HS345 Unit 10 Statistical Analysis Report Example

Fewer Gaps, but Fewer Than It First Looked: A Unit 10 Statistical Analysis Report on Automatic Refills for Blood Pressure Medicine

[Student Name]

Purdue University Global

HS345: Biostatistics

Unit 10 Statistical Analysis Report

[Instructor Name]

[Date]

The pharmacy chain, its patients and every count are composite; the methods papers and text cited are real.

Summary

Automatic refill enrollment appears to prevent four or five medication gaps for every 100 patients over six months, not the eight a first look suggests. Older patients were more likely to enroll and less likely to have gaps for reasons unrelated to the program, and separating them by age removes about a third of the apparent benefit. The program is still worth offering, with the more modest figure used in planning.

The Data

The chain's records cover [2,400] adults filling a blood pressure medicine at one of six stores over six months. [1,560] were enrolled in automatic refills, in which the pharmacy refills the prescription on schedule and texts the patient when it is ready; [840] were not. Enrollment was by patient choice at the counter, not by random assignment. The outcome is any gap of more than seven days without medicine on hand, judged from fill dates and days supplied.

Description

Gaps among enrolled patients: [281] of [1,560], 18.0 percent. Gaps among patients not enrolled: [215] of [840], 25.6 percent. Risk difference: 7.6 percentage points. Risk ratio: 0.70.

Enrolled patients were older on average: [67] percent were 65 or older, against [33] percent of those not enrolled.

A Test of the Crude Difference

A chi-square test of the two-way table gives a statistic of about 19.1, and with one degree of freedom that corresponds to p well under 0.001. At 95 percent confidence, the crude risk difference lies between 4.1 and 11.1 percentage points. On its face, enrolled patients had fewer gaps, and chance is an unlikely explanation for a difference this size in a sample this large (Bland, 2015).

Splitting by Age

Age is linked to enrollment, and it is linked to gaps through routes that bypass the program entirely: older patients in this chain are more often on Medicare plans with mail-order backups and see their doctors more regularly. That makes age a likely confounder (Jager et al., 2008).

Patients 65 and older: enrolled, [156] of [1,040] with gaps, 15.0 percent; not enrolled, [53] of [280], 18.9 percent. Risk difference 3.9 points.

Patients under 65: enrolled, [125] of [520], 24.0 percent; not enrolled, [162] of [560], 28.9 percent. Risk difference 4.9 points.

Within each age group the difference is four to five points, and the crude figure of nearly eight appears only because the enrolled group holds twice as many older patients, who have fewer gaps either way.

A weighted summary across the two strata, a Mantel-Haenszel risk difference, comes to about 4.5 points, bracketed at 95 percent confidence by about 0.8 and 8.1 points. The interval still excludes zero, but it is wider and closer to it than the crude interval.

What Remains Uncertain

Age is not the only difference between patients who chose enrollment and those who did not. People who sign up for a reminder service may already be more organized about their health, and that cannot be measured from pharmacy records. Some of the remaining 4.5 points may reflect that self-selection rather than the program. Fill records also miss medicine obtained elsewhere, such as free samples or a second pharmacy, which would count as false gaps. These limits are typical of observational comparisons of programs that people opt into (Grimes & Schulz, 2002).

Checking the Gap Definition

A gap of more than seven days was chosen before the analysis because most blood pressure medicines lose much of their effect within a week of the last dose, and because it matches the window the chain's pharmacists already use when they call patients about late refills. To see whether the result depended on that choice, the analysis was repeated with a fourteen-day threshold. Gaps became less common in both groups, [11.2] percent among enrolled patients and [16.9] percent among the rest, but the age-adjusted difference stayed close to four points. A conclusion that holds across two reasonable definitions is more trustworthy than one that appears under only one, and reporting the check lets a reader see that the threshold was not chosen to produce a favorable answer.

Results by Store

The six stores differed in how many patients enrolled, from [48] percent at the smallest store to [77] percent at the busiest. If the benefit were real, it should appear in most stores rather than in one. The age-adjusted difference favored enrollment in five of the six stores, and the sixth, with only [190] patients, showed almost no difference with a wide interval. Pharmacists at the busiest store said they offer enrollment to every patient at the counter, while two smaller stores offer it only when patients ask about refills. That difference in how the program is offered may itself explain some of the variation in enrollment, and it suggests a simple way to increase reach without new cost. Store-level results rest on small numbers, so they are reported here as a consistency check rather than as six separate findings, and no store should be judged on its own figure.

Who Still Has Gaps

Even among enrolled patients, nearly one in five had a gap. Chart notes for a random [40] of them point to three causes: prescriptions that ran out of authorized refills while the pharmacy waited for the prescriber, patients who were traveling, and changes in insurance that held up a fill. Automatic refills address none of these, which is why they reduce gaps without ending them.

Recommendation

The chain should continue offering automatic refills and should offer them actively at the counter to patients under 65, whose gap rate is highest. For planning, it should assume a benefit of about four to five fewer gaps per 100 patients, not eight. To learn the true effect, the chain could offer enrollment by default to a random half of new prescriptions at two stores for six months, which would remove the self-selection that this analysis cannot.

A Note on Methods

The report moves from a crude comparison to a stratified one because the first table answered the wrong question: whether enrolled patients had fewer gaps, rather than whether enrollment caused fewer gaps. Stratification by a single confounder is transparent and easy to explain to managers. A regression model with several covariates would be the next step if more patient data were available, but it would not solve self-selection either. Only random assignment can do that, which is why the recommendation ends with a small trial.

References

Bland, M. (2015). An introduction to medical statistics (4th ed.). Oxford University Press.

Grimes, D. A., & Schulz, K. F. (2002). Bias and causal associations in observational research. The Lancet, 359(9302), 248-252. https://doi.org/10.1016/S0140-6736(02)07451-2

Jager, K. J., Zoccali, C., MacLeod, A., & Dekker, F. W. (2008). Confounding: What it is and how to deal with it. Kidney International, 73(3), 256-260. https://doi.org/10.1038/sj.ki.5002650