FRCS Statistics, Ethics & Law — Questions and Answers
Question 1: A new diagnostic test for bowel cancer has a sensitivity of 85% and a specificity of 90%. What does the specificity of 90% tell you?
- 85% of patients with bowel cancer will test positive
- 90% of patients without bowel cancer will test negative (Correct answer)
- 10% of patients with bowel cancer will be missed
- 85% of patients without bowel cancer will test negative
Correct answer: 90% of patients without bowel cancer will test negative
Specificity is the proportion of truly disease-free individuals who test negative (true negative rate). A specificity of 90% means 90% of patients without bowel cancer will correctly test negative. The false positive rate is 10% (1 − specificity). High specificity minimises false positives.
Question 2: What is the number needed to treat (NNT) if a treatment reduces the absolute risk of complication from 20% to 15%?
- 5
- 10
- 20 (Correct answer)
- 15
Correct answer: 20
NNT = 1 / absolute risk reduction (ARR). ARR = 20% − 15% = 5% = 0.05. NNT = 1/0.05 = 20. This means 20 patients must be treated for one additional patient to avoid the complication. Lower NNT values indicate greater treatment efficacy.
Question 3: In a randomised controlled trial, what is the purpose of blinding participants and investigators?
- To reduce the sample size required
- To prevent selection bias at randomisation
- To reduce performance bias and detection bias by preventing knowledge of treatment allocation (Correct answer)
- To ensure equal numbers in each group
Correct answer: To reduce performance bias and detection bias by preventing knowledge of treatment allocation
Blinding prevents performance bias (if participants or clinicians modify behaviour based on knowing treatment allocation) and detection bias (if outcome assessors rate outcomes differently based on allocation knowledge). Double-blinding (both participant and investigator blinded) is the gold standard for reducing these biases.
Question 4: What is the difference between relative risk reduction (RRR) and absolute risk reduction (ARR)?
- They are the same measure expressed differently
- ARR is the percentage reduction in event rate between treatment and control groups; RRR is ARR divided by control event rate (Correct answer)
- RRR is always smaller than ARR
- ARR is only used for negative outcomes; RRR for positive outcomes
Correct answer: ARR is the percentage reduction in event rate between treatment and control groups; RRR is ARR divided by control event rate
ARR = control event rate − treatment event rate (e.g., 20% − 15% = 5%). RRR = ARR / control event rate (5%/20% = 25%). RRR appears more impressive than ARR but is less clinically meaningful because it does not reflect baseline risk. Both are needed alongside NNT for full interpretation.
Question 5: What type of study design provides the highest level of evidence in a hierarchy of evidence?
- Case report
- Cohort study
- Randomised controlled trial
- Systematic review and meta-analysis of RCTs (Correct answer)
Correct answer: Systematic review and meta-analysis of RCTs
The evidence hierarchy (from lowest to highest) is: expert opinion, case reports, case series, case-control studies, cohort studies, RCTs, and at the apex, systematic reviews and meta-analyses of multiple high-quality RCTs. Systematic reviews synthesise the best available evidence and control for individual trial limitations.
Question 6: In a clinical trial, a p-value of 0.03 is reported. What does this mean?
- There is a 3% chance the treatment is effective
- There is a 97% chance the null hypothesis is true
- If the null hypothesis were true, there is a 3% probability of observing results at least as extreme as those found (Correct answer)
- The result is clinically significant with 97% certainty
Correct answer: If the null hypothesis were true, there is a 3% probability of observing results at least as extreme as those found
A p-value is the probability of observing results at least as extreme as those found, assuming the null hypothesis (no effect) is true. A p-value of 0.03 means there is a 3% probability this result occurred by chance alone. By convention, p<0.05 is considered statistically significant, but statistical significance does not equal clinical significance.
FRCS Statistics, Ethics & Law
A new diagnostic test for bowel cancer has a sensitivity of 85% and a specificity of 90%.
What does the specificity of 90% tell you?