PHLT 8331 Week 9 Confidence Interval Interpretation Example

What a Yes-or-No Decision Leaves Out: Reading Two Confidence Intervals From a Composite Anticoagulation Registry as Ranges of Population Values the Data Are Compatible With

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Walden University

PHLT 8331: Fundamentals of Biostatistics

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What a Yes-or-No Decision Leaves Out: Reading Two Confidence Intervals From a Composite Anticoagulation Registry as Ranges of Population Values the Data Are Compatible With

Why Revisit Results Already Reported

Two results from earlier weeks were reported with a significance decision: the 7.7-point mean improvement in time in therapeutic range after patients moved to pharmacist management, and the net shift of 37 patients toward good control in the same group. Both were statistically significant, and a reader who stopped there would know only that the null hypothesis of no change was rejected. This paper rereads each result through its confidence interval, which shows the range of population values the data are compatible with and therefore how large or small the true change might plausibly be. All figures are composite.

What a Confidence Interval Is and Is Not

A 95% confidence interval comes from a procedure that, if repeated across many samples from the same population, would produce intervals containing the true value 95% of the time. That is a statement about the procedure. Many writers describe one computed interval as 95% likely to hold the population value, but under the frequentist reasoning that produces it, the true value is fixed and the interval either contains it or does not. Greenland et al. (2016) list this as one of the most common misinterpretations of confidence intervals. A more useful reading is that the interval contains the population values most compatible with the data, given the model and its assumptions, with values near the center more compatible than values near the edges.

Compatibility Intervals

Amrhein et al. (2019) proposed calling such ranges compatibility intervals, to discourage reading them as sharp boundaries between values that are possible and impossible. A value just outside the interval is only slightly less compatible with the data than a value just inside it. This framing matters for both results below.

Result 1: The Mean Improvement in Time in Range

The paired analysis in Week 4 found a mean improvement of 7.7 percentage points, with a 95% interval from 5.2 to 10.2. Read as a compatibility interval, the data are most compatible with an average improvement near 7.7 points in the source population, and reasonably compatible with improvements as small as about 5 points or as large as about 10. They are not very compatible with no change at all, which lies well outside the interval.

What the Range Means for Clinics

Translated into days over six months, the interval runs from roughly 9 to 19 more days in range per patient, centered near 14. Even the low end of that range is a meaningful gain for a patient on warfarin. The interval therefore supports a stronger statement than the significance decision alone: not only did time in range change, but every value the data favor represents a clinically worthwhile improvement, before considering the regression-to-the-mean concern raised in Week 4.

Result 2: The Net Shift Toward Good Control

McNemar's test in Week 7 found that 58 patients moved into good control and 21 moved out of it, a net shift of 37, or 17.5% of the 212. The 95% interval for the net shift runs from about 9.6% to 25.3%. Read as a compatibility interval, the data are compatible with anything from about 10 to about 25 net patients in every 100 moving into good control.

What the Width Tells Us

This interval is wide relative to its center: the top of the range is roughly 2.5 times the bottom, so the plausible effect could be modest or substantial, and the network should plan for either. The significance decision hides that imprecision. A clinic planning staffing on the basis of this result should recognize that the true net improvement could be modest or substantial, and a larger sample or longer follow-up would narrow the range.

Describing an Interval That Includes Zero

Neither interval here includes zero, but the same reading applies when one does. An interval from minus 2 to plus 9 points, for example, would not show that the program had no effect. It would show that the data fit a small harm, no effect or a sizable benefit equally well, and that the study cannot distinguish among them. Altman and Bland (1995) warned that reading such a result as evidence of no effect is a common and costly error.

Why Interval Width Depends on Sample Size

The two intervals differ in width partly because they measure different things and partly because of how much information each draws on. The mean improvement uses every patient's continuous change score, while the net shift uses only whether each patient crossed the 65% threshold, discarding information about how far they moved. Dichotomizing a continuous measure generally widens intervals for this reason. A reader comparing the two should recognize that the narrower interval for the mean improvement reflects the richer measurement, not a more certain underlying effect.

Intervals and Decisions

Intervals support decisions better than significance verdicts because decisions depend on magnitude. A clinic deciding whether to expand the pharmacist service needs to know whether the plausible improvement justifies the cost. If the service costs the equivalent of what the clinic would pay to achieve, say, 5 more points of time in range by other means, the interval for the mean improvement, whose lower end is about 5 points, suggests the service is at least worth that much even under a cautious reading. The significance verdict alone could never support that kind of reasoning, because it says nothing about how large the benefit might be. Intervals make the reasoning about value possible.

Summary

The two significance decisions said only that change occurred. The intervals add how much: an improvement in time in range plausibly between about 5 and 10 points, every value of which would matter clinically, and a net shift toward good control plausibly between about 10% and 25%, a range wide enough to caution against precise planning. Reporting intervals, and reading them as ranges of compatible values, gives decision makers the information the yes-or-no verdict compresses away.

References

Altman, D. G., & Bland, J. M. (1995). Statistics notes: Absence of evidence is not evidence of absence. BMJ, 311(7003), 485. https://doi.org/10.1136/bmj.311.7003.485

Amrhein, V., Greenland, S., & McShane, B. (2019). Scientists rise up against statistical significance. Nature, 567(7748), 305-307. https://doi.org/10.1038/d41586-019-00857-9

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