An open-label randomized parallel-arm active study evaluated the safety and efficacy of a continuous infusion of potassium chloride versus an existing intermittent infusion regimen in critically ill adults with plasma potassium concentration between 2.5 mmol/L and 3.8 mmol/L. The primary outcome was the difference in mean plasma potassium concentration over time between the 2 groups. The study reported a difference in mean plasma potassium concentration over time between groups of 0.2 mmol/L. A 90% confidence interval (CI) showed that the difference was statistically significant. What would be the effect on the width and significance of the CI if the confidence level is increased to 95%?
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A C% confidence interval (CI) is a range of plausible values calculated from sample data that captures the true population value with a C% confidence level. The confidence level C refers to how often a CI includes the true population value if the process is repeated multiple times.
A CI to estimate a population value (eg, difference of 2 population means) is constructed by taking a sample value (eg, difference of 2 sample means) and adding and subtracting a margin of error based on a desired confidence level C.
Therefore, for the same data, a CI with a greater confidence level (eg, 95% CI) is always wider (eg, capturing 95% of the distribution) than a CI with a lower confidence level (eg, 90% CI).
In this question, the difference in mean plasma potassium concentration over time between groups is estimated at 0.2 mmol/L, and the 90% CI showed that the difference was statistically significant (ie, the CI excluded 0, the null value for a difference). Increasing the confidence level from a 90% CI to a 95% CI results in an interval that is wider than the 90% CI (Choices A and B).
However, because the boundaries of the 90% CI are not provided, it is not possible to determine whether the wider 95% CI will exclude 0 (the null value). For example, for the narrower 90% CI, the lower and upper boundaries may both be positive values; but for the wider 95% CI, the lower boundary may be a negative value whereas the upper boundary may be a positive value. Therefore, the statistical significance of the 95% CI cannot be determined (Choice C).
Educational objective:
A confidence interval (CI) with a greater confidence level is always wider than a CI with a lower confidence level for the same data. A CI for a difference in means is significant if the interval excludes the null value (ie, 0), and it is not significant if the interval includes the null value.