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Epidemiologic Measurements: A review

Counts, ratios, proportions, and rates

NBC Nightly News, Saturday September 5, 2015
Salmonella Linked to Cucumbers from Mexico

Since July 3, 2015:
27 states involved
One person has died (California) – 51 cases in this state
No cases reported thus far in Florida
285 persons have become ill; 53 hospitalized
54% of the ill persons are children younger than18; 57% are female
Organism: Salmonella Poona
Found worldwide in both cold-blooded and warm-blooded animals, and in the environment.
Source: Imported cucumbers from Mexico distributed by Andrew & Williamson Fresh Produce
Eleven illness clusters have been identified in seven states.
An illness cluster is defined as two or more people who do not live in the same household who report eating at the same restaurant location, attending a common event, or shopping at the same location (grocery store) in the week before becoming ill.

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The facts:

Food may be contaminated during food processing or food handling.
Food may become contaminated by the unwashed hands of an infected food handler.
Beef, poultry, milk, and eggs are most often infected with salmonella but vegetables may also be contaminated.
Contaminated foods usually look and smell normal.
Symptoms include: diarrhea, fever, and abdominal cramps.
Symptoms develop 12 to 72 hours after infection
Illness usually lasts 4 to 7 days.
Most people recover without treatment; diarrhea and dehydration may be so severe that hospitalization is necessary.
Older adults, infants, and those who have impaired immune systems are at highest risk.

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Epidemiologic measurements: The Basics
Four types of data

Description	Examples
Nominal	Categorical – unordered categories Two levels – dichotomous More than two levels – multichotomous	Sex, disease (yes, no), race, marital status, educational status
Ordinal	Categorical – ordering informative	Preference rating (e.g., agree, neutral, disagree)
Discrete	Quantitative – Integers	Number of cases
Continuous	Quantitative – Values on a continuum	Dose of ionizing radiation, temperature, tire pressure

Types of data

Categorical: Nominal or ordinal
No numerical scale, just groups.
Male/Female, Yes/No, Married/Single/Divorced

Quantitative: Takes on numerical values.

Discrete data: integers or counts that differ by fixed amounts, no intermediate values are possible.
Examples are number of children, number of times married, number of sick days you have accrued
Continuous data take on many values on a finely-grained scale.
Examples are temperature, weight, age

Categorical data

Nominal

Ordinal

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Level A

Level C

Level B

Quantitative data:
Discrete and Continuous

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Another Epidemic:
Reported late 2012

The American Association of Poison Control Centers reported 2,950 cases of exposure to detergent packets like Tide Pods
The patients were typically 10 to 20 months old and suffered serious consequences after biting or ingesting the contents of a laundry detergent pod.
Symptoms included intense vomiting, somnolence, absence of response, seizure-like symptoms, and respiratory distress.
Only one patient required intubation with a prolonged hospital admission
Others were released following 48 hours of intubation.

Reported poisonings

Product introduced February 2012
In early May, Texas poison control centers report receiving 57 emergency calls in a 20-day period
May-June 2012, CDC undertakes investigation
Surveillance of calls to Poison Control Centers involving suspected ingestion of the content of detergent pods
Charlotte, NC reported 2 cases
Philadelphia, PA reported 2 cases
No deaths (PA cases required subsequent speech therapy)
Nationwide from May 17-June 17, 2012: 1008 laundry detergent exposures
485 cases involved pods

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Counts: Provide only limited interpretation

Cases of Reporting

Location Disease Period Population

Charlotte 20 2012 100

Philadelphia 100 2012 1000

Annual Rate of Occurrence = Count ÷ Population

Charlotte 20 / 100 = 1 / 5

Philadelphia 100 / 1000 = 1 / 10

* Simplest, most frequently performed measure in epidemiology

• Refers to the number of cases of a disease or other health phenomenon being studied

• Useful for allocation of health resources

• Limited usefulness for epidemiologic purposes without knowing size of the source population

Counts

Epidemiological Outcomes

Ratio: Relationship between two numbers
Example: males/females
In a ratio the values of x and y are independent such that the values of x are not contained in y
Proportion: A ratio where the numerator is included in the denominator
Example: males/total births
Example: deaths from pod ingestion/deaths from all household cleaning agents
Rate: A proportion with the specification of time
Example: the annual rate of occurrence in the pod poisoning scenario

Like a proportion, ratio is a fraction,

BUT without a specified relationship between the numerator and denominator

Example: Occurrence of Major Depression

Female cases = 240 240

------------------------ = ---- 2:1 female to male

Male cases = 120 120

Ratios

Proportion

In a proportion, x is contained in y
A proportion is typically expressed as a percentage, such that the rate base is 100

In epidemiology, proportions tell us the fraction of the population that is affected.

Persons included in the numerator are always included in the denominator:

Proportion: --------

A + B

Indicates the magnitude of a part, related to the total.

Proportions

Proportions – Example:

Injuries involving children

P = A / (A + B) = (1,400 / 11,050) = 0.127

For ease of usage, multiply a proportion by 100 to get a percentage: p = 0.127 = 12.7%

A	B	Total (A + B)
# child pod poisoning cases	# child bouncy castle injuries	Total study population
1,400	9,650	11,050

Rate

A rate may be thought of as a proportion with the addition that it represents the number of health-related states or events in a population over a specified time period

A proportion in which TIME forms part of the denominator

Epidemiologic rates contain the following elements:

* a defined time interval (day, week, month year,

decade, century, etc)

* number (or count) of events occurring in that time

interval

* estimate (or count) of the population at risk in the

time interval

* a multiplier or constant (x 10; x 100; x 1000; etc)

Rates

Calculate crude annual death rate in the US:

Annual death count

Crude death rate = ----------------------- x 1,000

Reference population

(during midpoint of year)

Death count in U.S. during 1990: 2,148,463

U.S. population on June 30, 1990: 248,709,873

2,148,463

Crude death rate = -------------- x 1,000 = 8.64 per 1,000

248,709,873

Rates – Example

In epidemiology, the occurrence of a disease or condition can be measured using rates and proportions.

We use these measures to express the extent of these outcomes in a community or other population.

Rates tell us how fast the disease is occurring in a population.

Proportions tell us what fraction of the population is affected.

(Gordis, 2000)

Morbidity Measures

Incidence is always calculated for a given period of time
An attack rate is an incidence rate calculated for a specific disease for a limited period of time during an epidemic

Population at risk

X 1,000

Number of new events during a time period

Incidence Rate =

Morbidity Measures

Point prevalence measures the frequency of all current events (old and new) at a given instant in time
Period prevalence measures the frequency of all current events (old and new) for a prescribed period of time

Population at risk

X 1,000

Number of existing events, old and new

Prevalence =

What might be the reason for:

A disease or health-related event having a high prevalence rate?

A disease or health-related event having a low prevalence rate?

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High prevalence may reflect:

High risk

Prolonged survival without cure

Low prevalence may reflect:

Low risk

Rapid fatal disease progression

Rapid cure

Examples: Rhinovirus (common cold vs Ebola virus)

Relationship Between Incidence and Prevalence (cont.)

Cancer of the pancreas
Incidence low
Duration short
Prevalence low
Adult onset diabetes
Incidence: Increasing
Duration long
Prevalence high

Roseola infantum
Incidence high
Duration short
Prevalence low
Essential hypertension
Incidence high
Duration long
Prevalence high

Calculation Practice

You want to investigate the cases of skin

cancer recorded on Knightro Beach:

Point prevalence on 3/11/2013

Period prevalence for year 2012

Incidence rate for year 2012

What information will you need?

Morbidity Measures

Prevalence is not a rate
Point prevalence measures the frequency of all current events (old and new) at a given instant in time
Period prevalence measures the frequency of all current events (old and new) for a prescribed period of time

Population at risk

X 1,000

Number of existing events, old and new

Prevalence =









Diagnosed cases of Skin Cancer

On Knightro Beach

Point Prevalence (3/11/2013)

= (10/450)*1000

= 22 per 1000

# of existing cases = 10

Total population at risk = 450















Diagnosed cases of Skin Cancer

on Knightro Beach, 2012

Average population at risk = 500

Incidence rate (year 2012)

= (5/500)*1000

= 10 per 1000

Period prevalence (year 2012)

= (15/500)*1000

= 30 per 1000

# of new cases = 5

# Existing cases (10) + New cases (5)



Attack rate (cumulative incidence rate)

Describes diseases or events that affect a larger proportion of the population than the conventional incidence rate.
Used when new cases rapidly occur over a short period of time in a well-defined population
Ex. Cases of bacterial gastroenteritis (food poisoning) within a community following a church picnic

Crude vs. age-adjusted rates

The crude rate of an outcome is calculated without any restrictions, such as by age or sex, on who is counted in the numerator or denominator

These rates are limited if we try to compare them between subgroups of the population or over time because of potential confounding influences, such as differences in the age-distribution between groups

The importance of age-adjustment

In 2002, the crude mortality rate in Florida was 1,096 per 100,000 compared with 579 per 100,000 in Utah

The crude mortality rate ratio is 1.9, meaning the rate in Florida was 1.9 times higher than in Utah

However, the age distribution differs considerably between Florida and Utah.

In Florida 6.3% of the population is under five years of age and 16.7% of the population is 65 years and older.
Corresponding percentages in Utah are 9.8% and 8.5%.

Importance of age-adjustment (continued)

Using the direct method of age-adjustment based on the 2000 US standard population yielded rates of 762 in Florida and 782 in Utah per 100,000
Thus, after adjusting for differences in the age distribution, the rate in Florida is 0.97 times that in Utah

Objective: Be familiar with tables, graphs, and numerical methods for describing epidemiologic data

Tables
Line listing
Frequency distribution
Graphs
Bar chart, pie chart
Histogram
Epidemic curve
Box plot
Two-way (or bivariate) scatter plot
Spot map
Area map
Line graph

Frequencies example: Aphasia

Summary Table

Class

Frequency

Class percentage = class relative frequency x 100

Describing Qualitative Data – Qualitative Data Displays

Bar Graph:

Used for frequency distributions when qualitative in nature.

Space placed between bars to show measurement is not continuous.

Methods for Describing Quantitative Data

The Data

Describing Quantitative Data

Histogram

Uses the height of a vertical bar (y axis) to show frequency of occurrence and the size of the interval is represented by the width of the bar on the horizontal bar
(x axis).

Shapes of large distributions

Polygon:
Places the midpoint of the intervals on the X axis, places a dot at the frequency of an interval based on the y axis, and then connects the dots by straight lines.

A dot is placed at the midpoint of each class interval represented on the

X axis

Height of the dot = the frequency of the relative class frequency.

Measures of Central Tendency

Mean: the sum of scores divided by the number of scores (average)

Median: the score with an equal amount of scores above and below it (50th percentile)

Mode: the score that occurs the most often in a set of data

Measures of dispersion (variability)

Variability – the spread of the data across possible values

3 commonly used measures of Variability

1) Range

2) Variance

3) Standard Deviation

Range = Largest measurement minus the smallest measurement

Loses sensitivity when data sets are large

These 2 distributions
have the same range.

How much does the
range tell you about
the data variability?

Measures of dispersion

2) Variance

May provide a better way of describing the variety that exists among the values in a data set

The average of the squared differences of the observations from the mean

Standard Deviation

Normal curve calculated from diastolic blood pressures of 500 men, mean 82 mmHg, standard deviation 10 mmHg.

BMJ Statistics at Square One

Correlation coefficient:
Understanding the literature

Denoted by “r”
Measures the strength and direction of the association between two variables
Values range between -1 and +1
Positive values indicate that the two variables are positively correlated (vary in the same direction)
Negative values indicate that the two variables are negatively correlated , meaning the two variables vary in the contrary direction.
Values close to +1 or -1 reveal the two variables are highly related.

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“P” values: Understanding the literature

The p-value is a probability, which is the result of a statistical test.
This probability reflects the measure of evidence against the null hypothesis.
Small p-values correspond to strong evidence
The level of significance of 0.05 (or 5%) is often chosen.
If the p-value is less than this limit, the result is significant and it is agreed that the null hypothesis should be rejected and the alternative hypothesis—that there is a difference—is accepted.

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