NU704 Unit 7 Measures of Association Problem Set Example

Fourteen of 201 Against 31 of 214: A Unit 7 Measures of Association Problem Set on an Insulin Discharge Pilot

[Student Name]

Purdue University Global

NU704: Biostatistics, Epidemiology, and Social Determinants of Population Health

Unit 7 Measures of Association Problem Set

[Instructor Name]

[Date]

The pilot figures are illustrative, prepared to practice the calculations for the composite project; the sources cited are real.

The Two-by-Two Table

The bundle period is treated as the exposed group and the year before as the unexposed group. In the bundle group, 14 patients returned and 187 did not, 201 in all. In the comparison group, 31 returned and 183 did not, 214 in all. These are illustrative figures for practice, not project results, chosen to resemble what a modest improvement on units of this size might look like after six months.

Problem 1: The Two Risks

Each period's risk is its returns over its discharges. For the bundle period, 14 divided by 201 equals 0.0697, or about 7.0 percent. In the comparison group, 31 divided by 214 equals 0.1449, or about 14.5 percent.

Problem 2: Proportional Change

Dividing the bundle period's risk by the earlier year's, 0.0697 over 0.1449, gives a relative risk of 0.48. Patients in the bundle period had about half the risk of a glucose-related return. Working on the logarithm of the ratio, as is standard, puts its 95 percent limits at 0.26 and 0.88. Because the interval excludes 1, the data are not compatible with no difference at the conventional level, though anything from a 12 percent to a 74 percent reduction remains consistent with these counts.

The relative risk reduction is one minus the relative risk, 0.52, or 52 percent.

Problem 3: The Difference in Points

Subtracting the later risk from the earlier one, 0.1449 minus 0.0697, leaves an absolute reduction of 0.0752, or 7.5 percentage points (95 percent CI roughly 1.6 to 13.4 points). The absolute figure tells a nurse executive how many returns would be avoided per hundred patients, which the relative figure alone cannot.

A halving sounds dramatic; seven or eight fewer returns per hundred patients is what the unit would actually see.

Problem 4: Patients Treated per Return Avoided

Dividing one by the absolute risk reduction gives the number needed to treat, here 13.3, which is rounded up to 14 because patients come whole. About fourteen patients would need to receive the bundle to prevent one glucose-related return within 30 days. Laupacis et al. (1988) introduced the measure because it expresses benefit in terms clinicians and managers can weigh against effort and cost. The wide interval around the absolute reduction means the true number could be as low as about 8 or as high as about 60.

Problem 5: Odds Ratio

The odds of return in the bundle group are 14 divided by 187, or 0.0749; in the comparison group, 31 divided by 183, or 0.1694. The odds ratio is 0.0749 divided by 0.1694, or 0.44 (95 percent CI 0.23 to 0.86). The odds ratio is lower than the relative risk because the outcome is not rare, about 14 percent in the comparison group. Viera (2008) explains that odds ratios exaggerate the apparent effect relative to risk ratios as the outcome becomes more common, so describing 0.44 as 'a 56 percent drop in risk' would overstate what the data show.

Problem 6: Which Measure Fits?

Because the project follows defined groups of patients forward and counts outcomes, it measures risk directly, so the relative risk and absolute risk reduction are the natural measures. The odds ratio is mainly useful in case-control studies, where risk cannot be calculated, and in logistic regression. For decision makers, the project should put the point difference and the patients-per-return figure first, with the relative risk for comparison with published studies.

Problem 7: A Test of Association

Run through a chi-square test, the four cells give a statistic near 6.06; with a single degree of freedom, that corresponds to p of roughly .014. This agrees with the confidence interval for the relative risk, which excludes 1. The p-value, however, adds little beyond the interval; as the American Statistical Association has stressed, it does not tell readers how large or how important the difference is (Wasserstein & Lazar, 2016).

Problem 8: What These Measures Cannot Prove

Comparing two periods on the same units leaves room for explanations other than the bundle. Other things may have changed between the periods: a new hospitalist group, a different patient mix, seasonal variation or broader efforts to reduce readmissions. The project will therefore track the outcome monthly on a run chart, look at whether the change coincides with the bundle's start, compare with a unit that did not adopt the bundle if one is available and describe other changes during the period.

Conclusion

Using illustrative counts, the bundle period would show a relative risk of 0.48, an absolute reduction of 7.5 percentage points and roughly fourteen patients treated per return prevented, all with wide intervals. Leading with absolute measures, reporting intervals and acknowledging the limits of a before-and-after design will keep the project's eventual results honest.

References

Laupacis, A., Sackett, D. L., & Roberts, R. S. (1988). An assessment of clinically useful measures of the consequences of treatment. New England Journal of Medicine, 318(26), 1728-1733. https://doi.org/10.1056/NEJM198806303182605

Viera, A. J. (2008). Odds ratios and risk ratios: What's the difference and why does it matter? Southern Medical Journal, 101(7), 730-734. https://doi.org/10.1097/SMJ.0b013e31817a7ee4

Wasserstein, R. L., & Lazar, N. A. (2016). The ASA statement on p-values: Context, process, and purpose. The American Statistician, 70(2), 129-133. https://doi.org/10.1080/00031305.2016.1154108