Use of a Clustered Model to Identify Factors Affecting Hospital Length of Stay

J Clin Epidemiol Vol. 52, No. 11, pp. 1031–1036, 1999 Copyright © 1999 Elsevier Science Inc. All rights reserved.

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Use of a Clustered Model to Identify Factors Affecting Hospital Length of Stay Yael C. Cohen,1 Haya R. Rubin,2 Laurence Freedman,1,3 and Benjamin Mozes1,* 1Gertner Institute for Health Policy Research, The Chaim Sheba Medical Center, Tel Hashomer, and Sackler School of Medicine, Tel Aviv University, Tel Aviv, Israel; 2John Hopkins University School of Medicine and School of Hygiene and Public Health, Baltimore, Maryland; and 3Bar Ilan University, Ramat Gan, Israel

ABSTRACT. Predictive models have been used to identify factors that may prolong hospital length of stay (LOS). However, because predictors of LOS are collinear, the proportion of variance associated with each factor in a multivariate stepwise regression model may not reflect its mathematical contribution in explaining LOS. In an attempt to model factor contribution to LOS more realistically, we evaluated a clinically based clustered model. This model uses classes of candidate predictors, that is, patient attributes, adverse events, treatment modality, and health provider identity. Clusters of variables are permitted to enter into the model in a theoretically based predetermined sequence, so that the additional contribution of each cluster of factors can be assessed while the contribution of preceding factors is preserved. The clustered model was tested and compared with a free stepwise multivariate analysis in a cohort of patients undergoing prostatectomy for benign prostatic hypertrophy. We found that both models explained a similar proportion of the variance in LOS (56%–57%). However, some important differences were evident. Prostate size, associated with 12% of the variance in the clustered model, was not an independent predictor in the free model. A higher proportion of variance was associated with process variables, such as treatment modality in the free model. We conclude that use of a clustered model may facilitate more realistic assessment of the relative contribution of factors to LOS. J CLIN EPIDEMIOL 52;11:1031–1036, 1999. © 1999 Elsevier Science Inc. KEY WORDS. LOS, clustered regression model, prostatectomy

INTRODUCTION Expenditures for hospital stays comprise a major component of health care costs. Thus, reducing hospital length of stay (LOS) without worsening the medical outcome is a major goal in the era of rising costs and limited resources. Two major initiatives for reducing LOS have been: (1) prospective payment to hospitals per admission according to diagnostic related group (DRG). This system gives hospitals financial incentives to reduce LOS; however, it has been criticized for its tendency to promote earlier discharge of patients in unstable condition and for underpaying some classes of medical centers [1,2]; and (2) Control systems that apply explicit criteria for evaluation of the appropriateness of each hospitalization day. Such systems are frequently hindered by the medical community’s resistance to external observers [3,4]. An additional approach to reducing LOS is based on the analysis of outcome studies, which, in the past decade, have been a subject of considerable interest and growth in activ*Address for correspondence: B. Mozes, MD, Gertner Institute for Health Services Research, The Chaim Sheba Medical Center, Tel Hashomer 52621, Israel. Accepted for publication on 15 April 1999.

ity [5]. By applying this approach, factors that are related to LOS are identified, based on data collected from large cohorts of patients with different background characteristics and from different medical care facilities. These factors can then be the basis for focused intervention programs aimed at reducing hospital LOS while maintaining the quality of care. The efficiency and impact of such intervention depend on the possibility of identifying factors with greatest impact on LOS and on directing resources and efforts toward addressing them. Studies determining the relationship of various factors to LOS usually use stepwise regression models that allow factors to compete freely with each other [6–10]. However, possible predictors of LOS are highly correlated and, more importantly, do not affect LOS independently. For example, patient attributes are often associated with specific treatments, making it difficult to separate those factors. Therefore, the proportion of variance in LOS explained by a factor in these multivariate models does not necessarily reflect the relative influence of LOS from modifying this factor. Various approaches to model building in multivariable analysis, aimed to overcome pitfalls similar to those just described, have been described in the statistical literature.

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Harrell et al. [11] have discussed various strategies of model fitting that include forming clusters of clinical variables and found them to be superior to standard “step-up” variable selection. Feinstein [12] has advocated using clinical judgment and considering temporal sequence when entering variables in multivariable analysis. In this study, we evaluate the application of such an approach in the analysis of the variance in LOS. We predefined clusters of candidate predictors as patient attributes or process variables, and we introduced them into the model in multiple ordered phases so that the additional contribution of each could be assessed. We refer to this as a clustered model. This article examines whether use of a clustered regression model improves the ability to identify factors affecting LOS and their relative importance. This modeling strategy is compared with a free stepwise model among patients undergoing prostatectomy for benign prostatic hypertrophy (BPH) in three medical centers.

METHODS Patients The study included all 508 patients who underwent prostatectomy due to BPH, in three referral and university-affiliated medical centers in Israel, during 1991 and 1992. All patients were considered eligible for the study regardless of their medical history and age. Data Collection All patients underwent a personal structured interview by a trained nurse before the operation. Further details of perioperative and comorbidity data were collected by a nurse from the hospital charts. The patient interview included questions concerning sociodemographic data and medical history. Additional items recorded included type of surgery (transurethral or open prostatectomy), LOS, and occurrence of various adverse events. Variable Definition and Data Analysis IDENTIFICATION OF POTENTIAL FACTORS ASSOCIATED WITH LOS. A literature search was conducted to identify factors known to be related to LOS among the general patient population as well as inpatients who were similar to our study sample, that is, undergoing either prostatectomy or other surgical procedures. This search yielded the following variables: age, socioeconomic status, comorbidity, disease severity, hospital, nursing intensity, physician practice style, adverse effects, surgical technique, and use of analgesics [7–10,13– 19]. Additional potential factors were suggested based on our clinical experience. Comorbidity was scored by two systems: HCFA [20] and Charlson [21]. Appendix 1 contains a detailed list of variables and their definitions.

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CLUSTERING OF VARIABLES. Factors were clustered together according to their implications regarding possible interventions to reduce LOS. We used the following clustering scheme: Patient attributes: Sociodemographic variables, urological variables, medical history, comorbidity states, and laboratory data. Possible interventions addressing this cluster of predictors of LOS would be modification of criteria for selection of patients for prostatectomy and improvement in control of comorbidity before surgery. Treatment modality: Transurethral resection of prostate (TURP) or open prostatectomy. Possible interventions addressing this cluster of predictors are based on modifying the criteria for selection of treatment modality. Occurrence of adverse effects: Urological or nonurological. Possible interventions addressing this cluster of predictors would attempt to shorten LOS by identifying and correcting potential flaws in surgical technique or in perioperative care. Identity of health provider: Which of the three participating medical centers. Possible interventions addressing this predictor may change departmental or institutional policies and protocols, introduce different incentive systems, or change the organization of the health facility. OUTCOME VARIABLE. LOS was defined as the number of days in hospital, starting from the day of surgery, not counting the day of discharge. Logarithmic transformation resulted in a near-normal distribution of LOS (in days), and therefore log LOS was used as the outcome variable. At the end of this section, we describe the effect of this transformation on the residuals of the regression model. MODEL DEVELOPMENT. The patient population from the three centers was pooled to develop each model. We used the SAS/STAT statistical package [22]. Analysis of variance (ANOVA; for categorical variables) and Pearson correlation (for continuous variables) were used to find associations between each of the variables included and log LOS. Variables that correlated (P , 0.15) with log LOS were selected as candidates for the multivariate model. We developed two models as follows: (1) The clustered model: Construction of the model was based on a multiphase process repeated for each of the clusters of variables already described here. In each phase, candidate variables from a given cluster are permitted entrance into a stepwise linear regression model, after forcing into the model variables that were entered in previous phases. Clusters of variables are introduced into the model in the predefined order already given here. Variables enter the model if the P value of their independent contribution was less than 0.10. This procedure corresponds to assuming a causal model in which cluster 1 variables (patient attributes) can affect any of the variables in clusters 2–3 (treatment and adverse events) as well as having a direct effect on length of stay. Similarly, cluster 2 variables are assumed to affect cluster 3 variables or directly affect LOS, and cluster 3 variables are

Clustered Model to Identify Factors Affecting Hospital Length of Stay

assumed only to affect LOS. In other words, variables in one cluster may causally affect variables in a “later” cluster, but they are not affected themselves by those “later” cluster variables. Cluster 4 variables (health provider) are reserved for the last phase, not because they are last in the causal chain, but because we wanted to delineate the effects of their policies with regard to LOS after accounting for the effects of the other variables. When presenting the results from this clustered approach (see Table 1), the estimated regression coefficients and the multiple correlation coefficients (R2) for variables in cluster 1 are taken from the final phase 1 model, for cluster 2 variables from the final phase 2 model, etc. In this way, the regression coefficients and the correlation coefficients have a “causal” meaning. For example, for a variable in cluster 1, such as prostate size, the reported regression coefficient represents the total effect of this variable on LOS caused by a large (versus small) prostate. This total effect includes both the direct effect of prostate size on LOS as well as its indirect effect on LOS resulting from its effect on cluster 2 or 3 variables, such as treatment modality. See for example reference [22] for a more detailed statistical explanation. (2) The free stepwise model: Candidate variables from all above categories were simultaneously allowed to compete freely to enter into a forward stepwise, linear regression model. The criterion for entry of a variable into the model was the same at each phase of the clustered model. We examined the residuals of the final model chosen by the stepwise regression method. There was evidence of a small degree of kurtosis (52.58) and skewness (0.76) but we judged this to be unlikely to seriously distort the results. In addition, we tested for homoscedasticity by relating the absolute residual to the predicted value and found no significant relationship. RESULTS Complete data, including both interviews and medical records, were available for 502 (98.8%) of the patients. The mean age was 70.6; 40.3% of the patients underwent open prostatectomy. There was a similar number of patients in each center. The mean LOS was 8.18 days (Table 1). Variables included in the final multivariate clustered model were associated with 56.9% of the variance in LOS (Table 2). In phase 1, the patient attribute variables that entered the model were age, prostate size indicators, severity of prostate obstruction, and comorbidities and were associated with 24.3% of the variance. In phase 2, choice of surgical technique (TURP vs. open surgery) entered the model and was associated with an additional 13.6% of the variance. In phase 3, adverse effect variables were allowed to enter the model and were associated with an additional 11.9% of the variance. Finally, in phase 4, the identity of the medical center entered the model and was associated with an additional 7.1% of the variance.

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TABLE 1. Patient characteristics

Variable Patient attributes Age (mean 6 SD) Indwelling urinary catheter Hydronephrosis Prostate size by DREa Smallb Moderatec Larged Comorbidity Ischemic heart disease Diabetes mellitus Operation type Open prostatectomy TURPe Adverse effects Need for reoperation Wound infection Nonurological complications Medical center A B C LOSf (mean 6 SD)

(n 5 508) 70.6 6 7.9 years 24.2% 5.6% 21.0% 50.1% 28.8% 34.5% 17.0% 40.3 59.7 2% 2.2% 11.6% 35.0% 33.2% 31.6% 8.18 6 5.74 days (min 2, max 45)

aDigital

rectal examination. than one finger. cBetween one and two fingers. dGreater than two fingers. eTransurethral resection of prostate. fLength of stay. bLess

The free model was associated with 56.5% of the variance (Table 3). The major differences between these two models (the clustered and the free model) consisted of absence of prostate size in the free model (associated with 11.9% of variance in the clustered model). When we forced the variable “prostate size” into the free model, the P value was 0.17 (moderate size vs. small size) and 0.60 (large size vs. small). There were differences in the proportion of variance associated with the process variables surgery type (24.4% in free model vs. 13.4% in the clustered model), and medical center (12.2% in free model vs. 6.8% in clustered model). Use of backward stepwise procedure produced a model identical to that produced by forward stepwise regression. Interaction terms were considered in both the free and the clustered model after the entry of all the significant main effects, including prostate size 3 type of surgery; prostate size 3 age; medical center 3 age; medical center 3 wound infection; and medical center 3 re-operation. None of them entered into the free model. The interaction term: Medical center 3 wound infection entered into the clustered model (P 5 0.09, additional R2 of 2.5%), but not included in Table 2. Stratified analysis of LOS by prostate size and surgery type, among patients who underwent TURP, demonstrated statistically significantly longer LOS among patients with large prostate glands compared with those

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TABLE 2. Structured multiphase regression model Outcome Variable: Log LOS

Variable entered Phase 1 Patient-attributes cluster Large prostate by DREa Moderate prostate by DREb Indwelling urinary catheter Age Hospitalization due to UTIc Congestive heart failure Diabetes Hydronephrosis Phase 2 Operation type cluster Open surgery vs. TURPd Phase 3 Adverse effects cluster Need for reoperation Wound infection Other urological complicationse Feverf Nonurological complicationse Phase 4 Medical center cluster Center B vs. center A Center C vs. center A

Coefficient

Partial R2

Model R2

P.F

0.48 0.19 0.24 0.008 0.18 0.20 0.12 0.18

0.118 0.014 0.068 0.015 0.010 0.006 0.006 0.005

0.118 0.132 0.200 0.215 0.225 0.231 0.237 0.243

0.0001 0.0058 0.0001 0.0021 0.0130 0.0448 0.0439 0.0664

0.47

0.136

0.379

0.0001

0.76 0.57

0.063 0.022

0.442 0.464

0.0001 0.0001

0.24 0.13 0.10

0.025 0.006 0.003

0.489 0.495 0.498

0.0001 0.0139 0.0885

0.41 0.27

0.038 0.033

0.536 0.569

0.0001 0.0001

aGreater

than two fingers vs. less than one finger by digital rectal examination (DRE). one and two fingers vs. less than one finger. cUTI 5 urinary tract infection. dTURP 5 transurethral resection of prostate. eSee Appendix 1. f.38°C more than 2 days. bBetween

with smaller prostate glands (7.5 days and 6.2 days respectively, P # 0.05). DISCUSSION In this study, we applied a method for ANOVA of LOS that attempts to incorporate clinical considerations more explicitly than those of free stepwise methods. Specifically, this clustered modeling approach ensures the forcing of important patient attributes into a model when assessing the impact of other factors on which they are at least partly dependent. By forcing precedent or causal factors to enter first into the model and by retaining their original contribution thereafter, we ensure that the independent relationship of those factors is measured, and we more realistically reflect the relative contribution of each factor to the variation in LOS. We determined the sequence of variables to enter the model according to our understanding of likely causal links between these factors. Patient attribute variables were the first cluster, being present before any intervention, followed by modality of intervention, which could be dependent, to some extent, on patient attributes. The third cluster sequenced was adverse events based on the knowledge that type of intervention and patient attributes have an impact

on the occurrence of such complications [23–26]. Medical center identity was chosen as the last component to capture the influence of policies or processes unique to each center that affect LOS regardless of patients, attributes, or clinical course during hospitalization. For example, some centers may have protocols to keep patients longer than others. When comparing the clustered model to the free one, the following important differences were found: The patient attribute variable indicating prostate size that contributed 12% to the variance in the clustered model was not present as a significant predictor in the free model. Modality of intervention, that is, type of surgery, and health provider variables, that is, medical center, were more strongly associated with LOS in the free model, compared with the clustered model. An additional theoretical advantage stems from our clustering scheme. By clustering factors together according to possible interventions intended to affect them, the expected impact of various interventions to shorten LOS can be assessed according to the relative contribution of the cluster of factors related to those interventions. Specifically, in the case of prostatectomy for BPH, when comparing the relative contribution of various factor clusters to the LOS variance in the clustered model, a few im-

Clustered Model to Identify Factors Affecting Hospital Length of Stay

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TABLE 3. Multivariate stepwise regression model, free variable competition; outcome variable: Log LOS

1 2 3 4 5 6 7 8 9 10 11 12 13

Variable entered

Coefficient

Partial R2

Model R2

P.F

Open surgery vs. TURPa Center B vs. center A Need for reoperation Indwelling urinary catheter Center C vs. center A Other urological complicationsb Wound infeciton Congestive heart failure Hospitalization due to UTIc Feverd Age Nonurological complications Hydronephrosis

0.47 0.42 0.70 0.16 0.27 0.23 0.53 0.24 0.18 0.15 0.006 0.11 0.13

0.244 0.091 0.067 0.041 0.031 0.022 0.023 0.013 0.011 0.008 0.007 0.004 0.003

0.244 0.335 0.402 0.443 0.474 0.496 0.519 0.532 0.543 0.551 0.558 0.562 0.565

0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0003 0.0008 0.002 0.005 0.034 0.090

5 transurethral resection of prostate. Appendix 1. cUTI 5 urinary tract infection. d. 38°C, more than 2 days.

aTURP bSee

portant points emerge. Among the patient attributes, large prostate glands are associated with longer LOS. This could be considered in the cost-effectiveness analysis of alternative medical therapies [27]. Specifically, although surgery is usually the most cost-effective treatment, in patients with large prostates medical therapy may have an advantage. Furthermore, we noted that of all the clusters of variables, modality of therapy was the most strongly associated with LOS (13.4%), independent of prostate size. Thus, changing criteria for procedure selection, in this case performing TURP rather than open surgery, would be likely to have the greatest impact. Transurethral resection of prostate has been found to be equivalent to open surgery in improving symptoms of prostatism and quality of life [28]; however, it is associated with a higher rate of recurrence and need for reoperation [29]. Whether TURP, rather than open prostatectomy, will provide equivalent clinical benefit as well as reduce LOS may vary depending on the precise risk–benefit for each patient given their risk profiles. Adverse effects were associated with an additional 11.9% of the variance independent of measured patient attributes and choice of procedure. Preventing complications through improved processes improves quality of care and reduces LOS, and it is therefore highly desirable, although perhaps more difficult and costly to achieve. Nevertheless, such efforts represent a very important frontier for LOS reduction. The smallest impact would be changes in center discharge policy (up to 7% of the variance). Experience with the clustered model for LOS so far is limited to examination of the population presented here. Further study is required to evaluate the contribution of this method in identifying and affecting factors associated with prolonged LOS. Furthermore, the decisions as to which factors to cluster together, and how to sequence these clusters, were based on the authors’ reasoning and clinical experience.

Additional improvements are likely to evolve as applications are attempted in other populations and clinical fields.

CONCLUSION The aforementioned technique for evaluating the relative contribution of various factors to hospital LOS may be applied to different patient populations and interventions and can be easily integrated into outcome studies. Because of the theoretical advantages described, this procedure may result in a sounder assessment of the possible contribution of each type of intervention. We believe that application of this method may help clinicians and administrators to focus their efforts on shortening LOS more efficiently. APPENDIX 1 VARIABLE DEFINITION 1. Sociodemographic variables: Age (continuous and categorized up to 69, 70–79, over 80), education (number of schooling years), living arrangement (at home with another person, alone or in an institution), occupation (professional, industry, services, nonskilled), employment status (full, partial, or unemployed). 2. Urological variables: Recurrent operation (yes/no), hospitalizations during last year due to urological problems (yes/no), urinary retention and indwelling urinary catheter (yes/no), urinary tract infections (yes/no), evidence of hydronephrosis (yes/no), diverticula (yes/no) or calculi (yes/no) on ultrasound, computerized tomography scan or intravenous pyelogram, prostate size estimation by rectal examination (categorized as large when two fingers or more, or small otherwise), noninvasive therapy for BPH (yes/no).

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3. Medical history and comorbidity states: Number of hospitalizations in past year for nonurological indications, other diseases present: up to four diseases considered per patient, ICD-9 coded by physician according to diagnosis on medical file, and responses to specific questions concerning cardiovascular and pulmonary illness. These codes were used to build HCFA [28], Charlson [29] and comorbidity indices. Binary indicator variables were constructed for a number of diseases often known to affect quality of life (past myocardial infarction, ischemic heart disease, non–insulin-dependent diabetes mellitus, hypertension, chronic obstructive pulmonary disease, past cardiovascular accident, congestive heart failure, and peptic disease). Total number of diagnoses was taken as a comorbidity measure variable. Laboratory data including hematocrit, albumin, creatinine, BUN, presence of positive urine culture or hematuria. 4. Operation type (TURP or open prostatectomy) 5. Occurrence of adverse events: Presence of any of the following immediate urological complications: hemorrhage with need for blood transfusion, hemorrhage without transfusion, wound problems (discharge, inflammation or abscess), fever (.388C for more than 2 days), meatus complications (stricture or meatitis), urinary retention, urinary tract infection, surgical complication (such as perforation of prostatic capsule or bladder), anesthesia complications (severe headache and backache and spinal anesthesia), need for immediate recurrent operation. Presence of any nonurological complication: Exacerbation of chronic disease: angina, arrhythmia, diabetes mellitus, chronic lung disease, hypertension Acute medical condition: myocardial infarction, stroke, pulmonary embolism, gastrointestinal bleed, state of confusion, depression, severe drug reaction, syncope, thrombophlebitis, hypotension 6. Medical center (one of the three participating centers at which the surgery was performed)

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