HA535 Unit 3 Heart Failure Length of Stay Statistics Example

Average Four Point Six Eight Days, Median Four, Longest Twenty-Three: A Healthcare Descriptive Statistics Report on Heart Failure Length of Stay Across a Composite Regional System, Reading Center, Spread, Shape and Discharge Destination

[Student Name]

Purdue University Global

HA535: Data Analytics for Health Care Managers

Unit 3 Healthcare Descriptive Statistics

[Instructor Name]

[Date]

The system, the 486 discharges and every statistic are composite and bracketed for the writer's own data; figures are described in words for this page.

The Data

All [486] discharges from the heart failure diagnosis-related groups at three hospitals in one fiscal year, after duplicate removal and the corrections made in Unit 2. Each stay's length is the number of midnights between admission and discharge.

Center and Spread

Mean [4.68] days; median [4]; standard deviation [2.96]; interquartile range [3] to [6]; 90th percentile [8]; maximum [23]; skewness [1.81]. A long right tail drags the average upward, which is why it exceeds the median. For skewed data such as length of stay, the median describes a typical patient better, and the 90th percentile describes the long stays that consume beds.

Shape

A histogram shows most stays between two and six days and a tail stretching to [23]. Using the common rule of the third quartile plus one and a half times the interquartile range, the outlier fence sits at [10.5] days; [22] stays lie beyond it. Length of stay distributions are typically skewed and are often modeled with skewed distributions rather than the normal curve, which is why summaries built only on the mean and standard deviation can mislead (Marazzi et al., 1998). The [22] stays beyond the fence are less than five percent of patients but hold about [14] percent of heart failure bed days.

By Hospital

Side-by-side box plots compare the three hospitals:

1. Flagship: mean [4.99], median [4]; the widest box and the longest tail.

2. Suburban: mean [4.41], median [4].

3. Rural: mean [3.68], median [4]; few long stays.

The flagship's mean sits well above its median; the rural hospital's mean sits just below its own. The medians are identical. The difference among hospitals lies in the tail, not in the typical patient.

Geometric Mean

Because Medicare publishes expected stays as geometric means, the report computes one: [3.91] days, beside a bracketed [GMLOS] placeholder for the diagnosis-related group. The geometric mean dampens the effect of long stays and sits closer to the median.

Where Patients Went

Discharge destinations: home [52] percent, home with home health [24] percent, skilled nursing facility [18] percent, other [6] percent. Median length of stay for patients discharged to skilled nursing was [6] days, against [4] for those going home. Of the [22] outlier stays, [15] ended in a skilled nursing facility.

What the Destination Suggests

The tail is largely made of patients waiting for post-acute placement. Research on delayed discharge describes longer stays and worse experiences for patients who are medically ready but waiting for a place to go (Rojas-García et al., 2018). That points the system toward placement processes, not only clinical care.

Why Not Remove the Outliers

Some analysts trim stays beyond the fence before reporting averages. For a description meant to guide managers, that would hide the most important part of the picture. The long stays are not data errors; they are patients who occupied beds. Trimming is appropriate only when a value is wrong, which the Unit 2 review already handled.

Bed Days by Decile

Ranking stays from shortest to longest and dividing them into tenths shows how unevenly beds are used: the longest tenth of heart failure stays uses about [24.0] percent of all heart failure bed days, while the shortest tenth uses about [3] percent. A small group of patients drives a large share of capacity.

Questions for Managers

Which of the long-stay patients were medically ready to leave before they left? How long did each wait for a skilled nursing bed, and why? Does the flagship's longer tail reflect sicker patients or slower placement? The utilization analysis in Unit 8 will begin to answer these questions.

Stability Over the Year

A run chart of monthly median length of stay shows no trend and no shift across the fiscal year, so the pattern is the usual state of the system rather than a bad season (Provost & Murray, 2011).

What to Report

Report the median and 90th percentile alongside the mean, broken out by hospital, and report the number and destination of stays beyond the outlier fence each month.

Limits

The report covers one year of data, and some long stays may reflect complications rather than placement waits. Destination coding at the rural hospital was incomplete before repair, so its skilled nursing share may still be understated. Severity of illness was not measured here, so differences between hospitals may partly reflect sicker patients at the flagship.

Conclusion

Heart failure stays are typical in the middle and costly in the tail. The tail sits mostly at the flagship and mostly among patients bound for skilled nursing, which tells managers where to look next and what to measure each month.

References

Marazzi, A., Paccaud, F., Ruffieux, C., & Beguin, C. (1998). Fitting the distributions of length of stay by parametric models. Medical Care, 36(6), 915-927. https://doi.org/10.1097/00005650-199806000-00014

Provost, L. P., & Murray, S. K. (2011). The health care data guide: Learning from data for improvement. Jossey-Bass.

Rojas-García, A., Turner, S., Pizzo, E., Hudson, E., Thomas, J., & Raine, R. (2018). Impact and experiences of delayed discharge: A mixed-studies systematic review. Health Expectations, 21(1), 41-56. https://doi.org/10.1111/hex.12619