Measuring the Occurrence
of Disease 2
Sue Lindsay, Ph.D., MSW, MPH
Division of Epidemiology and Biostatistics
Institute for Public Health
San Diego State University
Measures of Mortality
• Annual Mortality Rate
• Case Fatality Rate
• Proportionate Mortality
• Years of Potential Life Lost
Types of Mortality Rates
• Crude Rates
• Specific Rates
• Adjusted Rates
Annual All Cause Mortality Rate
Total No. of Deaths From
All Causes in 1 Year
Annual Rate
Per 1,000
=
No. of Persons in the
Population at Midyear
Age-Specific Mortality Rate
Annual Rate
Per 1,000 in
Children
< 10 yrs.
=
Total No. of Deaths From
All Causes in 1 Year In Children
Younger Than 10 Years
No. of Children in the Population
Younger Than 10 Years at Midyear
Disease-Specific Mortality Rate
Annual Rate
From Lung
=
Cancer
Per 1,000
Total No. of Deaths From
Lung Cancer in 1 Year
No. of Persons in the
Population at Midyear
Disease and age-specific mortality rate
Annual Rate
From
Leukemia
Per 1,000 in
Children
< 10 yrs.
=
Total No. of Deaths From
Leukemia in 1 Year In Children
Younger Than 10 Years
No. of Children in the Population
Younger Than 10 Years at Midyear
Disease Specific Mortality Rates:
Important Concepts
• The denominator equals the number of people at risk of dying.
Any person counted in the denominator must be at risk of
becoming a death in the numerator
• The time period is arbitrary but must be specified (most often
annual)
• A good index of disease severity
• Can be used as a measure of the risk of disease and can
approximate incidence rates
• When the case fatality rate is high
• Duration of the disease is short
The Case-Fatality Rate
CaseFatality
Rate
=
No. of Persons Dying Of
Disease After Disease
Onset
No. of Persons With The Disease
During a Specified Period of Time
Case-Fatality Rate: Important Concepts
• Measures the severity of disease
• Most commonly used in infectious diseases
• The denominator is limited to persons who already have
the disease
Proportionate Mortality
PM
=
No. of Deaths From a
Specific Cause in 1 Year
Total Deaths in the
Population in 1 Year
Proportionate Mortality: Important Concepts
• Usually expressed as a percentage
• Percentage of deaths from heart disease
• Provides a quick look at major causes of death
• Does not yield the risk of dying - Mortality rates
provide this
Years of Potential Life Lost (YPLL)
• Death at younger ages is associated with greater
loss of future productive years of life
• Used as an alternative measure of the burden of
disease
MORTALITY RATES PER 100,000
INJURIES
PNEUMONIA
STROKE
CANCER
HEART DX
Years of Potential Life Lost before
Age 65
CONGENITAL
AIDS
HEART
INJURIES
CANCER
Problems With Mortality Data
• Information from death certificates may not be
accurate
• Quality varies
• Primary and secondary causes of death
• Changes in disease coding and definition will
impact mortality rates
• Validity may be disease specific
Age Adjustment
• Age is one of the main determinants of disease
onset and mortality
• The age distribution of a population will influence
the total mortality rate and often influence the
incidence rate of disease
• Age adjusted mortality rates correct for
differences in age distribution in a population
Age Adjustment Methods
• Direct Age Adjustment
• Uses the age-specific mortality rates of each population of
interest and the age distribution of a “standard” population
• Indirect Age Adjustment
• Uses the age-specific mortality rate of a “standard” population
and calculates a Standardized Mortality Ratio (SMR)
Age-Adjustment Example
Crude Mortality Rates in Alaska and Florida
Number of Deaths
Total Population
Crude Mortality Rate
Florida
Alaska
131,044
12,335,000
1,062.4 per
100,000
2,064
524,000
393.9 per
100,000
Source: Vital Statistics of the U.S. (1991)
Percentage Distribution of
Age Groups in Florida and
Alaska Populations, 1988
Percentage of Total
45
Florida
Alaska
40
35
30
25
20
15
10
5
0
<5
5-19
20-44
Age
45-64
65+
Age Adjustment: Direct Method
• Select a standard population (choice is arbitrary)
• U.S. 1988 Total US Population
• Apply the age-specific mortality rates of both Florida and
Alaska to the standard population distribution to calculate
the expected number of deaths that would occur in each
age group in the standard population
• Sum the expected number of deaths over all age groups.
Calculate the overall age-adjusted mortality rate for both
Florida and Alaska.
Florida: Direct Method
Age
Group
<5
5-19
20-44
45-64
>65
U.S.
Florida
Age-Specific Population
Death Rate/ (standard)
100,000
284
57
198
815
4425
18,300,000
52,900,000
98,100,000
46,000,000
30,400,000
Calculation of
Expected Deaths
.00284X18,300,000=
.00057X52,900,000=
.00198X98,100,000=
.00815X46,000,000=
.04425X30,400,000=
245,700,000
Expected
Deaths
51,972
30,153
194,238
374,900
1,345,200
1,996,463
1,996,463
Age Adjusted Death Rate =
= 812.6 per 100,000
245,700,000
Alaska: Direct Method
Age
Group
Alaska
Age-Specific
Death Rate/
100,000
U.S.
Population
(standard)
<5
5-19
20-44
45-64
>65
274
65
188
629
4350
18,300,000
52,900,000
98,100,000
46,000,000
30,400,000
.00274X18,300,000=
50,142
.00065X52,900,000=
34,385
.00188X98,100,000=
184,428
.00629X46,000,000=
289,340
.04350X30,400,000= 1,322,400
245,700,000
1,880,695
Age Adjusted Death Rate =
Calculation of
Expected Deaths
1,880,695
245,700,000
Expected
Deaths
= 765.4 per 100,000
Age-Adjustment Example: Direct Method
Crude Mortality Rate
Age Adjusted Mortality Rate
Florida
Alaska
1,062.4/100,000
393.9/100,000
812.6/100,000
765.4/100,000
Age Adjustment: Indirect Method
• Select a standard population (choice is arbitrary)
• U.S. 1988 Total US Population
• Apply the age-specific mortality rates of the standard
population to the age distributions of Alaska and Florida to
calculate the total expected deaths in each age group if
they were subjected to the mortality experience of the
standard population. Sum expected deaths over all age
groups.
• Calculate Standardized Mortality Ratio (SMR)
Standardized Mortality Ratio (SMR)
SMR =
Total Observed Deaths in the Population
Total Expected Deaths in the Population
IF SMR=1:
Observed mortality is the same as expected mortality
If SMR >1:
Mortality is higher than expected.
IF SMR<1:
Mortality is lower than expected.
Florida: Indirect Method
Age
Group
U.S.
Death Rate/
100,000
(standard)
Florida
Population
<5
5-19
20-44
45-64
>65
251.1
47.2
161.8
841.9
5,104.8
850,000
2,280,000
4,410,000
2,600,000
2,200,000
Observed
SMR =
=
Expected
Calculation of
Expected Deaths
.00251X850,000=
.000472X2,280,000=
.001618X4,410,000=
.008419X2,600,000=
.051048X2,200,000=
2,134
1,076
7,135
21,889
112,305
144,539
131,044
= 0.91
144,539
Expected
Deaths
Alaska: Indirect Method
Age
Group
<5
5-19
20-44
45-64
>65
U.S.
Death Rate/
100,000
(standard)
Alaska
Population
251.1
47.2
161.8
841.9
5,104.8
60,000
130,000
240,000
80,000
20,000
SMR = Observed =
Expected
Calculation of
Expected Deaths
.00251X60,000=
.000472X130,000=
.001618X240,000=
.008419X80,000=
.051048X20,000=
2,064
2,295
Expected
Deaths
151
61
388
674
1,021
2,295
= 0.90
Age-Adjustment Example: Indirect Direct
Crude Mortality Rate
Standardized Mortality Ratio
Florida
Alaska
1,062.4/100,000
393.9/100,000
0.91
0.90
Age-Adjustment: Important Concepts
• Both methods depend on the choice of the standard population
• Standard populations can be:
• Independent of either study population, a combination of the
two populations, the larger of the two populations, etc.
• Age-adjusted rates (direct method) are not “real”. It is important
to know the population that was used as the standard.
• SMR (indirect method) is a ratio not a rate. It gives only relative
information and does not describe the mortality of the population.
Age-Adjustment: Important Concepts
• Direct method uses age-specific death rates. Requires
that this detailed information be known
• Indirect methods are used if age-specific rates are
unstable or unknown
• Both methods can be used for other types of rates:
i.e. incidence
• Do not confuse with multivariate “adjustment for age”
Measurement
• Quality of measurement is often the weakest
and least considered area of study design
• Don’t make this mistake!
• Poorly designed or executed measures can
effect the interpretation of your study!
• You can get the wrong answer!
How do we measure?
• Self-report
• Historical documentation (medical records)
• Direct observation
• Direct examination
• Specimen collection and measurement
Why do we measure?
• Characterize patients at baseline
• Determine eligibility for the study
• To stratify or randomize
• To assess similarity of comparison groups
• To assess risk factors, protective factors and
outcomes
What can be measured?
• Demographics
• History: symptoms, diagnosis, exposures
• Disease state: physical exam, imaging,
autopsy
• Analysis of body fluids
• Body composition: BMI, DEXA scan, MRI
What can be measured?
• Movements of fluids and molecules (cardiac output)
• Electrophysiology (ECG, EEG, nerve conduction
• Psychometry (cognition, emotional status etc.)
• Behaviors
• Subjective outcomes such as quality of life and
satisfaction with care
Types of Measurement Scales
• Qualitative:
• Nominal, unordered, categorical, dichotomous or
polychotomous
• Ordinal or semi-quantitative (Likert scale)
• Quantitative:
• Ordered discrete with intervals that are integers: number of
cigarettes smoked
• Continuous: ordered continuous intervals: weight, BP, etc.
Quality of Measurement: Validity
Validity is the degree to which the
variable you are measuring actually
accurately measures the phenomenon
you are interested in.
Validity
• Face Validity
• How well the measure works based on intuitive
judgment? Does it make sense that it should be
measured this way?
• Sampling validity
• How well does the measure represent the aspects
of the phenomenon you are interested in?
• Is time-to-run one mile a good measure of cardiovascular
health?
Construct Validity
• How well does the measure conform to our current
theoretical models or concepts of the phenomenon?
• Which biomarker is the best estimator of level of smoking?
• Which lab test best reflects vulnerability to opportunistic
infections?
• Which lab test best reflects our current understanding of the
biology of stress?
• Levels of what hormone indicate that a patient is in
menopause?
Criterion-Related Validity
• Correlational validity. Does your measure correlate well to a
widely accepted criterion or “gold standard”
• Does your self-report stress scale correlate with other known
measures of stress?
• Can your assay for viruses produce the correct results when you use
it to test a known amount of virus?
• Predictive validity. A variable’s ability to predict outcomes.
• Does your depression index predict suicide?
• Do levels of a serum tumor maker predict cancer recurrence?
Convergent Validity
• Acceptance of the variable is based on multiple
lines of evidence
• Low density lipoprotein cholesterol has been
validated to measure the risk of atherosclerosis by:
•
•
•
•
Histopathologic studies of diseased tissues
Epidemiologic studies of populations and families
Multiple animal models
Interventional studies with lipid lowering agents
Quality of Measurement:
Accuracy and Precision
• Accuracy: The degree to which a variable
agrees with a reference or “gold” standard or
is free of systematic error (bias).
• Precision (reliability): The degree to which the
variable is reproducible, or is free from random
error.
Relationship of Precision and Accuracy:
The target shooting analogy
Random
error
-
+
-
+
Systematic
error
+
-
-
+
Selecting Measures for Your Study
• Find standardized measures of established validity, if
available, but use a technique only if it captures the
phenomenon you are interested in (construct validity).
• Consult with experienced experts about applying an
established measure or designing a new measure for
your specific purpose.
• Pilot the measure for practice and assessment of
validity, accuracy, and precision.