Statistics for the Surgeon: Beyond the P-Value

Let's be honest: most surgeons hate statistics. We like concrete things—bones, plates, screws. Statistics feels abstract, manipulative, and dry. However, Evidence-Based Medicine (EBM) is the currency of modern practice. You cannot decide which implant to use, which approach to take, or how to counsel a patient without being able to critically read a paper.

This guide strips away the math and focuses on the concepts you need to survive the exam and the literature.

Visual Element: A normal distribution curve showing the "Alpha" (0.05) tails and the "Beta" (Power) area.

1. The Basics: Data Types

You can't choose a test if you don't know what data you have.

1. Nominal: Named categories (Male/Female, Infected/Not Infected). Binary.
2. Ordinal: Ordered categories (Likert scale, VAS pain score, Kellgren-Lawrence grade). Ranked.
3. Interval/Ratio: Continuous numbers (Height, Weight, Range of Motion). Measured.

Why it matters:

• Continuous data (Normal distribution) -> Parametric Tests (T-test).
• Ordinal/Skewed data -> Non-Parametric Tests (Mann-Whitney).

2. The P-Value and the Null Hypothesis

• Null Hypothesis (H0): "There is NO difference between Treatment A and Treatment B."
• The P-Value: The probability of finding this result (or one more extreme) if the Null Hypothesis were true.
  • P < 0.05: We reject the Null. The result is unlikely to be due to chance alone.
  • P > 0.05: We cannot reject the Null. (Note: We don't "accept" it; we just failed to disprove it).

Trap: P-value ≠ Effect Size. A study of 100,000 patients might find a 0.1 degree difference in ROM is "statistically significant" (p<0.001). This is clinically irrelevant. Always look at the magnitude of difference.

3. Errors: Alpha and Beta

Science is never 100% sure. We make bets.

• Type I Error (Alpha): The False Positive.
  • We say there is a difference, but there isn't.
  • We accept a 5% risk of this (p=0.05).
• Type II Error (Beta): The False Negative.
  • We say there is NO difference, but there actually is one.
  • Usually caused by Underpowered Studies (sample size too small).

4. Power Analysis

Power = 1 - Beta. Typically set at 0.80 (80%). This means we have an 80% chance of detecting a difference if it exists.

• Pre-hoc Power Analysis: Mandatory before starting a study. "How many patients do I need?"
• Post-hoc Power Analysis: Useless. Don't do it.

5. Confidence Intervals (CI)

The P-value's smarter brother. A 95% CI means: "If we repeated this study 100 times, the true population value would fall within this range 95 times."

• Why it's better: It gives you the Effect Size and the Precision.
• Interpretation:
  • Difference in Means: If CI crosses 0 -> Not Significant.
  • Odds Ratio / Relative Risk: If CI crosses 1 -> Not Significant.

6. The "Cheat Sheet" of Tests

Memorize this grid.

7. Survival Analysis

In arthroplasty, we care about "Time to Failure."

• Kaplan-Meier Curve: Plots the probability of survival over time.
• Censoring: Patients who are lost to follow-up or die (from other causes) are "censored" (marked with a tick) but included in the analysis up to that point.
• Log-Rank Test: The test used to compare two Kaplan-Meier curves (e.g., Cemented vs Uncemented).

8. Regression Analysis

Used to predict an outcome based on variables.

• Linear Regression: Outcome is a continuous number (e.g., predicting post-op ROM).
• Logistic Regression: Outcome is binary (e.g., predicting Infection Yes/No). Outputs an Odds Ratio.
• Multivariate Regression: The "Magic Wand." It controls for confounders. "After adjusting for age, BMI, and smoking, diabetes was still a predictor of infection."

9. EBM Metrics: NNT and NNH

• Relative Risk (RR): "Drug A reduces risk by 50%." (Sounds great).
• Absolute Risk Reduction (ARR): "Risk went from 2% to 1%." (Sounds less impressive).
• Number Needed to Treat (NNT): 1 / ARR. "You need to treat 100 patients to prevent 1 infection."
  • This is the most honest metric for a surgeon. Is it worth operating on 100 people to help 1?

Conclusion

Statistics is a language. You don't need to be a poet, but you need to be able to read the signposts.

• Check the Power.
• Look at the Confidence Intervals.
• Ask: "Is this statistically significant difference actually clinically important?" (MCID - Minimum Clinically Important Difference).

Don't let the P-value bully you.