Measures of effect - confidence intervals

Definition

A confidence interval provides a range of plausible values for a true population parameter (e.g. treatment effect), with a specified confidence level (conventionally 95%) indicating that if the study were repeated many times, 95% of the calculated intervals would be expected to contain the true value - conveying precision of an estimate, complementing (not replacing) the point estimate itself
Reported alongside virtually every effect estimate in clinical research, making correct interpretation a foundational skill for critically appraising any study result

Confidence interval width is directly related to sample size and result variability - larger studies and less variable data produce narrower (more precise) confidence intervals, while smaller studies or highly variable data produce wider (less precise) intervals - a wide confidence interval indicates substantial remaining uncertainty about the true effect size, even if the point estimate itself looks favourable

A confidence interval that crosses the null value (1.0 for ratio measures like relative risk/odds ratio/hazard ratio, or 0 for difference measures like absolute risk reduction) indicates the result is not statistically significant at the corresponding significance level, providing the same essential information as a p-value threshold but with the added benefit of conveying effect size range and precision simultaneously
A statistically significant result (confidence interval not crossing the null) with a very wide interval still carries substantial uncertainty about the true effect magnitude, even though the direction of effect is reasonably established

Confidence intervals should be examined alongside the point estimate, not ignored in favour of the point estimate alone, since a favourable-looking point estimate with a very wide confidence interval warrants more cautious clinical interpretation than the same point estimate with a narrow interval
A confidence interval spanning both a clinically meaningful benefit and a clinically negligible/harmful range indicates the study cannot yet reliably distinguish between these possibilities, regardless of statistical significance

Null value crossing as the statistical significance indicator (1.0 for ratios, 0 for differences), sample size's relationship to interval width, wide interval interpretation despite statistical significance, confidence interval vs p-value complementary information

A confidence interval conveys more useful clinical information than a p-value alone, since it shows both statistical significance (whether it crosses the null value) and the plausible range of effect magnitude - a statistically significant result with a very wide confidence interval spanning both clinically trivial and clinically important effect sizes still leaves genuine uncertainty about how large the true effect actually is, information a p-value alone does not convey

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