Multi-departmental Comparison of Hospital Length of Stay: A Statistical Analysis

Elizabeth Migliori, Nilgun Secer, Aayushi Manek, Johanna Molina, Kajol Patel, Lynda Pham,

Ramyiah Ponnudurai, Karishma Rajram, Robert Ramirez, Mehdi Nosrati

Procedure

IBM SPSS statistical software package was used to conduct analyses in this study.

Descriptive statistic function was used to calculate the mean and standard deviation for each group. The results were reported numerically in a table as well as graphically for visual comparison.

To determine the significance of difference between the mean values of these groups the data was subjected to pre-test checklist to determine the statistical method required to be used.

Data was tested for normal distribution, n quota, and homogeneity of variances to decide whether to test with One-Way ANOVA or Kruskal-Wallis method.

The n quota and homogeneity of variances passed the minimum threshold test, but the normality test result based on normal curve distribution, although valid for cardiology, was ambiguous for neurology and endocrinology.

Therefore, both ANOVA and Kruskal-Wallis methods were run to determine the degree of difference in LOS.

Post Hoc test using Tukey’s Honest Significant Difference was used to assess the significance of mean length of stay differences between cardiology and neurology, cardiology and endocrinology, and neurology and endocrinology.

The mean values of the analyzed data were cross checked with a larger, public dataset such as HCUP, to validate the findings in this study.

Hypotheses

H0 (null): After considering multiple contributing factors the LOS between three different hospital departments are not different from each other.

H1 (alternate): After considering multiple contributing factors the LOS between three different hospital departments are different from each other.

A group of 10 study members worked collaboratively to handle different aspects of this project.

The results of this study will be reported to the course instructor in presentation format by the whole team.

The authors have no conflict of interest to declare.

Demographic data

Data from 120 subjects from three different departments (40 each) were submitted for evaluation whether the length of hospital stay is different.

Our study group was blinded to as whether the three departments in this study belong to the same or different healthcare institutions, and whether they operated under a uniform administrative policies and organizational resources.

Also unknown to us were key demographic parameters such as age, gender, severity of illness and a whole host of other factors that impact hospital length of stay.

We used both the ANOVA test and the Kruskal-Wallis test to confirm the difference between the length of stay for all three departments was statistically significant and can be influenced by various factors.

By comparing our findings to data from HCUP we have learned our results are within a realistic range, and any solution that could be proposed would be applicable to all health institutions.

We lacked key demographic parameters, including the type and severity of illness, which amounted to a limited scope of the present study. There is also no uniformity of conditions that data was collected for analysis. As a result, it is not appropriate to generalize the findings. 

The study was performed under the limitation of not knowing if the three departments belong to the same or different hospitals, and whether they operated under uniform administrative policies and organizational resources.

Further studies should investigate the impending causes of the differences in length of stay in all three departments. The focus of these studies should be on the reasons for patients’ admission. The findings will provide insights into developing appropriate preventive healthcare measures that may assist in addressing the possible burden of hospitalization.

Figure 1. Descriptive Statistics describes our dataset to be comprised of three departments (cardiology, neurology, and endocrinology) with data from 40 subjects in each department. Fig.1a tabulates the mean and standard deviation for each group. Fig.1b is a bar graph of each group’s mean LOS where cardiology with highest value (7 days) and endocrinology lowest value (3.7 days).

Figure 2. As the first step in pre-test checklist, preceding analysis of difference between groups, the normal distribution of data in each group is tested. Fig.2a shows a normal distribution in cardiology dataset, however, it is unclear whether Figures 2b & 2c representing neurology and endocrinology, respectively, are normal or skewed to the left.

Figure 3. As the second and third steps in pre-test checklist, n quota and homogeneity of variances are measured. Fig.3a shows the n quota values standing at 40 (red box) are higher than the required minimum of 30, therefore, indicating this criterion is satisfied. Fig.3b displays the homogeneity of variances cover a range between 0.494 and 0.529 (red box), therefore, there is no statistically significant differences between the groups’ variances, satisfying this criterion.

Figure 5. On the other hand, if in aggregate the distribution in our three datasets can be considered as normal, the One-Way ANOVA is run. Fig.5a shows the result of ANOVA test, much like Kruskal-Wallis, is statistically significant, P<0.001 (red box). Fig.5b shows the multiple, pairwise comparisons between these three groups to identify the major contributor of this significant difference. All combinations show P<0.001, suggesting all pairs are significantly different from each other.

Analysis

The objective of this study was to identify if there was a difference in length of stay between patients admitted to Cardiology, Neurology and Endocrinology facilities.

Running descriptive statistics on the data sets reveals that 40 patients from each facility were measured thereby satisfying the n quota criterion. Figures 1a and 1b in the Results section show the mean and standard deviation for each group.

The means were compared to analyze the differences between the groups. As shown in Figure 2a, there is a normal distribution in the Cardiology set. It is unclear whether the Neurology and Endocrinology sets (Fig. 2b, 2c) are normal or skewed to the left.

Homogeneity of variance standing at a range of 0.494 to 0.529 showed there was no statistically significant difference between the variances.

As shown in Figure 4, a Kruskal-Wallis test was run to address the slight skewness of Figure 2b & 2c and the difference was found to be statistically significant.

Figure 5 illustrates the results of the One-Way ANOVA test, which similar to the Kruskal-Wallis test found a statistically significant difference between the three groups (P<0.001).

To further validate our findings, relevant HCUP information was examined (Fig. 6), exhibiting the reported average LOS as 4.6 days among 40 million discharges in 2006. The HCUP report (Fig. 6b), shows circulatory conditions to be the most frequent cause of hospital stays and supports the mean values in the dataset.

As shown in Fig.5a the result of ANOVA test, much like Kruskal-Wallis (Fig. 4), is statistically significant, P<0.001. Therefore, the null hypothesis is rejected and the alternative hypothesis is accepted.

Hospital length of stay has been a major concern for patients and the health care industry in respect to quality of care, cost, quality of life, and survival. In our literature search we encountered many research studies that separately addressed factors that contribute to a patient’s length of stay. However, we did not encounter a research design where the impact of multiple factors to be taken into consideration while comparing the length of stay in three independent cohorts of patients. We sought to address this gap in information with the data provided for this study. This study compares hospital length of stay among three independent patient cohorts while considering multiple factors, which was not encountered in the search.

Methods: 120 subjects from three different hospital departments (40 each) were evaluated for differences in length of stay. Mean length of stay from three departments were calculated by descriptive statistics and the data were subjected to ANOVA and Kruskal-Wallis tests for statistical analyses.

Results: The difference between the length of stay for all three departments was statistically significant by both tests (P<0.001), rejecting the null hypothesis. Cardiology department patients (μ = 7.05 days) had a significantly longer length of stay compared neurology department patients by 1.53 days (μ = 5.53 days, p < .001) and endocrinology department patients by 3.38 days (μ = 3.68 days, p < .001). Neurology department patients compared to endocrinology department patients had a significantly longer length of stay by 1.85 days (μ = 3.68 days, p < .001).

Discussion: In a first of its kind this study showed the hospital length of stay is a health care measure that is i) significantly different in three different hospital departments, and ii) influenced by factors such as socioeconomic status, comorbidity, organizational resources, and hospital acquired infection.