Statistics and Other Maths

Question 1

What is the formula for A-a Gradient?

Answer 1

(FiO₂ x (Atmospheric pressure - PH₂O) - PaCO₂/0.8) - PaO₂

Simplified (150 - PaCO₂/0.8) - PaO₂

Question 2

Formula for Number Needed to Treat

Answer 2

1/ARR (Absolute Risk Reduction)

Question 3

Formula to convert from risk to odds

Answer 3

Odds = risk ÷ (1 - risk)

Question 4

Formula to convert from odds to risk

Answer 4

Risk = odds ÷ (odds + 1)

Question 5

Formula for sensitivity

Answer 5

Sensitivity = True Positive ÷ (True Positive + False Negative)

i.e. proportion of patients with disease who test positive

More sensitive = fewer false negatives = exclude a disease with negative test

Question 6

Formula for specificity

Answer 6

Specificity = True Negative ÷ (True Negative + False Positive)

i.e. proportion of patients without disease who test negative

More specific = fewer false positives = rule a condition in with positive test

Question 7

Formula for Positive Predictive Value

Answer 7

PPV = True Positive ÷ (True Positive + False Positive)

i.e. what proportion of patients with a positive test have the disease

NOTE: depends in prevalence of disease

Question 8

Formula for negative predictive value

Answer 8

NPV = True Negative ÷ (True Negative + False Negative)

i.e. what proportion of patients with a negative disease do not have the disease?

NOTE: dependent on disease prevalence

Question 9

Positive Likelihood Ratio

Answer 9

Positive Likelihood Ratio = Sensitivity ÷ (1 - Specificity)

Question 10

Negative Likelihood Ratio

Answer 10

Negative Likelihood Ratio = (1 - Sensitivity) ÷ Specificity

Question 11

Post-test odds if test is positive

Answer 11

pre-test odds x positive likelihood ratio

Question 12

Post-test odds if test is negative

Answer 12

Pre-test odds x negative likelihood ratio

Question 13

What study should be used to determine prevalence?

Answer 13

Cross sectional study

Question 14

What study should be used to determine incidence?

Answer 14

Cohort study

Question 15

What study type can be used to determine prognosis?

Answer 15

Cohort study

Question 16

Selection Bias

Answer 16

Means of selecting patients into arms of the study is not the same between arms

Question 17

Measurement Bias

Answer 17

Measurements of exposures and outcomes different in different arms

Question 18

Lead Time Bias

Answer 18

Survival post diagnosis is longer because disease is diagnosed earlier in its course

Question 19

Length Time Bias

Answer 19

Diagnose more indolent disease with screening versus the cases that present clinically.

i.e. the cases picked up by screening are milder/slower growing and likely have better survival than cases that develop between screening interval which are likely to be aggressive given their rate of development

Question 20

Health Volunteer Bias

Answer 20

Healthy people are more likely to participate in screening programs