Biostatistics and Bioethics
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Solve questions (25) →Contents
- 29.1 Basic Statistical Concepts (Sensitivity, Specificity, PPV, NPV)
- 29.2 ROC Analysis
- 29.3 Study Designs (Randomised, Cohort, Case-Control)
- 29.4 Hypothesis Tests and the p Value
- 29.5 Kappa Statistic and Inter-Observer Agreement
- 29.6 Ethical Principles (Autonomy, Beneficence, Non-Maleficence, Justice)
- 29.7 Informed Consent and Radiation Ethics
- Key Points for the Board
- Current guidelines on this chapter's topics
Learning objectives and modules3 modules · about 2 h 20 min
Learning objectives
After this chapter you will be able to:
- Calculate sensitivity, specificity, PPV, NPV and likelihood ratios (LR) from a 2×2 table; explain the effect of prevalence.
- Interpret the ROC curve and the area under the curve; explain the choice of threshold.
- Distinguish study designs and levels of evidence; recognise the main types of bias.
- Interpret hypothesis tests, the p value, confidence intervals, type I and type II error and statistical power.
- Assess agreement between observers and methods with kappa and Bland-Altman analysis.
- Apply ethical principles and informed consent to procedures involving radiation.
Modules
The chapter is divided into study modules without changing the order of the text: read, watch the animations, then answer the questions linked to those headings.
- Module 129.1–29.3 Basic Statistical Concepts (Sensitivity, Specificity, PPV, NPV) · ROC Analysis · Study Designs (Randomised, Cohort, Case-Control)55 min · 3 animations · 21 questionsAnswer the questions →
- Module 229.4–29.5 Hypothesis Tests and the p Value · Kappa Statistic and Inter-Observer Agreement55 min · 3 animations · 24 questionsAnswer the questions →
- Module 329.6–29.7 Ethical Principles (Autonomy, Beneficence, Non-Maleficence, Justice) · Informed Consent and Radiation Ethics · Key Points for the Board30 min · 9 questionsAnswer the questions →
Times are estimates: 130 words per minute, 3 min per animation, 1.5 min per question.
MOST FREQUENTLY ASKED IN THIS CHAPTER
29.1 Basic Statistical Concepts (Sensitivity, Specificity, PPV, NPV)13 questions
2×2 Table (Diagnostic Test Performance)
The basis of all measures of diagnostic test performance is the 2×2 contingency table:
| Disease PRESENT (+) | Disease ABSENT (−) | |
|---|---|---|
| Test Positive (+) | True Positive (TP) | False Positive (FP) |
| Test Negative (−) | False Negative (FN) | True Negative (TN) |
Data Types and Descriptive Statistics (EANM)
Sensitivity
→ High sensitivity → patients should not be missed.
→ High Sensitivity + Negative result → rule disease out.
Specificity
→ High specificity → false positives should be few.
→ High Specificity + Positive result → rule disease in.
Positive Predictive Value (PPV)
Negative Predictive Value (NPV)
→ Prevalence ↑ → PPV ↑, NPV ↓. Prevalence ↓ → PPV ↓, NPV ↑.
→ No, they are intrinsic properties of the test. PPV and NPV, however, depend on prevalence.
Left: test results and the 2×2 table in a population of 400, pre- and post-test diseased counts in a 100-person grid, and a threshold moving over the healthy and diseased distributions. Right: PPV and NPV against prevalence, pre- versus post-test probability for several likelihood ratios, and the ROC curve.
Sensitivity, specificity and likelihood ratios belong to the test; what a result means for a patient depends on the pre-test probability (prevalence) and the chosen threshold.
Source: formulas and interpretation thresholds from the book (29.1-29.2); Sn/Sp examples from the book (Figure 29.1, question b29:1). ROC calculated with an equal-variance binormal model (AUC = Φ(d′/√2)).
How to use: a single click on the drawing pauses and resumes; ↑ ↓ or the buttons below change the test, the likelihood ratio or the AUC; use the time bar below to set the prevalence or the threshold where you want it.
Figure 29.1: Performance measures derived from the 2×2 table and the effect of prevalence on PPV and NPV at fixed sensitivity/specificity.
Accuracy
Likelihood Ratios (LR)
Positive Likelihood Ratio (LR+):
Negative Likelihood Ratio (LR−):
Pre-test and Post-test Probability
→ A positive test result strongly increases the probability of disease → rules disease in.
→ A negative test result strongly reduces the probability of disease → rules disease out.
→ Independent of prevalence.
Left: test results and the 2×2 table in a population of 400, pre- and post-test diseased counts in a 100-person grid, and a threshold moving over the healthy and diseased distributions. Right: PPV and NPV against prevalence, pre- versus post-test probability for several likelihood ratios, and the ROC curve.
Sensitivity, specificity and likelihood ratios belong to the test; what a result means for a patient depends on the pre-test probability (prevalence) and the chosen threshold.
Source: formulas and interpretation thresholds from the book (29.1-29.2); Sn/Sp examples from the book (Figure 29.1, question b29:1). ROC calculated with an equal-variance binormal model (AUC = Φ(d′/√2)).
How to use: a single click on the drawing pauses and resumes; ↑ ↓ or the buttons below change the test, the likelihood ratio or the AUC; use the time bar below to set the prevalence or the threshold where you want it.
Figure 29.2: Moving from pre-test to post-test probability according to the likelihood ratio (LR) (Bayes' theorem).
Examples of Diagnostic Test Performance in Nuclear Medicine
29.2 ROC Analysis3 questions
Definition and Basic Concepts
AUC (Area Under the Curve)
Determining the Optimal Threshold
→ The test performs at chance level → no discriminatory power (diagonal line).
→ AUC comparison (DeLong test).
→ J = Sensitivity + Specificity − 1 → determines the optimal threshold.
Left: test results and the 2×2 table in a population of 400, pre- and post-test diseased counts in a 100-person grid, and a threshold moving over the healthy and diseased distributions. Right: PPV and NPV against prevalence, pre- versus post-test probability for several likelihood ratios, and the ROC curve.
Sensitivity, specificity and likelihood ratios belong to the test; what a result means for a patient depends on the pre-test probability (prevalence) and the chosen threshold.
Source: formulas and interpretation thresholds from the book (29.1-29.2); Sn/Sp examples from the book (Figure 29.1, question b29:1). ROC calculated with an equal-variance binormal model (AUC = Φ(d′/√2)).
How to use: a single click on the drawing pauses and resumes; ↑ ↓ or the buttons below change the test, the likelihood ratio or the AUC; use the time bar below to set the prevalence or the threshold where you want it.
Figure 29.3: Choice of threshold for healthy and diseased distributions and the corresponding ROC curve, AUC and Youden index (schematic).
Applications of ROC Analysis in Nuclear Medicine
29.3 Study Designs (Randomised, Cohort, Case-Control)5 questions
Hierarchy of Evidence (Evidence Pyramid)
From top to bottom (strongest to weakest):
1. Systematic review and meta-analysis → the strongest level of evidence 2. Randomised controlled trial (RCT) → the gold-standard experimental design 3. Cohort study → observational, prospective or retrospective 4. Case-control study → observational, retrospective 5. Cross-sectional study → a snapshot 6. Case series / case report → weak evidence 7. Expert opinion → the base of the evidence pyramid
Figure 29.4: The evidence pyramid: study designs ranked by strength of evidence.
Randomised Controlled Trial (RCT)
→ Can establish causality + confounders are balanced by randomisation.
→ All randomised patients are analysed according to their initial groups → even if there is non-adherence to treatment.
→ The patient and the investigator do not know the group.
Cohort Study
Case-Control Study
Cross-Sectional Study
Meta-Analysis and Systematic Review
→ Case-control.
→ None can establish it definitively, but the prospective cohort is the strongest observational evidence.
→ A cross-sectional study.
→ High heterogeneity → results are inconsistent between studies.
Figure 29.5: Time direction, grouping logic and measures of the main study designs (schematic).
Study Designs Comparison Table:
| Feature | RCT | Cohort | Case-Control | Cross-sectional |
|---|---|---|---|---|
| Direction | Prospective | Pro/Retrospective | Retrospective | Snapshot |
| Intervention | Yes | No | No | No |
| Causality | Yes | Limited | No | No |
| Measure | RR, ARR, NNT | RR | OR | Prevalence, OR |
| Rare disease | Unsuitable | Unsuitable | Suitable | Unsuitable |
| Cost/Duration | High | Medium-High | Low | Low |
29.4 Hypothesis Tests and the p Value18 questions
Basics of Hypothesis Testing
The p Value
Type I and Type II Error
Type I Error (α error – False Positive):
Type II Error (β error – False Negative):
Statistical Power:
→ Saying there is a difference when there is none (false positive) → α error.
→ Saying there is no difference when there is one (false negative) → β error.
→ 1 − β → the probability of detecting a real difference.
→ Power increases, Type II error decreases.
Left: H₀ and H₁ distributions with α, β and power areas, confidence intervals from 100 repeated studies, and a forest plot with five studies added one by one. Right: power against sample size, the share of intervals containing the true value and 1, study weights and the pooled effect.
Finding a significant result needs adequate power; power and narrow confidence intervals depend on sample size, and meta-analysis pools studies by weighting them for their precision.
Source: Type I/II error, power and confidence interval from the book (29.4); the five forest-plot studies from Figure 29.7; pooled effect and I² calculated on this page by fixed-effect inverse variance. Power by normal approximation (two groups, two-sided).
How to use: a single click on the drawing pauses and resumes; ↑ ↓ change the effect size in the power step and the sample size in the confidence interval step (use the buttons below for α); use the time bar below to go to any moment; ← → change steps.
Figure 29.6: Type I (α) and Type II (β) error and statistical power (1 − β) shown on the distributions (schematic).
Confidence Interval (CI)
Left: H₀ and H₁ distributions with α, β and power areas, confidence intervals from 100 repeated studies, and a forest plot with five studies added one by one. Right: power against sample size, the share of intervals containing the true value and 1, study weights and the pooled effect.
Finding a significant result needs adequate power; power and narrow confidence intervals depend on sample size, and meta-analysis pools studies by weighting them for their precision.
Source: Type I/II error, power and confidence interval from the book (29.4); the five forest-plot studies from Figure 29.7; pooled effect and I² calculated on this page by fixed-effect inverse variance. Power by normal approximation (two groups, two-sided).
How to use: a single click on the drawing pauses and resumes; ↑ ↓ change the effect size in the power step and the sample size in the confidence interval step (use the buttons below for α); use the time bar below to go to any moment; ← → change steps.
Figure 29.7: Example forest plot: confidence interval width, an interval containing 1, and the pooled effect in meta-analysis (schematic).
Common Statistical Tests
Parametric Tests (assumption of normal distribution):
Non-parametric Tests (no assumption of normal distribution):
→ t-test (parametric) or Mann-Whitney U (non-parametric).
→ ANOVA (parametric) or Kruskal-Wallis (non-parametric).
→ Chi-square or Fisher (expected frequency < 5).
→ Paired t-test or Wilcoxon.
Figure 29.8: Choice of statistical test according to data type and comparison design.
EANM – Choice of Test:
Correlation Analysis (EANM)
Strength of Correlation by |r| Value:
| Absolute r value | Correlation |
|---|---|
| 0-0.2 | Very low |
| 0.2-0.4 | Low |
| 0.4-0.6 | Moderate |
| 0.6-0.8 | High |
| 0.8-1.0 | Very high |
Survival Analysis (EANM)
The Multiple Comparisons Problem
Clinical vs Statistical Significance
→ Statistical significance does not mean clinical significance → effect size and NNT should be assessed.
→ If 5 patients are treated, 1 patient benefits.
→ Very conservative → Type II error increases.
29.5 Kappa Statistic and Inter-Observer Agreement6 questions
Inter-observer Agreement
The Kappa Statistic
Interpretation of Kappa Values (Landis & Koch Classification):
| Kappa Value | Level of Agreement |
|---|---|
| < 0.00 | Poor |
| 0.00 – 0.20 | Slight |
| 0.21 – 0.40 | Fair |
| 0.41 – 0.60 | Moderate |
| 0.61 – 0.80 | Substantial |
| 0.81 – 1.00 | Almost Perfect |
Types of Kappa
ICC (Intraclass Correlation Coefficient)
Bland-Altman Analysis
→ Substantial agreement (Landis & Koch).
→ Agreement at chance level → no real agreement between observers.
→ Weighted kappa.
→ ICC (Intraclass Correlation Coefficient).
→ Bland-Altman analysis.
Left: two readers' calls on 100 studies build up in a 2×2 table with P₀, Pₑ and kappa; then a scatter plot of two measurement methods with the correlation coefficient. Right: kappa on the Landis-Koch scale with nuclear medicine examples, and the Bland-Altman plot with mean difference and limits of agreement.
Percent agreement and correlation can overstate agreement: kappa corrects categorical readings for chance, and Bland-Altman shows systematic and proportional differences in continuous measurements.
Source: kappa formula, Landis-Koch classes, Deauville and V/Q examples and the Bland-Altman definition from the book (29.5). 2×2 tables and SUV measurements are representative (measurement error SD 0.3, fixed difference +0.6, proportional difference 12%).
How to use: a single click on the drawing pauses and resumes; ↑ ↓ or the buttons below change the scenario; use the time bar below to go to any moment; ← → change steps.
Figure 29.9: Landis-Koch interpretation of kappa values with nuclear medicine examples, and the components of a Bland-Altman plot (schematic).
Examples of Inter-Observer Agreement in Nuclear Medicine
29.6 Ethical Principles (Autonomy, Beneficence, Non-Maleficence, Justice)4 questions
The Four Basic Principles of Medical Ethics (Beauchamp & Childress)
1. Autonomy:
2. Beneficence (Doing Good):
3. Non-maleficence (Primum Non Nocere):
4. Justice:
→ Non-maleficence.
→ Autonomy.
→ Autonomy, Beneficence, Non-maleficence, Justice (Beauchamp & Childress).
→ The reflection of non-maleficence in radiation protection → every exposure must be justified.
Conflict of Ethical Principles
Research Ethics
Historical Development:
Ethics Committee (IRB – Institutional Review Board):
Special Situations in Nuclear Medicine Research:
Good Clinical Practice (GCP; ICH E6(R3))
29.7 Informed Consent and Radiation Ethics5 questions
Informed Consent
Elements of Informed Consent:
1. Disclosure:
2. Understanding:
3. Voluntariness:
4. Decision-Making Capacity (Competence/Capacity):
5. Consent:
Informed Consent in Nuclear Medicine
Diagnostic Procedures:
Therapeutic Procedures:
→ Disclosure, Understanding, Voluntariness, Decision-making capacity, Consent.
→ Written consent is mandatory.
→ Verbal consent is usually sufficient (varies by institution).
Ethical Foundations of Radiation Protection
The Three Basic Principles of the ICRP:
1. Justification:
2. Optimisation (ALARA – As Low As Reasonably Achievable):
3. Dose Limitation:
Figure 29.10: Relationship between the four basic principles of medical ethics and the ICRP principles of radiation protection (schematic).
Radiation Ethics in Special Populations
Pregnancy:
Paediatric Patients:
Breastfeeding:
Communicating Radiation Risk
Breaking Bad News: SPIKES
→ Justification, Optimisation (ALARA), Dose limitation.
→ Non-maleficence.
→ Absolutely contraindicated.
→ 6-12 months.
→ A campaign to reduce paediatric radiation doses.
Key Points for the Board
Diagnostic Test Performance
ROC Analysis
Study Designs
Hypothesis Tests
Summary Table of Statistical Tests:
| Data Type | 2 Groups | ≥3 Groups | Paired |
|---|---|---|---|
| Continuous (Parametric) | t-test | ANOVA | Paired t-test |
| Continuous (Non-parametric) | Mann-Whitney U | Kruskal-Wallis | Wilcoxon |
| Categorical | Chi-square / Fisher | Chi-square | McNemar |
| Correlation (Parametric) | Pearson | – | – |
| Correlation (Non-parametric) | Spearman | – | – |
Kappa Statistic
Ethical Principles
1. Autonomy → the patient's right to decide → informed consent 2. Beneficence → acting in the patient's interest 3. Non-maleficence → ALARA, justification 4. Justice → equal distribution of resources
Informed Consent
Radiation Ethics – Special Situations
Additional Notes from EANM Guidelines:
Current guidelines on this chapter's topics
The latest guidelines and consensus documents on the procedures covered in this chapter (official EANM index and primary sources, November 2026). Comparison of the text with these versions is in progress; consult the guideline itself for details.
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