HCS 493 Week 5 Advanced Techniques in Data Analysis Example

Signal or Noise After the Seven-Day Visit? A Control Chart, a Readmission Risk Score and a Stratified Comparison for One Hospital's Heart Failure Program

[Student Name]

University of Phoenix

HCS/493: Data Analytics for Health Care Managers

Week 5 Assignment

[Instructor Name]

[Date]

The hospital, its patients and its monthly counts are composites written for a model paper; methods and published results come from the sources listed.

A year after a composite community hospital began scheduling a clinic visit within seven days of discharge for every heart failure patient, the improvement team met to decide whether to keep paying for the extra clinic hours. The hospital's own 30-day readmission rate for heart failure had been 21.4% in the year before the change and 17.9% in the year after. The chief financial officer asked whether that drop was real or just a good year. Descriptive statistics could not answer that question. This paper uses two advanced techniques, statistical process control and risk stratification, to answer it and to find out which patients benefited most.

Why Two Averages Are Not Enough

Comparing one annual rate with another treats each year as a single number and hides what happened month to month. A drop could reflect a gradual trend that began before the program, one unusual month or ordinary random variation in a small population. With about 17 heart failure discharges a month, a few readmissions more or less change the monthly rate by several points.

Statistical Process Control

Statistical process control plots data over time with a center line and upper and lower control limits calculated from the data. Variation inside the limits with no pattern is common-cause variation, the noise every process has. Points outside the limits or specific patterns signal special-cause variation, a real change. Thor et al. (2007), in a systematic review, found statistical process control applied across a wide range of health care settings and reported that it helped teams manage change and improve processes, while noting that its power depends on correct application, including risk adjustment and stratification.

Building the P-Chart

Because the measure is a proportion, the share of discharges readmitted within 30 days, the team used a p-chart. Each month's point is readmissions divided by discharges. The center line for the 12 baseline months was 21.4%. Control limits were set at three standard errors above and below the center line, calculated for each month from its own number of discharges, so months with fewer patients have wider limits. With 17 discharges, the limits ran from roughly 0% to 51%.

Reading the Chart

The team applied three common rules for special causes: a single point outside a limit, a run of eight points in a row below or above the center, and six points in a row steadily rising or falling. No month fell outside the limits, because monthly counts are small. But beginning in the third month of the program, eight consecutive months fell below the baseline center line, which meets the shift rule. The team then recalculated a new center line for the program period at 17.9%.

What the Chart Shows and Does Not Show

The shift indicates that the process changed after the program began, and the timing, three months after launch as clinic scheduling reached full reliability, fits the program. A control chart can show that something changed and when; it cannot prove that the program, rather than another change at the same time, caused it. The team checked for other changes: a new cardiologist joined in month seven of the program, after the shift began, and no change to admission criteria occurred.

Risk Stratification

The next question was whether the program worked equally for all patients. To compare fairly, the team scored each patient with the LACE index, a published tool whose letters stand for its four inputs: days in hospital, an emergent rather than planned admission, a comorbidity score and the number of emergency visits in the previous half year (van Walraven et al., 2010). In the original validation, scores from 0 to 19 corresponded to an expected risk of death or unplanned readmission within 30 days from 2.0% to 43.7%, with a c statistic of 0.684.

The Stratified Comparison

Patients were divided into lower risk, LACE score below 10, and higher risk, 10 or above. Among lower-risk patients, the readmission rate fell from 14.1% to 13.2%, a change small enough to be random. Among higher-risk patients, it fell from 29.8% to 23.0%. Most of the program's benefit came from higher-risk patients, who were also the most likely to have missed follow-up before the program. Both groups were small, so the team treated the difference as a strong signal to act on rather than a precise estimate.

How Much to Trust Risk Scores

Kansagara et al. (2011) reviewed 26 readmission prediction models and found that most performed poorly or modestly, with c statistics mostly between 0.55 and 0.72, though a few models used at discharge reached 0.83, and that few models included functional status or social factors. For the hospital, that means the LACE score is useful for sorting groups and allocating resources but should not be used to deny follow-up to any individual patient labeled low risk.

Other Techniques Considered

The team considered logistic regression to estimate the program's effect while adjusting for age, kidney function and discharge day. It was deferred because the program applied to every patient, leaving no comparison group within the same period, and because the sample was small. An interrupted time-series design using the monthly data is planned once 24 months of program data are available.

The Decision

The committee voted to keep the program and to add a nurse home visit within 72 hours for patients with LACE scores of 10 or higher, funded by the clinic hours saved by moving lower-risk patients' first visit to a video appointment.

Next Analysis

The p-chart will continue monthly, with a new baseline from the program period, so the team can see whether the home visits produce a second shift. The chart will be stratified by risk group, and the team will add a balancing chart of 30-day mortality.

Conclusion

Two annual averages suggested improvement but could not rule out chance. A p-chart showed a sustained shift that began when the program matured, and risk stratification showed that higher-risk patients gained the most. Used together, with honest limits, these techniques turned a budget question into a targeted decision and a plan for the next cycle of improvement.

References

Kansagara, D., Englander, H., Salanitro, A., Kagen, D., Theobald, C., Freeman, M., & Kripalani, S. (2011). Risk prediction models for hospital readmission: A systematic review. JAMA, 306(15), 1688-1698. https://doi.org/10.1001/jama.2011.1515

Thor, J., Lundberg, J., Ask, J., Olsson, J., Carli, C., Harenstam, K. P., & Brommels, M. (2007). Application of statistical process control in healthcare improvement: Systematic review. Quality and Safety in Health Care, 16(5), 387-399. https://doi.org/10.1136/qshc.2006.022194

van Walraven, C., Dhalla, I. A., Bell, C., Etchells, E., Stiell, I. G., Zarnke, K., Austin, P. C., & Forster, A. J. (2010). Derivation and validation of an index to predict early death or unplanned readmission after discharge from hospital to the community. Canadian Medical Association Journal, 182(6), 551-557. https://doi.org/10.1503/cmaj.091117