IHP 525 Module 7 Milestone Three Example

Milestone Three: Adjusted Regression Results for the Bayview County Blood Pressure Program

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Southern New Hampshire University

IHP 525: Biostatistics

Module Seven Milestone Three

[Instructor Name]

[Date]

Milestone Three: Adjusted Regression Results for the Bayview County Blood Pressure Program

Milestone Two committed to a primary analysis, six secondary analyses, multiple imputation and three sensitivity checks. This milestone reports what those analyses found, in the order the plan specified, letting any reader confirm that no method was swapped after the data were examined. Results are presented as effect sizes with 95% confidence intervals first and p-values second.

Participants and Follow-Up

The evaluation included 240 program participants and 260 usual-care patients. Six-month readings were available for 218 participants (91%) and 231 comparison patients (89%). At baseline, participants were slightly older (mean 58.3 versus 56.9 years) and had higher systolic pressure (152.4 versus 149.8 mm Hg), differences that the adjusted models account for. Those lost to follow-up were younger and had higher baseline readings in both groups, which is why the plan called for imputation rather than relying on complete cases.

Why Adjustment Changes the Estimate

The unadjusted difference in mean change was 6.6 mm Hg in favor of the program. Because participants started higher, part of their larger drop could reflect regression to the mean, the tendency of extreme readings to move toward average on remeasurement. Including baseline pressure in the model separates that tendency from the program's effect. Age, sex and number of medications were added because each could plausibly influence both enrollment and pressure change.

Primary Result

In the linear regression using twenty imputed data sets, program participation was associated with a 6.1 mm Hg greater fall in systolic pressure than usual care, with a 95% confidence interval of 3.9 to 8.3 mm Hg and p below 0.001. The whole interval lies above zero, meaning every plausible value favors the program, and its lower end sits close to the 5 mm Hg benchmark the plan fixed before any data were opened, so the result is both statistically clear and practically important, although a benefit slightly smaller than 5 mm Hg cannot be excluded.

Table 1. Linear Regression of Six-Month Change in Systolic Pressure

Note. Estimates pooled across twenty imputed data sets; n = 500; R squared about 0.21.

Reading the Other Coefficients

Each 1 mm Hg higher starting pressure predicted a 0.32 mm Hg larger fall, confirming the regression to the mean that motivated adjustment. Age, sex and medication count had small coefficients whose intervals crossed zero, so the data do not show that these characteristics changed the size of the drop. The model explained about a fifth of the variation in change, which is typical for behavioral programs where daily habits and adherence vary widely.

Presenting Effects as Intervals

In keeping with Gardner and Altman (1986), every estimate in this milestone is paired with its interval so that decision makers can see the plausible range, not simply whether a threshold was crossed. A reader who wants to know whether the program might be only marginally useful can look at the lower bound of 3.9 mm Hg, and one wondering about the best case can look at 8.3.

Keeping Pressure Continuous

The primary outcome is change in pressure as a number, not whether people crossed a control line. Turning a measured value into a yes-or-no category, as Altman and Royston (2006) demonstrated, discards information, lowers power and can create misleading jumps at arbitrary cut points. Control is still reported, because clinicians and funders use it, but as a secondary outcome.

Control Rate: Logistic Regression

Among completers, 100 of 218 program participants (45.9%) reached a systolic reading below 140 at six months compared with 67 of 231 usual-care patients (29.0%). After adjustment, the odds of control were 2.14 times higher in the program group, with a 95% interval of 1.43 to 3.21. Peduzzi et al. (1996) found through simulation that logistic models carrying under roughly ten outcome events for each predictor gave biased coefficients and unreliable intervals. Here the smaller outcome category holds 167 controlled patients across five predictors, roughly 33 events per variable, well above that level.

Table 2. Secondary Outcomes Against the Bonferroni Threshold

Note. Adjusted for age, sex, baseline pressure and medication count.

Imputed Versus Complete-Case Estimates

Sterne et al. (2009) recommended presenting complete-case results alongside imputed ones so readers can judge whether the handling of missing data drove the conclusions. The complete-case adjusted difference was 6.4 mm Hg (4.2 to 8.6), close to the imputed 6.1. Under the deliberately pessimistic assumption that everyone missing a six-month reading had no improvement, the difference shrank to 5.3 mm Hg (3.1 to 7.5) but remained clearly above zero. Excluding the two sites with different measurement protocols gave 6.0 mm Hg (3.6 to 8.4).

Exploratory Subgroups

Among women, the adjusted difference was 3.9 mm Hg with an interval of -0.2 to 8.0, compared with 8.1 mm Hg among men; the test for interaction gave p = 0.07. This does not show that the program fails for women, since the interval is wide and includes meaningful benefit, and with six secondary tests planned the finding could be chance. It does justify asking women participants whether session times or content fit their needs. Age and setting subgroups showed no differences worth noting.

Limitations of These Results

Participants chose to enroll, so unmeasured differences such as motivation may remain despite adjustment, and the estimate should be read as an association that is consistent with benefit rather than proof of cause. Imputation assumes that missingness depends only on the variables in the model. Readings came from routine clinic measurements, which vary in technique across sites, and cuff size or rest time before measurement was not always recorded. Finally, six months is a short window, and whether the gap persists at one or two years is unknown.

Conclusion

After adjustment for age, sex, baseline pressure and medications, the program was associated with a 6.1 mm Hg greater fall in systolic pressure and roughly doubled odds of control, results that held across imputed, complete-case and pessimistic analyses. The final project will interpret these findings for county leaders and recommend next steps.

References

Altman, D. G., & Royston, P. (2006). The cost of dichotomising continuous variables. BMJ, 332(7549), 1080. https://doi.org/10.1136/bmj.332.7549.1080

Gardner, M. J., & Altman, D. G. (1986). Confidence intervals rather than P values: Estimation rather than hypothesis testing. BMJ, 292(6522), 746-750. https://doi.org/10.1136/bmj.292.6522.746

Peduzzi, P., Concato, J., Kemper, E., Holford, T. R., & Feinstein, A. R. (1996). A simulation study of the number of events per variable in logistic regression analysis. Journal of Clinical Epidemiology, 49(12), 1373-1379. https://doi.org/10.1016/S0895-4356(96)00236-3

Sterne, J. A. C., White, I. R., Carlin, J. B., Spratt, M., Royston, P., Kenward, M. G., Wood, A. M., & Carpenter, J. R. (2009). Multiple imputation for missing data in epidemiological and clinical research: Potential and pitfalls. BMJ, 338, Article b2393. https://doi.org/10.1136/bmj.b2393