A short list of statistics equations

These equations are important, because the questions upon which they are bases are rather binary. Either you get it right, in which case you get full marks, or you get it wrong, in which case you get nothing. This is an important concept to internalise, as there is nothing better than easy marks earned by the mindless rote-learning of equations.

Historical examples of such questions:

- Question 11 from the first paper of 2017 (prevalence, RR, attributable risk)
- Question 19.1 from the first paper of 2010 (Calculate ARR, RRR, NNT)
- Question 19.2 from the first paper of 2010 (Calculate sensitivity, specificity, PPV and NPV)
- Question 29.1 from the first paper of 2008 (Phases of a clinical trial; also calculate ARR, RRR, NNT)
- Question 29.2 from the first paper of 2008 (Calculate sensitivity, specificity, PPV and NPV)
- Question 15 from the first paper of 2007 (Calculate sensitivity, specificity, PPV, NPV and PLR)

Commit these equations to memory. Ideally, on the day before the exam. This part of the training program has the poorest cortical retention rate; one must walk to the written Part II venue very slowly and carefully so that this information doesn't fall out on the way from the train station.

**Absolute risk** **(AR)**= number of cases in group / total number of group

**Absolute risk reduction (ARR)** = AR in exposed - AR in unexposed

**Numbers needed to treat (NNT)** = 1 / ARR

**Relative risk (RR): **the difference in event rates between 2 groups expressed as proportion of the event rate in the untreated group

= AR in treatment group / AR in control group

**Relative risk reduction (RRR)** = (1 - RR)

Or: RRR = ( ARR / control group AR)

Or: RRR = ( AR in unexposed - AR in exposed / AR in unexposed)

**Odds ratio** **(OR)** = Odds of exposure among cases / odds of exposure among controls

**Attributable risk: **a measure of the absolute effect of the risk of those exposed compared to unexposed; = Incidence(exposed) – Incidence(unexposed)

**Sensitivity** = true positives / (true positives + false negatives)

**Specificity** = true negatives / (true negatives + false positives)

In other words:

Sensitivity is the measured positives divided by the actual positives (both measured and missed)

Specificity is the measured negatives divided by the actual negatives (both measured and missed)

For visual learners:

Disease | No disease | |

Positives | True positives | False positives |

Negatives | False negatives | True negatives |

**False positive rate** = (1 - specificity)

**False negative rate **= (1- sensitivity)

**Positive predictive value = ** (true positives / total positives)

**Negative predictive value = ** (true negatives / total negatives)

**Positive likelihood ratio** = sensitivity / (1-specificity)

**Negative likelihood ratio** = (1-sensitivity) / specificity

**Pre-test probability** = (true positive + false negative) / total sample

**Pre-test odds:** pre-test probability / (1- pre-test probability)

**Post-test odds: **likelihood ratio × pre-test odds

**Hazard ratio (HR) **= treatment hazard rate / control hazard rate

**Median ratio (MR) **= placebo median time / treatment median time

**Power = **(1 - false positive rate)

OR: Power** = **(1- beta error)

**Prevalence: **The proportion of individuals in a population having a disease or characteristic in a particular population at a given time.

Prevalence = number of affected individuals / total number in population

**Incidence: **The rate at which a certain event occurs, as the number of new cases of a specific disease occurring during a certain period in a population at risk.

Incidence = number of affected individuals / total exposed population