How Sure Can We Be? Confidence Intervals for Blood Pressure Outcomes in a DPH Project
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Doctor of Public Health Program, Aspen University
DPH 860: Advanced Biostatistics
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Month Day, Year
How Sure Can We Be? Confidence Intervals for Blood Pressure Outcomes in a DPH Project
A DPH project studies a sample to learn about a population. Inference is the process of using sample results to estimate population values and to express how uncertain those estimates are. This paper applies inference for means and proportions to a DPH project comparing 700 participants in a neighborhood hypertension program built around community health workers with 700 matched comparison adults.
Samples and Populations
The population of interest is adults with uncontrolled hypertension in the county's east-side neighborhoods who might join such a program. The sample is the 1,400 adults in the project. Any statistic from the sample, such as the mean fall in systolic pressure, is an estimate of the population value, and a different sample would give a somewhat different estimate.
Sampling Distributions and Standard Errors
Imagine repeating the study many times with 700 people per group: the resulting means would pile up in a sampling distribution centered close to the population mean. The standard error measures the spread of that distribution. For a mean, the standard error is the standard deviation over the square root of n; for a proportion, it is the square root of p(1-p)/n.
Estimates and Intervals
The table presents point estimates, standard errors and 95% confidence intervals for the main outcomes.
| Estimate | Point estimate | Standard error | 95% confidence interval |
|---|---|---|---|
| Mean systolic change, participants | -14.2 mmHg | 0.60 | -15.4 to -13.0 |
| Mean systolic change, comparison | -8.6 mmHg | 0.62 | -9.8 to -7.4 |
| Difference in mean change | -5.6 mmHg | 0.87 | -7.3 to -3.9 |
| Blood pressure controlled, participants | 58.1% | 1.9 points | 54.4% to 61.8% |
| Blood pressure controlled, comparison | 47.6% | 1.9 points | 43.9% to 51.3% |
| Difference in control | 10.5 points | 2.7 points | 5.3 to 15.7 points |
Working the Mean Difference
Among participants, systolic pressure fell by a mean of 14.2 mmHg with a standard deviation of 16.0, giving a standard error of 16.0 divided by the square root of 700, or about 0.60. Comparison adults' pressure fell 8.6 mmHg on average, with a standard deviation of 16.5, for a standard error near 0.62. Squaring the two standard errors, adding them and taking the square root gives about 0.87 for the difference, so the 95% interval for the 5.6 mmHg difference runs from about 3.9 to 7.3 mmHg greater reduction among participants.
Working the Proportion Difference
Control rose to 407 of 700 participants, or 58.1%, and 333 of 700 comparison adults, or 47.6%. The standard error for each proportion is about 1.9 percentage points. The standard error of the 10.5-point difference is about 2.7 points, giving a 95% interval of 5.3 to 15.7 points.
Interpreting Confidence Intervals
A 95% confidence interval is produced by a method that, over many samples, captures the true value 95% of the time. It is not a 95% probability that the true value lies in this particular interval. Greenland et al. (2016) describe this and many other common misinterpretations of intervals and P values, urging researchers to treat intervals as ranges of values reasonably compatible with the data given the model's assumptions.
Effect Size
Statistical significance does not tell how large or important an effect is. Sullivan and Feinn (2012) argue that effect sizes should be reported alongside P values. A 5.6 mmHg greater reduction in systolic pressure is clinically meaningful, since reductions of this size are associated with fewer strokes and heart attacks at the population level. The standardized difference, about 0.34, is small to moderate.
P Values in Context
The American Statistical Association warned that a P value says nothing directly about whether a hypothesis is correct or how large an effect is, and that findings should not be judged by whether they clear a line such as .05 (Wasserstein & Lazar, 2016). The project will report estimates with intervals first and P values second.
Assumptions
These intervals assume independent observations, approximately normal sampling distributions and random sampling from the population. With 700 per group, the central limit theorem supports normal approximations even if individual changes are somewhat skewed. Matching, however, means the two groups are not fully independent, so the project's final analysis will account for matched pairs.
What the Estimates Mean
The estimates suggest that program participants achieved blood pressure control about 10 percentage points more often than similar adults, with plausible values from about 5 to 16 points. For every ten participants, roughly one more achieved control than would have without the program, a result relevant to decisions about funding and scaling.
Limits of Inference
Confidence intervals address random error, not bias. If participants were more motivated than comparison adults in ways matching did not capture, the true effect of the program could be smaller than estimated. Intervals should be interpreted alongside the study design.
Why 1.96
For a 95% confidence interval based on a normal sampling distribution, the estimate plus or minus 1.96 standard errors captures the central 95% of that distribution. For smaller samples, the t distribution replaces 1.96 with a slightly larger multiplier. With 700 per group, the difference between the two is negligible.
Intervals and Hypothesis Tests
A 95% confidence interval for a difference that excludes zero corresponds to a two-sided test with P below .05. Intervals carry more information than tests, however, because they show the range of plausible effect sizes. An interval of 5 to 16 points tells a decision maker far more than the statement that the difference is statistically significant.
Relative and Absolute Measures
The 10.5-point difference in control is an absolute measure. The same result expressed as a ratio is about 1.22, meaning participants were about 22% more likely to achieve control. Both are correct, but absolute differences are usually more useful for planning, since they translate directly into numbers of people helped.
Number Needed to Treat
The reciprocal of the absolute difference, about 1 divided by 0.105, gives roughly 10: about ten adults would need to join the program for one additional person to achieve control. Its interval, from about 6 to 19, comes from inverting the limits of the difference's interval and conveys uncertainty in practical terms.
Reporting the Results
Results will be reported as estimates with 95% confidence intervals first, followed by P values. For example: participants were 10.5 percentage points more likely to achieve control, with a 95% interval of 5.3 to 15.7 points. This order keeps attention on the size of the effect and its uncertainty.
Conclusion
Inference for means and proportions allows the DPH project to estimate the program's effect with an honest statement of uncertainty. A 5.6 mmHg greater reduction in systolic pressure and a 10.5-point higher rate of control, with intervals excluding zero, support a meaningful benefit, while attention to assumptions and bias keeps the conclusions measured.
References
Greenland, S., Senn, S. J., Rothman, K. J., Carlin, J. B., Poole, C., Goodman, S. N., & Altman, D. G. (2016). Statistical tests, P values, confidence intervals, and power: A guide to misinterpretations. European Journal of Epidemiology, 31(4), 337-350. https://doi.org/10.1007/s10654-016-0149-3
Sullivan, G. M., & Feinn, R. (2012). Using effect size: Or why the P value is not enough. Journal of Graduate Medical Education, 4(3), 279-282. https://doi.org/10.4300/JGME-D-12-00156.1
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
How this DPH 860 Module 2 example is structured
Check the DPH 860 prompt in your Aspen classroom before using this example. It defines samples and populations, explains standard errors, tables estimates and intervals, works both differences by hand, then covers interpretation, effect size, P values, assumptions, meaning and limits.
DPH 860 Module 2 questions, answered
What does DPH 860 Module 2 usually ask for?
Aspen's DPH 860 covers statistical inference, so a paper estimating means and proportions with confidence intervals is typical. Follow your classroom prompt.
What does a 95% confidence interval mean?
It comes from a method that captures the true value in 95% of repeated samples; it shows values reasonably compatible with the data.
Why report effect sizes?
Because P values do not show how large or important an effect is.
Write yours, or have the desk draft it
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