items, where mFIM improvement for one month andcFIM improvement for one month were added to thepreceding four items, were used as explanatory
variables (Table 2b). In model 2, five explanatory
variables excluding “number of days from onset toadmission” were significant. The “standardized partial
regression coefficient,” which is the strength of the
explanatory variables relative to the objective variable,
were, from largest to smallest, mFIM improvement forone month, admission mFIM, admission cFIM, thepatient’s age, and cFIM improvement for one month.
The “residual” obtained by subtracting the predictedvalue from the measured value of mFIM gain was 0 ±12.3 for model 1 and 0 ± 8.3 for model 2.
As for the relationship between the measured valueof mFIM gain and the residual, for model 1, the residual
was negative (predicted value > measured value) for
patients for whom the measured value of mFIM gain
was 10 points or less, and the residual was often positive(measured value > predicted value) for patients forwhom the measured value of mFIM gain was 50 points
or more (Fig. 1a). In model 2, the absolute value of theresidual decreased for patients for whom the measured
value of mFIM gain was 10 points or less (Fig. 1b).
Discussion
This study demonstrates that, when predicting
mFIM gain for stroke patients admitted to a Kaifukuki
rehabilitation ward using multiple regression analysis,by adding FIM improvement for one month to the
Jpn J Compr Rehabil Sci Vol 8, 2017

18 Tokunaga M et al.: Multiple regression analysis with FIM improvement for one month added to explanatory variables
Table 1. Clinical characteristics of subjects in this study.
This study

National survey [4]54769.8±12.1 (70)Male 300, female 247
318, 175, 54
18.3±9.4 (16)91.3±39.1 (91)

9,031
73.3
56.7%, 43.3%―
29.6±13.981.3±45.1

Motor FIM score at admission
Cognitive FIM score at admission
Total FIM score at admission

45.6±24.8 (46)22.1±9.3 (24)67.7±32.3 (70)――71.1±31.3

Motor FIM improvement for one month
Cognitive FIM improvement for one month12.4±10.7 (11)2.4±3.5 (2)――66.8±24.4 (77)26.4±8.4 (29)  93.2±31.8 (107)――88.3±33.6

21.2±15.5 (19)4.2±4.7(3)25.4±18.3 (23)――17.1±17.4

Number of patients
Age
Sex
Infarction, hemorrhage, SAH
Number of days from onset to admission
Number of days in hospital

Motor FIM score at discharge
Cognitive FIM score at discharge
Total FIM score at discharge
Motor FIM gain
Cognitive FIM gain
Total FIM gain

FIM, Functional Independence Measure; SAH, Subarachnoid hemorrhage; ―, not described.
Data for this study are expressed as number of patients or mean ± standard deviation (median value).
Table 2. Multiple linear regression analysis to predict motor FIM gain.
a) Model 1: Prediction formula with four explanatory variables available at admission.

Age
Number of days from onset to admission
Motor FIM at admission
Cognitive FIM at admission

95% CI of B

Coeff
(B)

Lower

-0.444-0.202-0.4970.770-0.534-0.316-0.559
0.601

Upper

Std Coeff(β)

Significance(p)-0.355-0.088-0.4350.938-0.348-0.123-0.7980.461<0.0010.001<0.001<0.001

Coeff, Coefficient; Std Coeff, Standard coefficient; CI, Confidence interval.
p Value, <0.001; Coefficient of determination (R2), 0.368; Coefficient of determination adjusted for the degrees of
freedom (R*2), 0.364; Constant, 61.530.
b) Model 2: Prediction formula with six explanatory variables adding mFIM and cFIM improvements for one
month to the four explanatory variables.

Age
Number of days from onset to admission
Motor FIM at admission
Cognitive FIM at admission
Motor FIM improvement for one month
Cognitive FIM improvement for one month

95% CI of B

Coeff
(B)

Lower

-0.238-0.060-0.338
0.492
0.859
0.467

-0.301-0.138-0.384
0.354
0.781
0.214

p Value, <0.001; R2, 0.715; R*2, 0.711; Constant, 31.645.
There is no correlation between six explanatory variables of 0.8 or higher.
Jpn J Compr Rehabil Sci Vol 8, 2017

Upper

Std Coeff(β)

Significance(p)-0.1750.017-0.292
0.630
0.937
0.721

-0.186-0.036-0.543
0.294
0.596
0.105

<0.0010.128<0.001<0.001<0.001<0.001Tokunaga M et al.: Multiple regression analysis with FIM improvement for one month added to explanatory variables
19

Figure 1. Relationship between the measured value of mFIM gain and the residual.
Model 1, Prediction formula with four explanatory variables available at admission.
Model 2, Prediction formula with six explanatory variables adding mFIM and cFIM improvementsfor one month to the four explanatory variables.
Horizontal axis, Measured value of mFIM gain; Vertical axis, Residual obtained by subtracting
the predicted value from the measured value of mFIM gain; Dot, Each patient.
Table 3. Reports predicting FIM gain for stroke patients using multiple regression analyses.
FIM

Number ofpatients

Number of significant
explanatory variables

R2

R*2

Nishioka et al. [5]Tokunaga et al. [6]Tokunaga et al. [7]Scrutinio et al. [8]Tokunaga et al. [9]Total FIM
Motor FIM
Motor FIM
Total FIM
Total FIM

  178
1,884
2,542
  722
  256

6
7
6
5
3

0.426
0.421
―
0.275
0.275

―
―
0.405
―
―

This study

Motor FIM

  547

5

0.715

0.711

Reports [Reference number]

R , Coefficient of determination; R* , Coefficient of determination adjusted for the degrees of freedom.
22

explanatory variables, the coefficient of determination
adjusted for the degrees of freedom R*2 of theprediction formula improved from 0.364 to 0.711. In
particular, the prediction accuracy was improved forpatients with an mFIM gain of 10 points or less. In thereports [5-9] predicting FIM gain using multiple
regression analysis for stroke patients admitted toconvalescent rehabilitation hospitals, there was no
prediction formula adding FIM improvement for one
month to the explanatory variables, such as that usedin this study (Table 3).
The Japanese Guidelines for the Management of
Stroke 2015 [2] note that “simply increasing thevariables used for prediction does not necessarily
improve prediction accuracy [10, 11], demonstrating
an advantage of using the simplest prediction method[12].” On the other hand, there are reports that adding
items such as co-morbidity [13], Stroke Impairment
Assessment Set (SIAS) [14], and Nichijo-seikatsukino-hyokahyo (NSKH) [9] to the explanatory variables
can raise the prediction accuracy of multiple regression
analyses. Of course, research on improving prediction
accuracy by incorporating an appropriate number offactors that have a large influence on mFIM gain into
the prediction formula is also necessary.
Let us consider the magnitude of R*2 in the predictionof mFIM gain (improved from 0.364 to 0.711). In

Meyer et al.’s review of stroke patients admitted to“acute-phase hospitals,” R2 for predicting FIM gain
was as low as 0.08 to 0.4 (with an average of 0.22) [1].
R2 was also in the range of approximately 0.275 to
0.426 in the case of stroke patients who were admitted
to “convalescent rehabilitation hospitals” [5-9] (Table3). There is no clear criterion regarding how muchhigher R2 should be, but it is said that R2 ≥ 0.5 (desirably
R2 ≥ 0.7) [15]. Of the reports so far, the numerical valueof R*2 of 0.711 in multiple regression analyses forpredicting FIM gain was the largest, and attained thedesirable R2. The R*2 increase of discharge FIM due tothe addition of co-morbidity was 0.066 (from 0.732 to
0.798) [13], the R*2 increase of discharge FIM due tothe addition of SIAS was 0.03 (from 0.61 to 0.64) [14],and the R2 increase of FIM gain due to the addition of
NSKH was 0.036 (from 0.239 to 0.275) [9]. Comparedto these, the R*2 increase of FIM gain of 0.347(improved from 0.364 to 0.711) was large. In addition,
when performing an analysis using discharge mFIM as
the objective variable, R*2 of model 1 was 0.744, andR*2 of model 2 was 0.884 (data not shown).
The limitations of this study are as follows. (1)Whether the four explanatory variables are appropriate.
In the review of 16 reports that predicted discharge
FIM or FIM gain in stroke patients admitted to
Kaifukuki rehabilitation wards in Japan using multiple
Jpn J Compr Rehabil Sci Vol 8, 2017

20 Tokunaga M et al.: Multiple regression analysis with FIM improvement for one month added to explanatory variables
regression analysis, factors that were used in morethan five reports and were significant in more than halfof them were age, number of days from onset toadmission, admission mFIM, admission cFIM, total
FIM score at admission, and number of days in hospital[16]. Therefore, in this study, four items excluding
total FIM score at admission and number of days in
hospital were used as explanatory variables. (2) Thereis an opinion that the prediction of mFIM gain should
use only data available at the time of admission.
Although this is ideal, the prediction accuracy of thecurrent multiple regression analysis is considered to
be at “a level that can predict group trends, but is not
so high as to predict individual cases” [17] even when
predicting discharge FIM. In order to improve theprediction accuracy of mFIM gain, it is also necessary
to consider methods of adding FIM improvement forone month to the explanatory variables. (3) Since thenumerical value of R2 (or R*2) differs depending on thetarget patients, it is difficult to accurately compare thisnumerical value among reports of different target
patients. (4) The survey was conducted in one hospital.
(5) Its validity was not verified.
It may be possible to increase the prediction
accuracy to the level where prediction in individual
cases is accurate, by combining the addition of FIM
improvement for one month to the explanatory variables(shown to be useful in this study), the addition of
appropriate factors to explanatory variables, andstratifications of admission mFIM [7, 18, 19]. However,this subject is left for future research. Furthermore, it
may be desirable to conduct a survey at an even earlier
time than one month (such as FIM improvement for oneweek). The authors are conducting family interviews
one month after admission, and the prognosis prediction
at the time of admission is revised using FIM
improvement for one month. The prediction accuracy
should increase as the timing of this survey approaches
the discharge time (the median length of hospitalization
was 91 days). In the future, it will be necessary to clarify
how accurate the predictions can be made when FIM
improvement is evaluated much earlier than one monthfrom admission.

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