PHLT 8331 Week 5 Two-Group Mean Comparison Example

Two Groups, One Average Each: Comparing Time in Therapeutic Range Between Pharmacist-Managed and Physician-Managed Clinics in a Composite Registry, in Units a Clinic Already Uses

Student Name

Walden University

PHLT 8331: Fundamentals of Biostatistics

Instructor Name

Month Day, Year

Two Groups, One Average Each: Comparing Time in Therapeutic Range Between Pharmacist-Managed and Physician-Managed Clinics in a Composite Registry, in Units a Clinic Already Uses

The Comparison

The second hypothesis pair asked whether mean time in therapeutic range differs between patients at the two clinics that use pharmacist management and patients at the clinic that uses physician management. In the composite registry, 486 patients at the pharmacist-managed clinics and 318 at the physician-managed clinic had complete INR records for the most recent six months. This comparison uses an independent-samples t-test, because each patient belongs to only one group. It reports the difference in percentage points of time in range, the unit clinicians already use, and states the design's main weakness beside the result. All figures are composite.

Which Version of the Test

The two-sample t-test comes in two versions. The pooled, or Student, version assumes the two groups have equal variances. The Welch version does not. In this registry the standard deviations are 15.1 points at the pharmacist clinics and 18.4 at the physician clinic, a noticeable difference. Some analysts run a test for equal variances first and choose the version based on its result, but that two-step approach can distort error rates, while the Welch version holds its error rates whether the spreads match or not. Delacre et al. (2017) recommend using the Welch test by default for this reason. This comparison reports the Welch result.

Checking the Conditions

Patients in one group are separate from those in the other, satisfying independence between groups. Within each group, patients at the same clinic share routines, so their results are not fully independent; the comparison treats patients as independent units, which may make the standard error slightly small. Time in therapeutic range is left-skewed in both groups, but with several hundred patients per group, the sampling distribution of each mean is close to normal, and t-tests are known to be robust in samples of this size (Lumley et al., 2002).

The Result

At the pharmacist-managed clinics, patients averaged 67.2% of days in therapeutic range, against 61.9% at the physician-managed clinic, a gap of 5.3 percentage points. The Welch standard error of the difference was 1.24, giving t = 4.28 on about 584 degrees of freedom, p < .001. The gap's 95% confidence interval stretches from 2.9 to 7.7 percentage points.

Table 1

Time in Therapeutic Range by Type of Clinic Management (Composite Figures)

Note. Composite figures. Welch t = 4.28, df about 584, two-sided p < .001; 95% CI for the difference, 2.9 to 7.7 percentage points.

What the Difference Means in Practice

A difference of 5.3 percentage points in time in therapeutic range means that, over six months, patients at the pharmacist clinics spent on average about 10 more days with an INR in the target range than patients at the physician clinic. That is the kind of figure a clinic manager can picture. The medians tell the same story, which matters because time in range is skewed: the difference is not driven by a few extreme values.

The Design's Main Weakness

The two groups differ by clinic, not only by type of management. The physician-managed clinic serves a population with more uninsured patients and has a smaller nursing staff. Any of these differences could contribute to lower time in range there. Reviews of pharmacist-managed anticoagulation have found better control than routine care in most studies (Manzoor et al., 2017), so the result is plausible, yet a comparison across sites leaves management and clinic tangled together. A comparison within the same clinic before and after a change in management, or adjustment for patient characteristics, would address it in part.

Change Scores or Six-Month Readings?

For this between-clinic comparison, the outcome is the six-month time in range, not a change score, because patients at the physician clinic did not undergo a change in management and many joined the registry at different times. Change scores suit the within-patient question in Week 4; current values suit this one.

Adjusting for Patient Differences

One way to address part of the design's weakness is to compare patients at the different clinics after accounting for characteristics that affect anticoagulation control, such as age, insurance, the reason for taking warfarin and how long a patient has been on it. A regression model with time in range as the outcome and clinic type plus these characteristics as predictors would estimate the difference between clinic types among patients who are similar on the measured factors. In the composite registry, such adjustment reduced the difference from 5.3 to 4.1 percentage points, suggesting that some, but not all, of the raw gap reflects differences in who attends each clinic. Unmeasured differences, such as clinic culture or staffing, would remain. This analysis goes beyond the week's scope and is mentioned to show how the comparison could be strengthened. A matched comparison, pairing each pharmacist-clinic patient with a physician-clinic patient of similar age, indication and insurance, would be another route to the same goal and is easier to explain to a clinic audience. Either approach would narrow the gap between what the data show and what the clinics want to know.

Reporting the Comparison

A full report names the test version, gives each group's size, mean and standard deviation, and gives the gap, its 95% interval, the t value, the approximate degrees of freedom and the p-value. It also reports medians when the outcome is skewed and names the design's main weakness. Readers should be able to judge the size and precision of the difference, not only whether it passed a threshold.

Summary

Patients at the pharmacist-managed clinics had a mean time in therapeutic range 5.3 percentage points higher than patients at the physician-managed clinic, with a 95% confidence interval from 2.9 to 7.7 points. The difference is statistically clear and large enough to matter, but because it compares clinics, it cannot be attributed to management alone.

References

Delacre, M., Lakens, D., & Leys, C. (2017). Why psychologists should by default use Welch's t-test instead of Student's t-test. International Review of Social Psychology, 30(1), 92-101. https://doi.org/10.5334/irsp.82

Lumley, T., Diehr, P., Emerson, S., & Chen, L. (2002). The importance of the normality assumption in large public health data sets. Annual Review of Public Health, 23, 151-169. https://doi.org/10.1146/annurev.publhealth.23.100901.140546

Manzoor, B. S., Cheng, W.-H., Lee, J. C., Uppuluri, E. M., & Nutescu, E. A. (2017). Quality of pharmacist-managed anticoagulation therapy in long-term ambulatory settings: A systematic review. Annals of Pharmacotherapy, 51(12), 1122-1137. https://doi.org/10.1177/1060028017721241