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GP licensing preparation for DHA, SMLE, DOH, QCHP, OMSB, MOH UAE, NHRA, and Kuwait MOH.

Biostatistics

Formulas

29 formulas

A

ANOVA

Compare means of three or more groups.

F = \frac{between-group variance}{within-group variance}

A large F means at least one group mean differs. It does not name which group.

Attributable risk

How much extra disease the exposure adds.

A R = I_{e} - I_{u}

Iₑ: Incidence in the exposed
Iᵤ: Incidence in the unexposed

Subtract the incidence in the unexposed from the incidence in the exposed.

C

Case-fatality rate

Among people who have the disease, the share who die of it.

\frac{deaths from the disease}{cases} \times 100%

The denominator is cases, not the whole population. That is what separates it from mortality.

Cause-specific mortality

Deaths from one cause in the whole population.

\frac{deaths from the cause}{population} \times 1, 000

Often written per 1,000 people. Existing cases stay in the denominator.

Chi-square

High yield

Test association in a table, usually 2×2.

χ^{2} = \sum \frac{( O - E ) ^{2}}{E}

O: Observed count
E: Expected count

Expected count in a cell is (row total × column total) / grand total.

Coefficient of variation

High yield

Compare spread when the means are different.

C V = \frac{S D}{x ˉ} \times 100%

SD: Standard deviation
x̄: Mean

A higher CV means more scatter relative to the average.

Confidence interval

High yield

Estimate a mean and the range likely to hold the true value.

\overset{x}{ˉ} \pm z \times \frac{s}{n}

x̄: Sample mean
s: Sample standard deviation
n: Sample size
SE: s / √n

The piece after z is the standard error. A larger sample narrows the interval. For 95%, z is about 1.96.

I

Incidence

New cases over a period.

\frac{new cases}{population at risk}

People who already have the disease are taken out of the denominator.

L

Linear regression

Predict an outcome from one variable.

y = a + b x

y: Dependent variable
x: Independent variable
a: Intercept
b: Slope

y is the outcome. x is the predictor. b is how much y changes for each step of x.

M

10.

Mean

High yield

The average of a set of values.

\overset{x}{ˉ} = \frac{\sum x}{n}

Σx: Sum of the values
n: How many values

Add every value, then divide by how many there are.

11.

Median

High yield

A typical value that ignores extremes.

Middle value once the numbers are in order.

If the count is even, average the two middle values.

12.

Mode

The most common result in a set.

The value that appears most often.

A set can have more than one mode, or none if every value appears once.

N

13.

Negative predictive value

Of the negative tests, the share that are truly negative.

N P V = \frac{T N}{T N + F N}

TN: True negatives
FN: False negatives

NPV falls when the disease is common, because more negatives are missed cases.

14.

Normal distribution

A symmetric bell curve around the mean.

68% within 1 SD · 95% within 2 SD · 99.7% within 3 SD

About 95% of values sit within two standard deviations of the mean.

15.

Null hypothesis

The starting claim a test tries to reject.

No difference, or no association.

Reject it when the p-value is below the cutoff, usually 0.05.

O

16.

Odds ratio

High yield

Odds of disease in the exposed versus the unexposed.

O R = \frac{a d}{b c}

a: Exposed, with disease
b: Exposed, without disease
c: Unexposed, with disease
d: Unexposed, without disease

OR = 1 means the exposure is not tied to higher odds. Read the letters from a 2×2 table.

P

17.

Point prevalence

How common a disease is at one moment.

\frac{existing cases}{population}

This is a snapshot, the kind a cross-sectional study measures. It counts existing cases, not new ones.

18.

Positive predictive value

Of the positive tests, the share that are truly positive.

P P V = \frac{T P}{T P + F P}

TP: True positives
FP: False positives

PPV rises when the disease is common.

19.

Proportion

High yield

A part of a whole.

p = \frac{x}{n}

x: The part
n: The whole

Multiply by 100 to turn the proportion into a percent.

20.

p-value

How surprising the result is if the null hypothesis is true.

p < 0.05 → unlikely if there is truly no difference.

A small p-value is evidence against no difference. It is not the chance the result is wrong.

R

21.

Range

The distance from the smallest number to the largest.

Highest value minus the lowest value.

One pair of extremes sets it, so a single outlier can stretch it.

22.

Relative risk

How many times higher the risk is in the exposed.

R R = \frac{I _{e}}{I _{u}}

Iₑ: Incidence in the exposed
Iᵤ: Incidence in the unexposed

RR = 1 means no association. From a 2×2 table, Ie is a/(a+b) and Iu is c/(c+d).

S

23.

Sample variance

The average squared distance from the mean.

s^{2} = \frac{\sum ( x - x ˉ ) ^{2}}{n - 1}

x̄: Mean
n − 1: Sample divisor

A sample uses n − 1. Standard deviation is the square root of this.

24.

Sensitivity

Of the people who have the disease, the share the test calls positive.

\frac{T P}{T P + F N}

TP: True positives
FN: False negatives

A sensitive test misses few cases.

25.

Specificity

Of the people without the disease, the share the test calls negative.

\frac{T N}{T N + F P}

TN: True negatives
FP: False positives

A specific test raises few false alarms.

26.

Standard deviation

Typical distance of values from the mean.

S D = variance

On a normal curve, about 95% of values sit within 2 SD of the mean.

27.

Standard error

How much the sample mean would bounce from sample to sample.

S E = \frac{S D}{n}

SD: Standard deviation
n: Sample size

This is the term a confidence interval multiplies by z. Larger n makes the standard error smaller.

28.

Student's t

High yield

Compare a mean when the population SD is unknown.

t = \frac{x ˉ - μ}{s / n}

x̄: Sample mean
μ: Population mean
s: Sample standard deviation
n: Sample size

Use the sample SD in place of σ. The shape matches a z-score with s instead of the population SD.

Z

29.

Z-score

How many standard deviations a value sits from the mean.

z = \frac{x - x ˉ}{S D}

x: The value
x̄: Mean
SD: Standard deviation

z = 1 is one SD above the mean. z = −1 is one SD below it.