Since Taiwan instituted national health insurance 14 years ago, close to 98% of the population is covered by the program.1The program uses a uni- versal budget payment method to control medical care costs. Payment for excessive length of hospital stay (LOS) in relation to each disease is closely monitored, as LOS has a significant impact on the healthcare budget. Cerebrovascular disease was the second leading cause of death in Taiwan in 1984–
2003 (crude mortalities, 53.5–78.4/105 person- years),1and rehabilitating stroke patients often
have longer mean LOS than that for all diseases combined (9.4 days in Taiwan, 2003).1Therefore, it is essential to investigate the principal factors that affect LOS in order to manage healthcare costs. Although LOS is a factor in determining in- patient short-term prognosis, it may also be a di- rect or indirect indicator of long-term survival.2–4 Accurate LOS estimates for stroke patients and their families are important. These LOS estimates allow nursing home networks to prepare for delivering appropriate after-discharge home care.
©2009 Elsevier & Formosan Medical Association
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1Department of Rehabilitation, China Medical University Hospital, 2Biostatistics Center, and 3Department of Public Health, China Medical University, 4Graduate Institute of Health Administration, Asia University, and 5Department of Applied Mathematics and Institute of Statistics, National Chung-Hsing University, Taiwan.
Received: March 19, 2008 Revised: August 20, 2008 Accepted: March 8, 2009
*Correspondence to: Dr Hong-Dar Isaac Wu, Department of Applied Mathematics and Institute of Statistics, National Chung-Hsing University, 250 Kuo-Kuang Road, Taichung 402, Taiwan.
E-mail: honda@amath.nchu.edu.tw
Model-based Prediction of Length of Stay for Rehabilitating Stroke Patients
Chien-Lin Lin,1Pao-Hsuan Lin,2,3Li-Wei Chou,1Shou-Jen Lan,4Nai-Hsin Meng,1 Sui-Foon Lo,1Hong-Dar Isaac Wu5*
Background/Purpose: Accurate length-of-stay (LOS) estimates have an impact on medical costs for stroke patients. Most studies have reported only descriptive sample means or have provided linear-model-based estimates for LOS. This study calculated point and interval estimates by treating hospital discharge as an event, and utilizing the proportional hazards (PH) model to provide the estimation of hospital stay for first-ever stroke patients in a rehabilitation department of a clinical center.
Methods: Pairwise analysis for correlations between age, sex, comorbidity status, modified Barthel index (MBI) and functional independence measure (FIM) was performed. These explanatory variables are used in the K-sample comparisons, the χ2test for association, the PH regression analysis, and log-transformed linear (LTL) regression.
Results: The PH model gave a prediction on estimated mean LOS, with an absolute bias of 0.85 days, by combining MBI and FIM into a single variable, or a bias of 1.15 days and 1.16 days with MBI and FIM vari- ables, respectively. The LTL-based estimation generated a bias of 5.91 days. The PH model has relatively shorter confidence intervals than those obtained by sample-mean and LTL methods.
Conclusion: We recommend using the PH model for predicting mean LOS when the PH assumption for patients with different clinical characteristics is satisfied. However, the proposed method only applies to rehabilitating stroke patients. [J Formos Med Assoc 2009;108(8):653–662]
Key Words: length of stay, linear models, log-transform, proportional hazards models, rehabilitation
For hospitals, precise prediction of LOS facili- tates flexibility in managing bed occupancy. The effectiveness of various treatments and clinical management can be investigated by analysis of mean LOS. For the national insurance authority, surveying LOS between hospitals at the same or different levels, comparing LOS between areas, assessing the cost-effectiveness of current treat- ment strategies, and preparing randomized trials for outcome-oriented evaluations also depends on accurate LOS predictions.2,5–8
Estimation of mean LOS for stroke patients can be based on sample means9(which is “model- free”), according to specific categories defined by age, sex, comorbidity, and patient-modified Barthel index (MBI), functional independence measure (FIM), and other measures of function.10 Unless the available sample size is extremely large, calculating the sample mean with its large-sample property for prediction of LOS is not efficient.
On the other hand, obtaining a model-based pre- diction is appealing, in that it facilitates unified comparisons between different hospitals, and ren- ders meaningful monitoring of medical resources in a national healthcare insurance system.
Natural choices for model-based LOS analysis include: log-transformed linear (LTL) regression and median regression, both of which account for distributional skewedness.11,12A major limitation of these approaches is that patients can be dis- charged for numerous reasons (e.g. cure, transfer, or death11,13). Thus, the observed LOS may be a right-censored datum, which indicates that a direct result for the mean LOS estimate may be an un- derestimate. However, if discharge from hospital is treated as an event-time variable and proportional hazards (PH) regression is applied,14mean LOS can be obtained based on the theory of event- history data analysis. Notably, the PH model has been used widely when analyzing outpatient mortality or survival.3,4,9,15
The present study compared two analyses of mean LOS prediction: sample means, and the PH model. However, LTL assessment was also compared in order to illustrate its deviation to underestimate the mean LOS. Patients enrolled
in the analysis had experienced a cerebrovascular attack and were recruited from the Rehabilitation Department at China Medical University Hospital (CMUH) in central Taiwan.
Materials and Methods
Patients and data collection
We enrolled 586 patients who had experienced their first stroke, with cerebral hemorrhage or cerebral infarction, from a 1400-bed medical center at CMUH between January 1, 1997 and February 28, 2005. The patients were recruited from neurology, internal medicine, and emergency resuscitation departments and transferred (or re- hospitalized) to the Department of Rehabilitation at CMUH. Transfer date was set as the zero time point for event history analysis. The baseline data collected from hospital records were as follows: age, sex, coexistence of diabetes mellitus and/or hyper- tension, history of stroke and severe injury, and family disease history. These data were recorded typically within the first 6 hours of hospitaliza- tion for an acute-stage event. For patients who were admitted for rehabilitation, which com- prised physical, occupational or speech therapy, MBI and FIM questionnaires were administered within 24 hours of transfer. The MBI and FIM scores represent the generic severity of disability of inpatients, and have been applied widely in stroke research and various medical fields.10,17–20 Furthermore, the change in score following treat- ment is indicative of patient improvement.18 These scores are recorded routinely for patients in various departments, particularly at the Rehabilitation Department of CMUH. The data were ascertained from a computerized databank.
Patients who had a previous event other than stroke, such as trauma or head injury, were ex- cluded, as were patients who had received reha- bilitation. Figure 1 presents a brief description of the process used to collect data.
When an event-history analysis is used, patients are discharged as a result of curative treatment, and not for death or other causes. For outpatients
who were transferred to other hospitals and then returned, the first LOS at CMUH was treated as a right-censored observation. As a reference for comparison, sample means and 95% confidence intervals (CIs) unique to each category were cal- culated. The following two model-based estimates were considered.
Cox PH model
h(t;Z)= h0(t)exp(β1× age + β2× sex + β3× MBI + β4× FIM…),
where h(t;Z) is the incidence (or hazard) func- tion of event time with covariate Z (which is a vector of age, sex, MBI and FIM), and h0(t) is an unknown baseline incidence function. A simple estimate of mean survival, for an individual with a covariate-vector Z, is SˆZ(t)dt, where
SˆZ(t)= exp{–hˆ0(t) exp(bˆTZ)dt}.
In the above expression, βTZ= β1× age + β2× sex + β3× MBI + β4× FIM…. Estimations for parame- ters β and h0(t) follow standard statistical prin- ciples. The corresponding CIs are generated as (SL,PH(t)dt, SU,PH(t)dt), where SL,PH and SU,PH are upper and lower confidence limits, respec- tively, derived from the formulas offered in Klein and Moeschberger.16
LTL regression
log(LOS+ 1) = β0+ β1× age + β2× sex + β3× MBI + β4× FIM….
To eliminate any heterogeneity effect, the vari- ables age, FIM and MBI were categorized into sev- eral groups (Table 1). Finally, the estimate of mean log(LOS+ 1) was calculated easily using conven- tional linear model theory with the CI, denoted as (Cl, Cu); thus, the transformed CI was (exp(Cl) – 1, exp(Cu) – 1). Note that the underestimate based on the LTL model was attributed to the log- and exponential-transforms procedure.
The inter-relationship between LOS and poten- tial predictors of LOS were investigated prelimi- narily by comparing means and medians using descriptive statistics and Wilcoxon’s rank-sum test (or their multiple-sample counterparts). As an in- termediate step, the confounding structure of pre- dictors was identified by the joint distributions between the most significant variables using cor- relation coefficients and the χ2test for association.
Finally, the PH and LTL models were implemented to estimate regression coefficients, rate ratios, and associated mean LOS. A value of p< 0.05 was con- sidered statistically significant.
Results
Bivariate analysis of the confounding variables Sex was not significant in predicting LOS (Table 1).
Male and female patients had similar values for mean and median LOS, and other percentiles (rank-sum tests, p= 0.262). Age, however, was sig- nificant; multiple comparison tests revealed that patients aged< 50 and ≥ 80 years were statistically equivalent in mean/median LOS. Comorbidity status and physical therapy, occupational therapy and/or speech therapy had no predictive power.
The most significant variables were MBI and FIM scores (both p< 0.001).
To determine the validity of model-based pre- diction, the correlation structure was examined.
This assessment helped establish a group of pos- sible explanatory variables. As age (p= 0.047), MBI and FIM were the most significant variables (Table 1), their pairwise associations were examined (Tables 2 and 3). The joint distribution of FIM and 808 patients
with CVA
645 patients with inhospital records
586 first-time records with complete data 59 repeated inhospital
records excluded
156 with missing FIM or MBI and 7 with other non-eligibility deleted
Figure 1. Data processing with retrospective exclusion of non-eligible inpatient records. FIM= functional indepen- dence measure; MBI= modified Barthel index; CVA = cere- brovascular accident.
MBI scores was expressed by box-plots (Figure 2, FIMs with respect to different MBI groups) and a cross-classified table (Table 2). For different age groups, individual MBI and FIM scores were
compared (Table 3). Analytical results indicated that although MBI and FIM were measures for dif- ferent aspects of a stroke patient’s condition, they were highly correlated. When these scores were Table 1. K-sample (K≥ 2) comparison for LOS of 586 stroke patients with different sex, age, comorbidity, physical therapy,
occupational therapy, speech therapy, MBI score and FIM score
Statistics Test
Variables
n Mean SD Q1 Q2 Q3 K–W*
Sex Female 236 31.6 19.7 17.0 28.0 43.0 0.262
Male 350 29.9 19.4 14.0 28.0 41.0
Age (yr) < 50 105 28.3 19.3 13.0 23.0 41.0 0.047
50–64 189 33.1 19.9 19.0 30.0 45.0
65–79 250 30.4 19.6 16.0 28.0 42.0
≥ 80 42 26.1 17.2 12.0 25.0 34.0
Comorbidity None 226 31.0 20.3 15.0 28.5 43.0 0.850
DM 28 31.6 20.0 17.5 30.5 40.0
HYP 257 30.5 18.7 16.0 27.0 43.0
DM+ HYP 75 29.3 20.2 14.0 26.0 40.0
PT Yes 581 30.4 19.5 15.0 28.0 42.0 0.064
No 5 47.8 23.7 34.0 37.0 50.0
OT Yes 555 30.3 19.3 15.0 28.0 42.0 0.335
No 31 34.8 23.1 17.0 31.0 47.0
ST Yes 330 31.3 19.8 17.0 28.0 41.0 0.329
No 256 29.6 19.1 14.0 28.0 43.0
MBI 0 154 34.5 19.0 20.0 31.5 46.0 < 0.001
5–30 352 30.8 20.2 16.0 28.0 42.0
≥ 35 80 21.9 14.8 10.5 18.5 30.5
FIM < 29 146 36.7 21.7 21.0 33.0 48.0 < 0.001
29–63 286 31.4 19.2 16.0 29.0 43.0
≥ 64 154 23.3 15.4 11.0 21.0 33.0
*Kruskal–Wallis test, reduces to Wilcoxon’s rank sum test when K = 2. n = sample size; SD = standard deviation; Q1, Q2, and Q3 = 25%, 50% (median), and 75% points; K–W = Kruskal–Wallis; DM = diabetes mellitus; HYP = hypertension; PT = physiotherapy; OT = occupational therapy; ST = speech ther- apy; MBI = modified Barthel index; FIM = functional independence measure.
Table 2. Joint distribution (or cross classification) between FIM and MBI scores at patient admission*
MBI
Total Patient no.
0 5 10–20 25–30 ≥ 35
FIM < 20 43 (84.3%) 2 (3.9%) 5 (9.8%) 1 (2.0%) 0 (0.0%) 51
20–28 46 (48.4%) 7 (7.4%) 39 (41.1%) 3 (3.2%) 0 (0.0%) 95
29–44 53 (37.1%) 19 (13.3%) 54 (37.8%) 13 (9.1%) 4 (2.8%) 143
45–63 11 (7.7%) 15 (10.5%) 83 (58.0%) 24 (16.8%) 10 (7.0%) 143
64–80 1 (1.1%) 3 (3.4%) 25 (28.4%) 35 (39.8%) 24 (27.3%) 88
≥ 81 0 (0.0%) 1 (1.5%) 9 (13.6%) 14 (21.2%) 42 (63.6%) 66
Total 154 (26.3%) 47 (8.0%) 215 (36.7%) 90 (15.4%) 80 (13.7%) 586
*Pearson’s and Spearman’s correlation coefficients between FIM and MBI (at entry) were 0.727 (p< 0.001) and 0.725 (p < 0.001), respectively. FIM = functional independence measure; MBI = modified Barthel index.
treated as continuous variables or categorized into several groups, Pearson’s and Spearman’s corre- lation coefficients were both approximately 0.73 (both p< 0.001; χ2test, p< 0.001). Older patients had lower MBI and FIM scores. In particular, 28.4% and 30.8% of patients aged ≥ 65 years had MBI= 0 and FIM < 29, respectively (Table 3); how- ever, 24.9% and 26.3% of the entire sample (586 patients) had MBI= 0 and FIM < 29, respectively.
To investigate the relationship between LOS and MBI/FIM, a ceiling effect of the functional scores may result in a heterogeneous effect in subse- quent regression analysis. According to the data, this problem was negligible for FIM, and because those with MBI > 35 comprised a small group, the
heterogeneity effect within this group was aver- aged out (because of grouping). In summary, the MBI and FIM scores grouped in this analysis re- duced bias during regression analysis.
Regression models
Table 4 presents PH univariate analysis results with the regressors sex, age, MBI, MBI-diff, FIM, and FIM-diff. MBI-diff and FIM-diff represented the differences in FIM and MBI scores for dates of discharge and hospitalization. These two dif- ference scores were time-dependent covariates that had a dynamic meaning, in that the patients and/
or attending physicians assessed improvement, to determine whether a patient should have been discharged. Therefore, score changes were not suit- able for use as predictors for further estimation of mean LOS and other outcome variables, which were unknown at admission. A rate ratio (RR)> 1 indicated likely discharge compared with that for the reference group. The functioning scores and their differences were much more important than age and sex (Table 4). Large MBI and FIM scores at admission shortened LOS. The trends in RR for MBI (1.40 and 2.19) and FIM (1.23 and 2.20) were both significant. Conversely, patients who had a large difference in FIM or MBI scores usu- ally had long LOS (RR< 1). This indicated that clinical improvement in patient functioning was a result of effective rehabilitation, thereby encour- aging a prolonged LOS. However, those who did not obtain functional improvement tended to be discharged early.
Table 3. Joint distributions between age and MBI score (upper panel), and age and FIM score (lower panel) Age (yr)
Patient no.
< 50 50–64 65–79 ≥ 80 p*
MBI 0 22 (14.3%) 42 (27.3%) 70 (45.5%) 20 (13.0%) < 0.001
5–30 59 (16.8%) 115 (32.7%) 157 (44.6%) 21 (6.0%)
≥ 35 24 (30.0%) 32 (40.0%) 23 (28.8%) 1 (1.3%)
FIM < 29 18 (12.3%) 45 (30.8%) 70 (48.0%) 13 (8.9%) 0.005
29–63 45 (15.7%) 95 (33.2%) 121 (42.3%) 25 (8.7%)
≥ 64 42 (27.3%) 49 (31.8%) 59 (38.3%) 4 (2.6%)
*By conventional χ2test for association (Fisher’s exact test gave similar results but is not reported). MBI = modified Barthel index; FIM = functional independence measure.
125 100
75
50
25
0
0 5 10–20 25–30 35+
FIM
MBI +
+ +
+
+
Figure 2. Box plot of FIM scores according to different MBI groups, showing the relationship between individual patient MBI and FIM scores at admission. FIM= functional inde- pendence measure; MBI= modified Barthel index.
Table 5 presents the mean LOS estimates and associated CIs for the three methods (sample- mean, PH, and LTL). Subgroups were characterized by age versus a variable with MBI/FIM combined.
MBI and FIM were combined for the following reasons. First, MBI and FIM were highly correlated, and second, many patients had an MBI of 0 at admission. Patients with MBI= 0 were divided into two groups: those with FIM < 29 and those with FIM ≥ 29. The group with MBI 5–30 consisted of three subgroups (Table 2), who did not differ sig- nificantly for incidence of discharge. Briefly, the categorization (on age, MBI and FIM) in Table 5 produced the smallest absolute bias. The MBI/FIM combined analysis could be ignored, and only a single variable was utilized, FIM or MBI, to sim- plify analysis. Finally, patients aged ≥ 80 years were excluded from analysis of PH-based prediction, as most elderly patients in Taiwan had other con- cerns about their discharge, such as whether they
would be cared for by their families, or be trans- ferred to a nursing home. Exclusion of elderly patients resulted in a non-proportional-hazards phenomenon when compared with other groups.
The sample mean estimates for the first MBI/FIM group (MBI= 0 and FIM < 29) were 30.7, 39.1 and 32.5 days for the three age groups (Table 5). The corresponding means estimated by the PH model were 32.4, 35.8 and 32.0 days, respectively. All ab- solute biases (1.7, 3.3, and 0.5 days) were tolera- ble. For the other entries, the meaning was similar.
Generally, for the group 5≤ MBI ≤ 30, the PH model had a very precise prediction, with ab- solute biases of 0.1, 0.4, and 0.6. Conversely, the LTL model estimated mean LOS of 26.5, 32.8, and 27.5 days for the first group (MBI= 0 and FIM <
29), which resulted in a large absolute bias and wide CIs. Overall, by taking the weighted average according to the sample size of each entry, the PH model obtained a mean absolute bias of Table 4. Rate-ratio estimate for various explanatory variables using the univariate Cox proportional hazards
model
Variable RR 95% CI p
Sex Male 1.08 0.91–1.28 0.369
Female 1 – –
Age (yr) < 50 0.78 0.53–1.13 0.183
50–64 0.66 0.47–0.93 0.017
65–79 0.79 0.57–1.11 0.170
≥ 80 1 – –
MBI 0 1 – –
5–30 1.40 1.14–1.73 0.002
≥ 35 2.19 1.73–2.78 < 0.001
MBI-diff ≤ 0 1 – –
1–14 0.75 0.57–0.99 0.039
15–29 0.61 0.47–0.81 0.001
≥ 30 0.58 0.41–0.82 0.002
FIM < 29 1 – –
29–63 1.23 1.01–1.49 0.040
≥ 64 2.20 1.63–2.95 < 0.001
FIM-diff ≤ 0 1 – –
1–2 0.84 0.65–1.09 0.187
3–11 0.74 0.58–0.94 0.016
≥ 12 0.75 0.55–1.03 0.074
RR = rate ratio; CI = confidence interval; MBI = modified Barthel index; MBI-diff = difference in MBI score for dates of discharge and hospitalization; FIM = functional independence measure; FIM-diff = difference in FIM score for dates of discharge and hospitalization.
0.85 days, and that obtained with the LTL model was 5.91 days. The LTL-based analysis had a sys- temic bias that could only be avoided using ad hoc and posterior adjustments. Additionally, PH-based CIs of each category were markedly shorter than those of LTL analysis and sample mean estimates.
The effectiveness in using Cox’s PH technique as a building block for predicting LOS depends on the proportional hazards assumption. This as- sumption can be examined readily using standard statistical packages (e.g. SAS 8.2 and S-Plus 4.5).
For an illustration, only the Kaplan–Meier (KM) estimates for the survivor function for different MBI and FIM groups are shown (Figure 3). In both of the curves, proportionality was acceptable.
The same KM plot for different ages (excluding≥ 80 years) had a similar type and was omitted. In conclusion, the estimates based on Cox’s PH model were satisfactory for obtaining mean LOS prediction.
Discussion
This study addressed the need to better predict the LOS of patients during inpatient stroke reha- bilitation, which is an important medical and economic issue. PH regression was utilized for the following reasons: (1) PH regression provides con- venient explanations regarding the intensity of event of discharge for different patients, and can be implemented easily using various statistical packages. Moreover, PH regression is efficient; i.e.
it has short CIs. (2) PH regression can achieve a unified assessment of LOS for intra- and inter- hospital, and multilevel comparisons. (3) The hazard-regression model can be extended to a multivariate setting such that short-term events (e.g. LOS) and long-term events (e.g. mortality) can be modeled together in a general framework.
However, the PH model assumes proportion- ality, which is a strong condition that the among- group incidences may not satisfy. Consequently, Table 5. Prediction of mean LOS and the corresponding 95% CIs from the Cox PH model compared with the
method of naïve sample means and that based on an LTL regression model Age (yr)
< 50 ≥ 50, < 65 ≥ 65, < 80
mean lcl ucl mean lcl ucl mean lcl ucl
MBI= 0 and n 10 27 42
FIM< 29 Mean 30.7 21.5 39.9 39.1 30.6 47.7 32.5 26.6 38.4
PH 32.4 29.0 35.8 35.8 32.0 39.6 32.0 29.3 34.7
LTL 26.5 21.3 32.7 32.8 27.3 39.4 27.5 23.1 32.7
MBI= 0 and n 12 15 28
FIM≥ 29 Mean 33.3 21.2 45.5 38.4 27.2 49.6 37.7 30.1 45.3
PH 35.3 30.7 39.8 39.0 33.4 44.5 34.8 30.9 38.6
LTL 28.4 22.5 35.7 35.2 28.4 43.6 29.5 24.1 36.2
5≤ MBI ≤ 30 n 59 115 157
Mean 29.8 24.5 35.1 33.4 29.7 37.2 30.1 27.0 33.3
PH 29.9 27.8 31.9 33.0 30.8 35.2 29.5 28.0 30.9
LTL 22.6 19.4 26.4 28.1 25.0 31.5 23.5 21.2 26.1
MBI≥ 35 n 24 32 23
Mean 20.9 13.4 28.3 24.3 19.5 29.2 19.3 13.3 25.2
PH 20.8 19.8 21.7 22.9 21.7 24.1 20.5 19.6 21.4
LTL 15.2 12.4 18.6 19.0 15.8 22.8 15.9 13.1 19.2
LOS = length of stay; CI = confidence interval; PH = proportional hazards; LTL = log-transformed linear; lcl = lower 95% confidence limit; ucl = upper 95% confidence limit; MBI = modified Barthel index; FIM = functional independence measure.
1.00
0.75
0.50
0.25
0.00
0 20 40 60 80 100 120 140
Survival distribution function
Days
FIM < 29 FIM 29–63 FIM ≥ 64 1.00
0.75
0.50
0.25
0.00
0 20 40 60 80 100 120 140
Survival distribution function
Days
MBI = 0 MBI 5–30 MBI ≥ 35
A B
Figure 3. Kaplan–Meier survival estimates for different (A) MBI and (B) FIM groups. MBI = modified Barthel index;
FIM= functional independence measure.
imposing proportionality unavoidably introduces a bias to mean LOS estimates. To remedy this fault, as many confounders as possible must be collected at an early stage of a patient’s hospitalization.
Moreover, 17 (2.9%) right-censored observations existed. If they were further considered, sample means would be slightly larger than those calcu- lated in the present study, which would generate a larger absolute bias than 0.85 days for PH estimates.
To validate the model employed with contin- uously distributed variables, the dataset can be split randomly into a training set and a test set for analysis.21 On the other hand, the variables in this study are all categorized, so that an easy-to- use table can be prepared for clinicians. With this purpose in mind, a model with a parsimonious number of variables was constructed. Table 5 po- tentially offers such parsimony. Nevertheless, the results in Table 5 are not dogmatic. The MBI and FIM are essentially measuring similar activities.
FIM has cognitive tasks in addition to the motor activities seen on MBI. FIM is used traditionally in an inpatient setting and scored by therapists, and MBI is used typically for monitoring outpa- tients. In the present study, FIM was probably better to be used for prediction. Thus, if the com- bined MBI/FIM variable was to be replaced by a single FIM variable, the absolute bias of mean LOS prediction was 1.16 days (data not shown).
Other variables were analyzed in the present study. For example, the differences between MBI
and FIM scores are important to clinical practi- tioners. These differences are correlated strongly with LOS. Notably, LOS for stroke patients in re- habilitation was correlated positively with MBI and FIM differences (Table 4). However, this cor- relation was not predictive at hospitalization.
That is, physicians usually determine a patient’s prognosis and daily condition when deciding whether to discharge a patient; patients them- selves and their families sometimes request dis- charge as a result of self-assessed improvement.
Consequently, prior knowledge of a patient’s pro- gress is supposed to be unknown at hospitaliza- tion, in order to predict the possible LOS by the score differences.
In many studies, stroke type (such as cerebral hemorrhage, cerebral infarction, and transient is- chemic attack) is a very significant predictor of LOS, if LOS is defined as length of the entire hos- pital stay. The term “entire” implies that it contains the acute stage—therefore, the time of admission to the neurology, internal medicine and emer- gency resuscitation departments is defined as
“time zero”. In the present study, however, the defined LOS contained only the period from ad- mission to the rehabilitation department to dis- charge, so that it could be viewed as length of stay in the rehabilitation department. In that manner, that which was closely relevant to the character- istics at the acute stage will possibly decay during the rehabilitation stage. Certainly, it is still an in- teresting issue to be clarified, and is more likely
to be complicated by the causes of death that occur at this stage.
Comorbidity status may have an impact on LOS and subsequent survival.22,23 In a previous study of patients who experienced their first stroke, comorbidity was a confounder and an effect- modifier. To deal with this phenomenon by modeling LOS through PH-based regression, three approaches can be considered: a PH model with interaction terms; a PH model combined with a stratified analysis; and a stratified PH model that uses comorbidity as an index that stratifies the baseline cumulative incidence. These approaches are more complex statistical approaches. To sim- plify the present study, they were not utilized.
Finally, the MBI and FIM scores were limited by their reproducibility, although these scores have been well-tested in previous studies.10,18In future studies, MBI and FIM scores and other variables obtained via questionnaires should be examined for interrater reliability, so that uncer- tainty caused by sampling properties can be re- duced, and the impact of measurement errors can also be assessed. Moreover, because this was a ret- rospective study, some important variables could not be tracked, including the National Institutes of Health Stroke Scale, the history of diseases re- lated to cerebrovascular diseases and rehabilita- tion therapy, and risk factors such as smoking, alcohol consumption, other comorbidities, and various serum biochemical indicators. These data should also be collected uniformly to increase pre- diction accuracy. Therefore, the results obtained in the present study should be confined to a pop- ulation such as that defined in this study.
Acknowledgments
The authors would like to thank the National Science Council (NSC 92-2118-M-039-001), China Medical University (CMU 92-PH-04), and China Medical University Hospital (DMR-95-081), Taiwan, for financially supporting this research;
and Dr Mu-Jung Kao, Dr Pey-Yu Yang, and Dr Ting-I Hang for offering part of the data.
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