Basic mathematics needed for epidemiology and bio statistics. Slides include formulas and conceptual understanding of sensitivity, specificity, predictive values, likelihood ratios, odds, probability and many more.

1. Prepared by:
Anish Dhakal
(Aryan)
Prepared by:
Anish Dhakal
(Aryan)

2. Conventions:

3. • We know that Sensitivity is something we use to rule disease in.
Specificity is used to rule disease out. Hence,
• Sensitivity = True positive/Total diseased = a/a+c
• Specificity = True negative/Total negative = d/b+d
• You may use mnemonics: SnOUT and SpIN if you have trouble
remembering these which is for ruling disease out and in respectively.

4. • Though not used as frequently as sensitivity and specificity, we have
something known as positive and negative predictive value which
indicates how truly a test or exposure can predict the outcome
(positive or negative).
• Positive predictive value = True positive/Total test positives = a/a+b
• Negative predictive value = True negative/ Total test negatives = d/c+d

5. • Before moving forward, there is something known as accuracy of test
which is simply a ratio of true results to the total results.
• Accuracy = True positive + True negative / Grand total =
a+d/a+b+c+d

6. • Here comes the odds ratio, hazard risk and relative risk:
• Odds ratio is typically used in case control studies and its the measure
of how many times the odds rises with the concerned exposure
agent. If you have a odds ratio of 5 implicated for smoking in regard to
lung cancer means that exposure (cigarette smoking in this case) got
you 5 times more risk of getting lung cancer.
• Odds ratio = Odds that case was exposed / Odds that control was
exposed = a÷c / b÷d = ad/bc

7. • Relative risk on the other hand is usually used in cohort studies and
measures the risk of getting the outcome with the exposure versus
without the exposure. Though we use the term exposure & risk,
similar formulations apply for protective interventions like
vaccination.
• Relative Risk = Incidence among exposed/Incidence among non
exposed = (a/a+b) / (c/c+d)

8. • The rule of thumb for studying relative risk is whether it’s greater
than, equal to or lesser than 1. If in any confidence interval (for
example: RR = 0.8 - 1.4) , you get “1″ means that the test is not
statistically significant (we take a more conservative approach here)
or the exposure has very little value in causing the outcome. If RR is
less than 1 then there is a protective effect.
• Relative Risk Reduction (of a protective agent) = RRR = 1-Relative
Risk

9. • Hazard ratio is the ratio of hazard in the treatment group to the
control group. Hazard ratio of 2 means the treatment or the exposure
group has two times higher hazard risk at any given time. Hazard
ratios differ from relative risks and odds ratio in that RRs and ORs are
cumulative over an entire study, using a defined endpoint, while HRs
represent instantaneous risk over the study time period, or some
subset thereof. Hazard ratios suffer somewhat less from selection bias
with respect to the endpoints chosen and can indicate risks that
happen before the endpoint.
• Hazard ratio = Hazard in treatment group / Hazard in control group

10. • Number needed to treat (NNT) is the number of people that a
intervention or treatment is applied to prevent one outcome (usually
the disease). This has another form as Number needed to harm with
contrasting meaning.
• We learned about relative risk which is the ratio of two numbers (risk
with exposure verses risk without exposure). To calculate Absolute
Risk Reduction (ARR) we simply get the difference instead of ratios.
Absolute Risk Reduction is nothing more than a type of attributable
risk. If the exposure had increased the risk we would have called it as
Absolute Risk Increase (ARI).
• Number needed to treat = 1/Absolute Risk Reduction

11. • Likelihood ratio denote value in performing a test. They combine both
sensitivity and specificity in determining a value (positive or negative)
which would give a somewhat clearer picture about the diagnostic
test.
• If I say that the positive likelihood ratio of CT scan in detecting brain
hemorrhage is 50, it means that there is 50 time higher likelihood
that the test is going to show positive when disease present
compared to test positive when disease absent. Higher positive values
means the test is more valuable.

12. • Positive likelihood test (+) = Likelihood of positive (+) test when
disease present / Likelihood of positive (+) test when disease absent
= Sensitivity / 1-Specificity
• Negative likelihood ratio (-) = Likelihood of negative (-) test when
disease present / Likelihood of negative (-) test when disease absent
= 1-Sensitivity / Specificity

13. • From likelihood ratio it is very easy to understand Pretest and posttest
odds.
• Posttest odds = Pretest odds * Likelihood Ratio
• Note than here I said “odds” and not probability. Most students confuse
between them and end up with the wrong answer. Probability as you know
is the chance of occurrence. If you roll a dice the probability of occurring
any of the six digits is 1/6.
• Odds on the other hand is the ratio of the probability of event to the total
outcomes expect the event. In other words, odds is the ratio of success of
the outcome to the number of all failures possible.
• Odds = Probability / 1- Probability = P/1-P
• Probability = Odds / 1+Odds = O/1+O

14. • If you want to test yourself, here are 10 questions designed for the
same:
https://www.slideshare.net/AnishDhakal4/10-mcqs-in-epidemiology-
biostatistics-how-much-can-you-score