Disease Detectives Math

Point Prevalence

Number of current cases (new/preexisting) at a specificed point in time / population at the same specified point in time

Period Prevalence

Number of current cases (new/preexisting) over a specified period of time / average or mid-interval population at that specified time period

Relationship between Prevalence, Incidence, & Duration

P = I * D

Attack Rate

Rate that group experienced an outcome/illness:

of sick / total in that group

Relative Risk (Risk Ratio)

Attack Rate of Exposed / Attack Rate of Unexposed:

[a / (a+b)] / [c / (c+d)]

Estimates association between exposure and outcome.

If relative risk = 1 → No association

If relative risk > 1 → Positive association

If relative risk b/t 0-1 → Less risk & possible protective effects

No negative numbers should be outputted from this formula.

Odds Ratio

Odds of Exposure in Cases / Odds of Exposure in Controls: AD/BC

Tells that those who were exposed were __ more likely to become infected than those who were not exposed.

Chi Square (X²)

Used to compare observed results with expected results. Determines if difference between observed data and expected data is due to chance or due to relationship between the variables you are studying.

1.) Find value for each of the values in the table:

expected value = (total in row / total of all values) * total in column

2.) Subtract each expected number from each observed number.

3.) Square the difference from step 2 for each expected number.

4.) Divide the squares obtained in step 3 by each expected number.

5.) Add up all the divided values from step 4 to get the chi squared.

Shortcut For 2×2 Table:

[(ab-bc)² (a+b+c+d)] / [(a+b)(c+d)(b+d)*(a+c)]

Sensitivity

Measures a test’s ability to designate individual with disease as positive:

[a/(a+c)] x 100

Highly Sensitive → Few false negatives

Specificity

Measures a test’s ability to designate individual who doesn’t have disease as negative:

[d/(b+d)] x 100

Highly Specific → Few false positives

Positive Predictive Value

Probability that patient with positive result has disease:

[a/(a+b)] x 100

Negative Predictive Value

Probability that person with negative result is free of disease:

[d/(c+d)] x 100

Vaccine Efficacy/Effectiveness

VE = 1 - (ARV / ARU)

where ARU is attack rate (# of sick / total group) in unvaccinated, and ARV is attack rate in vaccinated

Example of Interpreting Results: Say VE calculates to 0.8 from formula. This is read as 80% efficacy. This means that being vaccinated gives an 80% lower risk of developing the disease compared to the placebo group in the study.

Note: Efficacy focuses on results from a clinical setting while effectiveness focuses on results from the real world.

Herd Immunity Threshold

Threshold = 1 - (1 / R0)

where R0 is the basic reproductive number (the average number of secondary cases typically caused by infection)

Basic Reproductive Rate (R0)

Expected number of cases directly generated by one case in the population where all individuals are susceptible to infection. Assume that no individuals are infected/immunized:

R0 = βτ

where B is infection producing contacts per unit time, T is infectious period

Effective Reproductive Rate

Measures number of persons infected by infectious person when some portion of population has already been infected:

R0 = Rt / Re x

where x is fraction of population that is suspectible

Incidence

Number of new cases / population at risk