Introduction to Biostatistics 06 – Confidence Intervals
Introduction to Biostatistics 06 – Confidence Intervals
This lecture focuses on Confidence Intervals (CIs), moving beyond simple hypothesis testing to estimate the size and reliability of a treatment effect. While p values tell us if a difference exists, CIs provide a range of values within which the true population parameter likely falls. The session covers how to calculate CIs for means, proportions, relative risk, and odds ratios, and introduces Tolerance Limits for clinical reference ranges.
Learning Objectives:
By the end of this lecture, students will be able to:
- Define a Confidence Interval and explain what it means for 95% of calculated intervals to contain the true population parameter.
- Calculate CIs for the difference between two means using the T-distribution and standard error.
- Use CIs for hypothesis testing, recognizing that if an interval includes zero (for differences) or one (for ratios), the result is not statistically significant.
- Estimate CIs for proportions and rates, and apply specialized charts when sample sizes are too small for normal approximations (e.g., zero-complication scenarios).
- Calculate CIs for Relative Risk (RR) and Odds Ratio (OR) using natural logarithms.
- Determine Tolerance Limits to define the range that covers a specific fraction of a population with a given level of confidence.
Topics covered in this lesson
- The theory of confidence intervals involves modifying the t-test equation to isolate and estimate the true difference between population means.
- Interpreting 95% confidence requires understanding how repeated sampling generates different intervals, the majority of which will capture the actual treatment effect.
- Distinguishing between clinical and statistical significance is illustrated by cases where large sample sizes produce a significant p-value for a negligible blood pressure change of only 4 mmHg.
- Standard confidence interval formulas for proportions fail when outcomes are near zero or one, requiring the use of specialized charts for small sample sizes.
- Calculating intervals for relative risk and odds ratios requires transforming the data into natural logarithms to account for their log-normal distribution.
- Tolerance limits provide a more conservative approach than standard confidence intervals when defining clinical reference ranges for small populations.
- A surgical outcomes example demonstrates why a surgeon with zero complications out of thirty should be assigned a calculated upper bound rather than an impossible 0% complication rate.
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