Statistics

Question 1

Stats: what is SD, SEM, RR, OR

Answer 1

Standard Deviation = Sqrt(Sum of (observation - mean)2/ N-1)

Standard error of the mean = SD/sqrt(N)

Relative Risk = incidence exposed/ unexposed

Odds Ratio = exposed cases * unexposed non-cases / exposed non-cases * unexposed cases (this is an estimate of RR)

Question 2

Attributable risk, population AR, PAR%

Answer 2

Attributable risk = exposure% incidence - control% incidence

Population attributable risk = attributable risk * prevalence

PAR % = cases caused by exposure/ all cases

• Assume lung cancer affects 1% of non-smokers and 5% of smokers, and that 30% of the population smokes. In a population of 100 there would be 70 non-smokers with 0.7 of them (1%) getting lung cancer and 30 smokers with 1.5 of them (5%) getting lung cancer. Total of 0.7+1.5 = 2.2 cases of lung cancer. Of these 2.2 cases, 1.2 cases (= 30 x 4%) are due to smoking.
• Attributable risk = 5% – 1% = 4%
• Population attributable risk = 4% x 30% = 1.2%
• PAR% = 1.2/2.2 = 55% (ie 55% of LCs caused by smoking)

Question 3

NNT

Answer 3

NNT = 1/ARR

absolute risk reduction = absolute adverse rate for placebo - treatment

Question 4

A clinical trial was undertaken of pregabalin versus oxycodone for the management of neuropathic pain. 100 patients were randomised in a 1:1 ratio to pregabalin and oxycodone. In the pregabalin group, 40 patients noted improvement in pain after 1 week, compared to 30 patients in the oxycodone group.
Which of the following statements is correct?

A. The number needed to treat for pregabalin versus oxycodone was 50.
B. The number needed to treat for pregabalin versus oxycodone was 10.
C. The number needed to treat for pregabalin versus oxycodone was 5.
D. The odds ratio for pregabalin versus oxycodone was 0.75.
E. The odds ratio for pregabalin versus oxycodone was 1.3.

Answer 4

C. The number needed to treat for pregabalin versus oxycodone was 5.

NNT = 1/ARR

Question 5

Type I and II errors

Answer 5

Type I (α) error: claiming there is a true difference when in fact there is not – p-values live here.

Type II (β) error: claiming that there is no difference when in fact that there is – power lives here.

Question 6

In a recently published trial, 27,295 participants with stable atherosclerotic vascular disease to receive rivaroxaban (2.5mg twice daily) plus aspirin (100mg once daily), rivaroxaban (5mg twice daily), or aspirin (100mg once daily). The primary outcome was a composite of cardiovascular death, stroke and myocardial infarction. The hazard ratio for the primary outcome in the rivaroxaban-plus-aspirin group compared to the aspirin-alone group was 0.76, 95% confidence interval 0.66 to 0.86.
Which of the following statements is correct regarding these results?

A. The results were not likely to have arisen as a result of chance.
B. The results were likely to have been affected by a lack of power.
C. The probability of a type I statistical error was more than 5%.
D. The associated p value would be more than 5%.
E. The relative risk reduction in the primary outcome was 76%.

Answer 6

A. The results were not likely to have arisen as a result of chance.

Question 7

Types of Bias

Answer 7

Selection (how representative is it)
Observation - unreliable or invalid measurement
Lead time bias - does screening increase survival

Question 8

In parallel, 2-arm superiority clinical trials, which of the following is a source of confounding?

A. Lack of randomisation.
B. Lack of blinding/masking.
C. Lack of intention-to-treat analysis.
D. Differential drop-out between the arms.
E. Significant cross-over between the arms.

Answer 8

A. Lack of randomisation.

Question 9

Sensitivity, specificity, PPV, NPV

Answer 9

Sensitivity = test positive/ with disease
Specificity = test negative/ without disease

PPV = true positive/ total positive
NPV = true negative/ total negative

Question 10

A validity study was undertaken of a new urine test for transitional cell carcinoma (TCC), with validation of its results against cystoscopy (with biopsy as required), in 100 patients who presented with haematuria and risk factors for TCC. The results of the validation study were as shown: Neg Pos (cystoscopy)
Neg 92 1
Pos. 3 4
In this study, what was the negative predictive value of the urine test for transitional cell carcinoma?

A. 5%
B. 57%
C. 80%
D. 95%
E. 99%

Answer 10

E. 99%

Question 11

Ideally, diagnostic tests should only be undertaken on patients in whom the likelihood of the underlying condition is considered high (based on clinical assessment).
The reason is to improve:

A. Sensitivity of the test.
B. Specificity of the test.
C. Reproducibility of the test.
D. Positive predictive Value.
E. Negative predictive value.

Answer 11

D. Positive predictive Value.

Question 12

A new test for the diagnosis of myocardial infarction has a sensitivity of 95% and a specificity of 90%. The prevalence of myocardial infarction in a population is 25%.
What is the post‐test probability of having myocardial infarction with a positive test?
A. 1
B. 0.93
C. 0.8
D. 0.76

Answer 12

Answer = D

Post‐test probability = Post‐test odds ÷ (Post‐test odds + 1)
Post‐test odds = Pre‐test odds x likelihood ratio
Likelihood ratio = Sensitivity ÷ (1 – Specificity)
Pre‐test odds = Pre‐test probability of disease ÷ (1 – Pre‐test probability of disease)

i. Pre‐test probability = prevalence of the disease = 25%
ii. Pre‐test odds of disease = 0.25 ÷ (1 ‐ 0.25) = 0.33
iii. Likelihood ratio = 0.95 ÷ (1 – 0.9) = 9.5
iv. Post‐test odds = 0.33 x 9.5 = 3.14
v. Post‐test probability = 3.14 ÷ (3.14 + 1) = 0.76