Instructor Resource

Chapter 3

Copyright © Scott B. Patten, 2015.

Permission granted for classroom use with Epidemiology for Canadian Students: Principles, Methods & Critical Appraisal (Edmonton: Brush Education Inc. www.brusheducation.ca).

Chapter 3. Basic measures based on

frequencies and rates

Objectives

• Distinguish the parameter families of prevalence and incidence.• Define key parameters within each family.• Explain the relationship between proportions and

odds.• Describe the relationship between prevalence and

incidence.• Define cumulative incidence and how to calculate

it.

“Basic” parameter families

• These are “basic” in the sense that they do not embody a comparison (e.g., they do not compare an exposed and nonexposed group).

“Basic” parameter families

Prevalence:• point prevalence• period prevalence• lifetime prevalence

Incidence:• incidence proportion• incidence rate

Prevalence

• This can be a count: the number of people with a disease.• It can be a proportion: the proportion of people

with a disease.• It can be odds: the odds of having a disease.

Prevalence is most often expressed as a proportion—you can assume we are talking about it as a proportion unless otherwise specified.

The prevalence family

• Point prevalence is the proportion of a population with a disease at a point in time.• Period prevalence is the proportion of a population

with a disease at any time during a specified time period.• Lifetime prevalence is the proportion of the

population with a disease at any time in their life (up to the time/age when assessed).

Lifetime prevalence

• Lifetime prevalence is not as important as the other 2 forms of prevalence (point and period).• It mixes up (confounds) “ever” having a condition

with “ever having a condition and surviving.”• It is usually used for lifelong conditions that can go

into remission but never go away (e.g., some mental disorders).

Expressing prevalence

• Imagine a classroom during the peak of the influenza season. There are 25 students in the class, 5 of whom have influenza:

• prevalence count: 5• prevalence proportion: 5/25• prevalence odds: 5/20

Expressing prevalence

• Note that the prevalence proportion and the prevalence odds are both ratios.• A ratio is 1 number (numerator) divided by another

(denominator).• In a proportion, the contents of the numerator are

included in the denominator, whereas this is not true for odds.

Ratios and probabilities

• In epidemiology, we are interested mostly in probabilities.• Prevalence can be conceptualized as the probability

that a member of the population has a disease.• The probability is estimated by calculating a

proportion, using data.• The relationship between proportions and

probabilities is central to epidemiological reasoning—we will see it again and again.

The incidence family

• Whereas prevalence quantifies how many people have a disease, incidence quantifies the development of new cases of a disease (risk).• Incidence can be calculated as a proportion or a

rate.• An incidence proportion must have a defined time

interval (a 5% risk in 1 day is different than a 5% risk over 1 year!).• An incidence rate has a person-time denominator

(e.g., person-days, person-years).

What is “person-time”?

• One person at risk of a disease observed for 1 year = 1 person-year. • One person at risk of a disease observed for 1

month = 1 person-month.• Person-time has units, e.g. year-1 or month-1.

Rates and proportions

• Rates and proportions are not the same thing.• This distinction is important to know, but be ware

that the terminology is used inconsistently.• For example, an “attack rate” is an incidence

proportion calculated after an exposure that has caused an outbreak of disease.• “Prevalence rate” doesn’t make much sense either,

but people use it anyway.

The incidence proportion

• Incidence proportions have new cases in the numerator.• They have population at risk in the denominator.• As a proportion, the denominator includes

everyone in the numerator.• Remember: They need a specified time interval (5%

risk over 1 day is different than 5% risk over 1 year).

Odds from proportions

odds=proportion

1− proportion

Proportions from odds

proportion=odds1+odds

Proportions and odds in rare diseases• Consider the 1 x 2 table representing sample data:

Has disease No disease Row totals

a b n

≈ odds =

• When a is very small (the disease is very rare):

Example calculations (n = 10)

Prevalence and incidence

incidence

recovery death

Point prevalence is the balancebetween inflow to the prevalencepool (incidence) and outflow (e.g.recovery and/or mortality).

Prevalence and incidence (continued)

incidence

recovery death

Prevalence Odds = Incidence Rate x Mean Duration

Units for person-time & duration• Time has units (e.g. years).• Person-time has units (e.g. years-1).• What happens to the units in this formula?

Prevalence Odds = Incidence Rate x Mean Duration

Crude mortality rates

• These are a special type of incidence rate (death is always a “new event”).• They are typically calculated as the number of

deaths in a year (numerator) divided by the midyear population (denominator).• The midyear population is an approximation of

person-years at risk of death during that year – so it is reasonable to call these a rate.

End