Stats/Epi

MacMahon & Pugh definition of epidemiology

The study of the distribution and determinants of disease frequency in man

What key concept did Last (1983) add to the MacMahon & Pugh definition?

Control of health problems (he also widened it to health-related states and events in populations)

What does PICO(T)(S) stand for?

Population; Intervention or Exposure; Comparator; Outcome; (Time; Setting or design)

PICO tip: how do you spot the C in a research question?

It usually follows “compared to” (e.g., placebo, usual care, no exposure)

Define exposure

Something we do (exercise), are (ethnicity), possess (a gene) or ingest (food, drug) that could affect health

Define intervention

An action taken that could prevent, treat or manage a disease

Define outcome

A measurement used to capture the effect of an exposure or intervention (e.g., quality of life, blood pressure)

Name the six types of research questions

Intervention; etiology; diagnosis; screening; prognosis; prevalence

Best design for an intervention (does a treatment work?) question

RCT (experimental), if randomizing is ethical and feasible

Experimental vs observational study: key difference

Experimental: investigator randomly assigns the exposure. Observational: subjects or clinicians choose; investigator just observes

Experimental vs observational: which has greater internal validity and which greater external validity?

Experimental = greater internal validity (less bias); observational = greater external validity

When should you use an observational design instead of an RCT?

When randomizing is unethical or impractical, outcomes are rare, or the exposure–outcome delay is long

Define risk

The probability that an event will occur in the future

Define odds

Probability an event occurs ÷ probability it does not = P ÷ (1 − P)

Convert risk to odds

Odds = Risk ÷ (1 − Risk)

Convert odds to risk

Risk = Odds ÷ (1 + Odds)

Risk = 0.20. What are the odds?

0.20 ÷ 0.80 = 0.25

What do odds > 1, = 1 and < 1 mean?

1: more likely than not; = 1: 50/50; < 1: less likely than not

When is odds ≈ risk?

When the outcome is rare (under about 10%)

Formula: cumulative incidence (incidence proportion, risk)

New cases during a time period ÷ number of people at risk (disease-free) at the START of the period

Who is left out of the cumulative incidence denominator?

Anyone who already has the disease at the start (and anyone immune/not at risk)

What must you always state with a cumulative incidence?

The time period (it’s a proportion over a specific period)

What is an attack rate?

The incidence proportion during an outbreak (a sudden increase in cases in a specific area)

Formula: incidence density (incidence rate)

New cases ÷ total person-time at risk

Units of incidence density

Cases per person-time (e.g., per 1,000 person-years)

When does a person stop contributing person-time?

At the first of: diagnosis, loss to follow-up or dropout, death, or end of study

When should you use incidence density instead of cumulative incidence?

When people are followed for different lengths of time (staggered entry, dropouts, deaths)

Can incidence density exceed 1?

Yes — it’s a rate, not a probability, and its value depends on the time unit

Relationship between cumulative incidence and incidence density

Both count NEW cases; CI is a probability over a set period (fixed group, full follow-up), ID is the speed of new cases per person-time (handles unequal follow-up)

Person-time: one person followed 5 y with no disease, one diagnosed at 2 y, one lost at 3 y, one died at 4 y, one followed 5 y. Person-years and ID?

5+2+3+4+5 = 19 person-years; 1 case → 1 ÷ 19 = 0.053 per PY = 53 per 1,000 PY

How do you interpret a cumulative incidence?

“Over [time], X% (or X per 10,000) of people at risk developed [disease].”

How do you interpret an incidence density?

“X new cases per 1,000 person-years of follow-up.”

Formula: point prevalence

Number of people with the disease at a specific point in time ÷ number of people in the population at that point in time

Formula: period prevalence

(Existing cases at start + new cases during the period) ÷ population during the period

Prevalence vs incidence

Prevalence = all existing cases (old + new) at a time = burden; incidence = only NEW cases over time = risk

Prevalence depends on which two things?

Incidence and disease duration

What happens to prevalence if a treatment prolongs life but doesn’t cure?

Prevalence rises (longer duration) even though incidence is unchanged

Three ways people leave the prevalent pool

Cure, death, leaving the population

Steady-state relationship between prevalence and incidence

P ÷ (1 − P) = ID × average duration; if P < 10%, P ≈ ID × duration

ID = 20 per 100,000 PY, average duration 5 years. Approximate prevalence?

≈ 100 per 100,000 (0.1%)

Survey question for point prevalence vs period prevalence

Point: “Do you currently have X?” Period: “Have you had X in the last n years?”

Prevalence is what kind of measure?

A static measure of the proportion of a population that is diseased

Define rate

An instantaneous potential for change in one quantity per unit change in another quantity (often time)

Define proportion

A fraction with the numerator included in the denominator

Incidence is what kind of measure?

A measure of change from non-disease to disease in a population at risk over a specific time period

Formula: crude mortality rate

Total deaths ÷ total population (usually per 1,000 or 10,000 per year)

Formula: cause-specific (absolute) mortality rate

Deaths from a specific cause ÷ total population

Formula: proportionate mortality

Deaths from a specific cause ÷ deaths from all causes

Definition: case fatality rate

The percentage of people with a particular disease who die from that disease

Which measures the risk of dying from a disease: case fatality rate or proportionate mortality?

Case fatality rate (proportionate mortality is NOT a measure of risk)

Infant mortality rate

Deaths under 1 year per 1,000 live births

Child mortality rate

Deaths under 5 years per 1,000 live births

Maternal mortality ratio

Maternal deaths per 100,000 live births in the same period

Maternal mortality rate

Maternal deaths per 1,000 women of reproductive age (15–44)

Perinatal mortality rate

Fetal (stillbirth) + neonatal deaths per 1,000 births

Why is mortality used to compare populations or professions?

Risk often can’t be measured directly — but populations differ in age, so you must standardize

Define surveillance

Ongoing, systematic collection, analysis and interpretation of health data to describe and monitor health events, to control and prevent disease

Four qualities of good surveillance

Timeliness; representativeness; sensitivity; specificity

Surveillance: timeliness

Data are recent enough to act on

Surveillance: representativeness

Data reflect the right population and show true trends over time

Surveillance: sensitivity vs specificity

Sensitivity = identifies people who have the disease; specificity = excludes people who don’t

Sampling frame

The set of people in the population eligible to take part

Weighting

Adjusting sample data so it better represents the population

Data cleaning

Processing data using inclusion–exclusion rules (e.g., removing outliers)

Outbreak: how do you find the food that caused it?

Compare attack rates in people who ate each food vs those who didn’t; the culprit has a high attack rate in eaters AND a low one in non-eaters

2×2 table layout

Rows: exposed (E+), unexposed (E−). Columns: disease (D+), no disease (D−). a = E+D+, b = E+D−, c = E−D+, d = E−D−

Formula: risk ratio (relative risk)

Risk in exposed ÷ risk in unexposed = [a ÷ (a + b)] ÷ [c ÷ (c + d)]

Formula: incidence density ratio

Incidence density in exposed ÷ incidence density in unexposed

Formula: odds ratio

(a ÷ c) ÷ (b ÷ d) = ad ÷ bc = odds of exposure in cases ÷ odds of exposure in controls

Formula: prevalence ratio

Prevalence in exposed ÷ prevalence in unexposed

Formula: matched-pairs odds ratio

b ÷ c = pairs where case exposed & control unexposed ÷ pairs where case unexposed & control exposed

Measure of association for a cohort study or RCT

Risk ratio (or IDR if person-time data)

Measure of association for a case-control study

Odds ratio

Measure of association for a cross-sectional study

Prevalence ratio

Measure of association for ecological studies, case reports and case series

None (no control group)

Can you calculate RR and OR in a retrospective cohort?

Yes, both

Why can’t a case-control study give you risk or RR?

Investigators choose how many cases and controls to enrol, so the proportion with disease is artificial

What does a measure of association = 1 mean?

No association

What does a measure of association > 1 mean?

Positive association — exposure linked with higher risk/odds (a risk factor)

What does a measure of association < 1 mean?

Negative association — exposure linked with lower risk/odds (protective)

RR = 1.5. How do you say it as a percentage?

50% higher risk in the exposed: (1.5 − 1) × 100

RR = 0.52. How do you say it as a percentage?

48% lower risk in the exposed: (1 − 0.52) × 100

When does the OR approximate the RR?

When the outcome is rare (under about 10%); otherwise the OR is farther from 1

Concordant pair (matched case-control)

Case and control have the SAME exposure status (both exposed or both unexposed) — ignored in the matched OR

Discordant pair (matched case-control)

Case and control have DIFFERENT exposure status — the only pairs used in the matched OR

What should a full interpretation of a measure of association include?

The value, direction, size, comparison group, time frame, and “associated with” (not “causes”)

Template to interpret an odds ratio

“The odds of [outcome] in those [exposed] were X times that of those [unexposed].” Add: approximates the RR if the disease is rare; association, not causation

Template to interpret a risk ratio

“The risk of [outcome] in the exposed was X times the risk in the unexposed over [time].”

Template to interpret an SMR

“There were X% more (or fewer) deaths than expected if the group had the reference population’s age-specific death rates.”

Relative vs absolute measures

Relative (RR, OR, IDR, PR) = strength of association, useful for causes; absolute (risk, AR, PAR) = actual amount of disease, public-health impact

Why can a small RR matter more than a big one?

RR 10 on a 1 in 100,000 baseline adds 9 per 100,000; RR 1.2 on a 20% baseline adds 4 per 100 — absolute impact depends on baseline risk

Formula: attributable risk

Incidence in exposed − incidence in unexposed

Formula: attributable fraction (attributable risk proportion)

(Incidence exposed − incidence unexposed) ÷ incidence exposed = (RR − 1) ÷ RR

Formula: incidence in the total population

Incidence exposed × proportion exposed + incidence unexposed × proportion unexposed

Formula: population attributable risk

Incidence in population − incidence in unexposed = prevalence of exposure × AR

Formula: population attributable risk %

PAR ÷ incidence in population × 100 = Pe(RR − 1) ÷ [Pe(RR − 1) + 1]

What does an attributable risk of 0.5 mean?

50 per 100 exposed people developed the disease because of the exposure

Incidence exposed 15 per 100, unexposed 2.5 per 100. AR and AF?

AR = 12.5 per 100; AF = 12.5 ÷ 15 = 83%

Ecological study

Compares exposure and outcome at the population (group) level, not in individuals

Ecological study: strengths

Fast; uses existing data; generates hypotheses