HA425 Unit 3 Door-to-Provider Data Analysis Example

One Average Hiding Two Departments: A Data Analysis of October Door-to-Provider Times at a Composite Community Hospital Emergency Department, Showing Why the Median and the 90th Percentile Tell Different Stories and How Arrival Hour Splits Them

[Student Name]

Purdue University Global

HA425: Operational Analysis and Quality Improvement

Unit 3 Data Analysis

[Instructor Name]

[Date]

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

The Data

The tracking system recorded [2,927] visits in October. [37] had no provider stamp and were excluded, leaving [2,890]. Door-to-provider time runs from arrival to the first stamp showing a provider has seen the patient, following standard emergency department definitions (Welch et al., 2011). Provider stamps can trail actual contact by a few minutes, so all times may be slightly long.

Center and Spread

Summary: mean [42] minutes; median [31]; standard deviation [36]; 90th percentile [104]. Figure 1, a histogram, is sharply skewed to the right: most patients are seen within 40 minutes, but a long tail stretches past two hours. The mean sits [11] minutes above the median because the tail pulls it up. For skewed waiting times, the median is the better single summary of a typical patient, and the 90th percentile better describes the experience patients complain about. The mean describes no actual patient; the median describes the typical one, and the 90th percentile describes the ones who write complaint letters.

Stratifying by Arrival Hour

Figure 2 shows box plots by four arrival blocks:

1. 07:00 to 11:00: median [18], 90th percentile [41].

2. 11:00 to 19:00: median [29], 90th percentile [78].

3. 19:00 to 23:00: median [64], 90th percentile [151].

4. 23:00 to 07:00: median [20], 90th percentile [45].

The evening block is a different operation. Its median is more than double the day's, and its tail is twice as long. The morning and overnight blocks look alike, and the day block sits between.

Over the Month

Figure 3, a run chart of the evening median by day, shows no trend and no shift: the evening median stayed between [52] and [78] minutes on every weekday. Weekends were lower. A run chart is a simple way to see whether a process is stable over time and whether a change is real or random (Perla et al., 2011). The evening problem is not a bad week; it is the usual pattern.

Arrivals and Waits

Figure 4 plots arrivals per hour against the median wait for each hour of the day. Waits rise sharply after 19:00, although arrivals between 19:00 and 21:00 are no higher than between 13:00 and 17:00. The same demand produces longer waits in the evening, which points to a change in capacity, not demand.

Is the Evening Different by Chance?

With roughly [520] evening visits in the month and medians that stayed high every weekday, chance is not a plausible explanation. A control chart would place almost every evening point above the day's center line. Statistical process control distinguishes common-cause variation, built into a process, from special causes, and the evening pattern behaves like a stable process with a different average (Benneyan et al., 2003).

Who Waits in the Evening

The evening tail is not made of one kind of patient. Mid-acuity patients, those who need a room and tests but are not critically ill, make up about [70] percent of the evening's waits over [90] minutes. High-acuity patients are roomed quickly at any hour, and low-acuity patients are often seen in a fast-track area until it closes at 21:00. The evening problem falls mostly on the middle group, which is also the group most likely to leave.

Leaving Without Being Seen by Block

The same split appears in walkouts. In October, [1.8] percent of day arrivals left without being seen, compared with [6.4] percent of evening arrivals. Walkouts rise with the wait, so the 90th percentile, not the mean, is the better early warning.

What the Analysis Suggests

The evening is a separate operation with its own constraint. The process map located a long wait for rooms; this analysis shows the wait concentrates after 19:00 at the same demand level. The next unit should model evening capacity.

How the Figures Were Built

All four figures were built in a spreadsheet from the tracking system's export. Arrival hour was taken from the registration stamp. Box plots show the median, the middle half of waits and the 90th percentile, rather than the extreme values, so a single long wait does not dominate the picture.

Limits

One month of data may not capture seasonal changes. Provider stamps may lag. Excluded visits may differ from included ones.

Recommendations for Reporting

Report the median and 90th percentile, not the mean, and report them by arrival block. A single monthly figure hides the problem the department most needs to fix.

Conclusion

October's average described no one. Split by hour, the data show a department that works well most of the day and poorly in the evening, at the same level of demand.

References

Benneyan, J. C., Lloyd, R. C., & Plsek, P. E. (2003). Statistical process control as a tool for research and healthcare improvement. Quality and Safety in Health Care, 12(6), 458-464. https://doi.org/10.1136/qhc.12.6.458

Perla, R. J., Provost, L. P., & Murray, S. K. (2011). The run chart: A simple analytical tool for learning from variation in healthcare processes. BMJ Quality & Safety, 20(1), 46-51. https://doi.org/10.1136/bmjqs.2009.037895

Welch, S. J., Asplin, B. R., Stone-Griffith, S., Davidson, S. J., Augustine, J., & Schuur, J. (2011). Emergency department operational metrics, measures and definitions: Results of the second performance measures and benchmarking summit. Annals of Emergency Medicine, 58(1), 33-40. https://doi.org/10.1016/j.annemergmed.2010.08.040