Agent-Skills.md

Agent Skills: Statistical Analysis

Statistical analysis toolkit. Hypothesis tests (t-test, ANOVA, chi-square), regression, correlation, Bayesian stats, power analysis, assumption checks, APA reporting, for academic research.

UncategorizedID: drshailesh88/integrated_content_OS/statistical-analysis
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skills/cardiology/statistical-analysis/SKILL.md

Statistical Analysis

Rigorous statistical analysis guidance for interpreting and reporting research findings in cardiology content.

Triggers

  • User needs to interpret trial statistics
  • User is reporting study results
  • User asks about statistical significance vs clinical significance
  • User needs help with effect sizes, confidence intervals, or p-values
  • User is evaluating the strength of evidence

Core Concepts

Test Selection Decision Tree

Comparing Two Groups:

  • Continuous outcome, normal: Independent t-test
  • Continuous outcome, non-normal: Mann-Whitney U
  • Categorical outcome: Chi-square or Fisher's exact

Comparing 3+ Groups:

  • Continuous, normal: ANOVA with post-hoc
  • Continuous, non-normal: Kruskal-Wallis
  • Categorical: Chi-square

Relationships:

  • Two continuous: Pearson (normal) or Spearman (non-normal)
  • Predict continuous: Linear regression
  • Predict binary: Logistic regression
  • Time-to-event: Cox proportional hazards

Effect Sizes (Always Report!)

| Measure | Use Case | Interpretation | |---------|----------|----------------| | Cohen's d | Mean differences | 0.2 small, 0.5 medium, 0.8 large | | Hazard Ratio | Survival analysis | <1 protective, >1 harmful | | Odds Ratio | Case-control | ~RR when outcome rare | | Risk Ratio | Cohort studies | Direct probability comparison | | NNT/NNH | Clinical utility | Number needed to treat/harm | | Absolute Risk Reduction | Clinical impact | ARR = Control rate - Treatment rate |

Confidence Intervals

Critical: Always report 95% CIs alongside point estimates.

  • CI crossing 1.0 (for ratios) = not statistically significant
  • CI width indicates precision
  • Narrow CI = more precise estimate
  • Wide CI = less precise, often underpowered

P-values: What They Are and Aren't

P-value IS: Probability of observing data this extreme if null hypothesis true

P-value IS NOT:

  • Probability hypothesis is true/false
  • Measure of effect size
  • Indicator of clinical importance

Reporting: p < 0.05 is arbitrary; report exact values (p = 0.03, not p < 0.05)

Clinical Trial Statistics

Key Metrics for Cardiology Trials

| Metric | Formula | Use | |--------|---------|-----| | ARR | Control - Treatment event rate | Absolute benefit | | RRR | (Control - Treatment) / Control | Relative benefit | | NNT | 1 / ARR | Number to treat for one benefit | | HR | Hazard in treatment / Hazard in control | Time-to-event |

Example Interpretation

"DAPA-HF showed empagliflozin reduced the composite endpoint (HR 0.74, 95% CI 0.65-0.85, p<0.001). The ARR was 4.9%, yielding an NNT of 21 over 18 months."

This tells us:

  • 26% relative risk reduction (1 - 0.74)
  • Statistically significant (CI doesn't cross 1.0)
  • Need to treat 21 patients to prevent one event
  • Clinically meaningful benefit

Common Errors to Avoid

P-hacking Red Flags

  • Multiple testing without correction
  • Selective outcome reporting
  • Subgroup fishing
  • Stopping trials early for "significance"

Interpretation Errors

  • Confusing statistical and clinical significance
  • Ignoring confidence interval width
  • Treating absence of evidence as evidence of absence
  • Comparing p-values across studies

Reporting Errors

  • Reporting only p-values without effect sizes
  • Omitting confidence intervals
  • Not specifying statistical tests used
  • Rounding inappropriately (keep 2 decimal places for ratios)

APA-Style Statistical Reporting

# t-test
t(48) = 2.31, p = .025, d = 0.67, 95% CI [0.12, 1.22]

# ANOVA
F(2, 87) = 4.56, p = .013, η² = .095

# Correlation
r(58) = .42, p = .001, 95% CI [.18, .62]

# Chi-square
χ²(2, N = 120) = 8.45, p = .015, φ = .27

# Regression
β = 0.34, SE = 0.08, t = 4.25, p < .001

# Hazard ratio
HR = 0.74, 95% CI [0.65, 0.85], p < .001

Power Analysis Guidance

Before interpreting underpowered studies:

  • Sample size adequate for expected effect?
  • Was power analysis pre-specified?
  • What effect size was study powered to detect?

A non-significant result in an underpowered study ≠ no effect

Checklist for Statistical Reporting

  • [ ] Effect size with confidence interval
  • [ ] Exact p-value (not just < or > threshold)
  • [ ] Statistical test specified
  • [ ] Assumptions verified
  • [ ] Multiple comparison correction if needed
  • [ ] Clinical significance discussed
  • [ ] Limitations of analysis noted