Measures of Morbidity and Mortal
Measures of Morbidity and Mortality, Part 2
Jennifer Deal, PhD Johns Hopkins University
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n By the end of this lecture, you should be able to: u Calculate survival using the Kaplan-Meier method u Define the median survival time and relative survival u Calculate and interpret adjusted rates, using direct and indirect adjustment
methods
Objectives
2
The material in this video is subject to the copyright of the owners of the material and is being provided for educational purposes under rules of fair use for registered students in this course only. No additional copies of the copyrighted work may be made or distributed.
Kaplan-Meier Method
Section A
1. Case fatality
2. Five-year survival rate
3. Observed survival rate u Person-years u Life tables u Kaplan-Meier method
Ways of Expressing Prognosis
4
Kaplan-Meier
Source: (1958). J Am Stat Assoc;53:457–81. 5
Follow-Up
6
Calculating Survival Using the Kaplan-Meier Method
(1) Times to
deaths from starting
treatment (months)
(2) Number alive at each time
(3) Number who died at each
time
(4) Proportion
who died at that time
Column (3) Column (2)
(5) Proportion
who survived at that time 1–Column (4)
(6) Cumulative proportion
who survived to that time (cumulative
survival)
4
10
14
24
7
Calculating Survival Using the Kaplan-Meier Method
(1) Times to
deaths from starting
treatment (months)
(2) Number alive at each time
(3) Number who died at each
time
(4) Proportion
who died at that time
Column (3) Column (2)
(5) Proportion
who survived at that time 1–Column (4)
(6) Cumulative proportion
who survived to that time (cumulative
survival)
4 6 1
10
14
24
8
Calculating Survival Using the Kaplan-Meier Method
(1) Times to
deaths from starting
treatment (months)
(2) Number alive at each time
(3) Number who died at each
time
(4) Proportion
who died at that time
Column (3) Column (2)
(5) Proportion
who survived at that time 1–Column (4)
(6) Cumulative proportion
who survived to that time (cumulative
survival)
4 6 1 0.167
10
14
24
9
Calculating Survival Using the Kaplan-Meier Method
(1) Times to
deaths from starting
treatment (months)
(2) Number alive at each time
(3) Number who died at each
time
(4) Proportion
who died at that time
Column (3) Column (2)
(5) Proportion
who survived at that time 1–Column (4)
(6) Cumulative proportion
who survived to that time (cumulative
survival)
4 6 1 0.167 0.833
10
14
24
10
Calculating Survival Using the Kaplan-Meier Method
(1) Times to
deaths from starting
treatment (months)
(2) Number alive at each time
(3) Number who died at each
time
(4) Proportion
who died at that time
Column (3) Column (2)
(5) Proportion
who survived at that time 1–Column (4)
(6) Cumulative proportion
who survived to that time (cumulative
survival)
4 6 1 0.167 0.833 0.833
10
14
24
11
Follow-Up
12
Calculating Survival Using the Kaplan-Meier Method
(1) Times to
deaths from starting
treatment (months)
(2) Number alive at each time
(3) Number who died at each
time
(4) Proportion
who died at that time
Column (3) Column (2)
(5) Proportion
who survived at that time 1–Column (4)
(6) Cumulative proportion
who survived to that time (cumulative
survival)
4 6 1 0.167 0.833 0.833
10 4 1
14
24
13
Calculating Survival Using the Kaplan-Meier Method
(1) Times to
deaths from starting
treatment (months)
(2) Number alive at each time
(3) Number who died at each
time
(4) Proportion
who died at that time
Column (3) Column (2)
(5) Proportion
who survived at that time 1–Column (4)
(6) Cumulative proportion
who survived to that time (cumulative
survival)
4 6 1 0.167 0.833 0.833
10 4 1 0.250
14
24
14
Calculating Survival Using the Kaplan-Meier Method
(1) Times to
deaths from starting
treatment (months)
(2) Number alive at each time
(3) Number who died at each
time
(4) Proportion
who died at that time
Column (3) Column (2)
(5) Proportion
who survived at that time 1–Column (4)
(6) Cumulative proportion
who survived to that time (cumulative
survival)
4 6 1 0.167 0.833 0.833
10 4 1 0.250 0.750
14
24
15
Calculating Survival Using the Kaplan-Meier Method
(1) Times to
deaths from starting
treatment (months)
(2) Number alive at each time
(3) Number who died at each
time
(4) Proportion
who died at that time
Column (3) Column (2)
(5) Proportion
who survived at that time 1–Column (4)
(6) Cumulative proportion
who survived to that time (cumulative
survival)
4 6 1 0.167 0.833 0.833
10 4 1 0.250 0.750 0.625
14
24
16
Follow-Up
17
Calculating Survival Using the Kaplan-Meier Method
(1) Times to
deaths from starting
treatment (months)
(2) Number alive at each time
(3) Number who died at each
time
(4) Proportion
who died at that time
Column (3) Column (2)
(5) Proportion
who survived at that time 1–Column (4)
(6) Cumulative proportion
who survived to that time (cumulative
survival)
4 6 1 0.167 0.833 0.833
10 4 1 0.250 0.750 0.625
14 3 1 0.333 0.667 0.417
24 1 1 1.000 0.000 0.000
18
Kaplan-Meier Survival Curve
19
Kaplan-Meier Curve Showing Time to Event for First AIDS- Defining Outcome
Source: (April, 2014). Lancet Infect Dis;14(4):281– 90. 20
1. No changes have occurred in survivorship over calendar time
2. Those lost to follow-up experience the same survivorship as those who are followed
Two Assumptions Made in Kaplan-Meier
21
1. No changes have occurred in survivorship over calendar time
2. Those lost to follow-up experience the same survivorship as those who are followed
Two Assumptions Made in Kaplan-Meier
22
These assumptions should look familiar; They are the same as for the life table
The material in this video is subject to the copyright of the owners of the material and is being provided for educational purposes under rules of fair use for registered students in this course only. No additional copies of the copyrighted work may be made or distributed.
Median Survival Time and Relative Survival
Section B
1. Case fatality
2. Five-year survival rate
3. Observed survival rate
4. Median survival time
5. Relative survival
Ways of Expressing Prognosis
2
n Length of time that half of the study population survives
n Why median rather than mean? u Less affected by extreme values u Only need to observe deaths of half of the study group rather than the entire group
Median Survival Time
3
Median Survival Time
4
1. Case fatality
2. Five-year survival rate
3. Observed survival rate
4. Median survival time
5. Relative survival
Ways of Expressing Prognosis
5
Relative Survival Rate
6
Relative survival = Observed survival
Expected survival
Observed vs. Expected Survival Rates: Cancer, all Sites
7
Observed vs. Expected Survival Rates: Cancer, all Sites
8
Observed vs. Expected Survival Rates: Cancer, all Sites
9
Observed vs. Expected Survival Rates: Cancer, all Sites
10
Five-Year Observed and Relative Survival Rates by Age for Colon and Rectum Cancer, SEER Program, 1990–1998
11
Age (Years) Observed
survival (%) Relative
survival (%)
<50 60.4 61.5
50–64 59.4 63.7
65–74 53.7 63.8
≥75 35.8 58.7
The material in this video is subject to the copyright of the owners of the material and is being provided for educational purposes under rules of fair use for registered students in this course only. No additional copies of the copyrighted work may be made or distributed.
Comparing Mortality in Different Populations
Section C
n Age is the single most important predictor of mortality
Age Adjustment
2
Crude Mortality Rates By Race, Baltimore City, 1965
3
Mortality per 1,000 population
White 14.3
Black 10.2
Death Rates by Age and Race, Baltimore City, 1965
Sources: (1965). Annual Vital Statistics Report, Maryland; Maryland State Department of Health, Department of Biostatistics. 4
Death rates by age/1,000 population
Race All ages <1 1–4 5–17 18–44 45–64 65+
White 14.3 23.9 0.7 0.4 2.5 15.2 69.3
Black 10.2 31.3 1.6 0.6 4.8 22.6 75.9
Direct age adjustment
5
Direct Age-Adjustment: Comparison of Total Death Rates in a Population at Two Different Time Periods
6
Early period Later period
Population Number of
deaths Death rate per 100,000
Population Number of
deaths Death rate per 100,000
900,000 862 96 900,000 1,130 126
Direct Age-Adjustment: Comparison of Age-Specific Death Rates in the Two Time Periods
7
Early period Later period
Age group
Population Number
of deaths
Death rate per 100,000
Population Number
of deaths
Death rate per 100,000
All ages 900,000 862 96 900,000 1,130 126
30–49 500,000 60 12 300,000 30 10
50–69 300,000 396 132 400,000 400 100
70+ 100,000 405 406 200,000 700 350
Direct Age-Adjustment: Carrying Out an Age-Adjustment Using the Total of the Two Populations as the Standard
8
Age group
Standard population
“Early” rate per 100,000
Expected number of
deaths using “early” rate
“Later” rate per 100,000
Expected number of
deaths using “later” rate
All 1,800,000
30–49 800,000 12 96 10 80
50–69 700,000 132 924 100 700
70+ 300,000 406 1,218 350 1,050
Total number of deaths expected in standard population
2,238 1,830
2,238 1,800,000
Age-adjusted rates, “Early” = = 124.3 1,830
1,800,000 “Later” = = 101.7
Direct Age-Adjustment: Comparison of Age-Specific Death Rates in the Two Time Periods
Early period Later period
Age group
Population Number
of deaths
Death rate per 100,000
Population Number
of deaths
Death rate per 100,000
All ages 900,000 862 96 900,000 1,130 126
30–49 500,000 60 12 300,000 30 10
50–69 300,000 396 132 400,000 400 100
70+ 100,000 405 406 200,000 700 350
9
Direct Age-Adjustment: Carrying Out an Age-Adjustment Using the Total of the Two Populations as the Standard
10
Age group
Standard population
“Early” rate per 100,000
Expected number of
deaths using “early” rate
“Later” rate per 100,000
Expected number of
deaths using “later” rate
All 1,800,000
30–49 800,000 12 96 10 80
50–69 700,000 132 924 100 700
70+ 300,000 406 1,218 350 1,050
Total number of deaths expected in standard population
2,238 1,830
2,238 1,800,000
Age-adjusted rates, “Early” = = 124.3 1,830
1,800,000 “Later” = = 101.7
Direct Age-Adjustment: Comparison of Total Death Rates in a Population At Two Different Time Periods
11
Observed death rate per 100,000
Age-adjusted death rate per 100,000
Early period 96 124.3 Later period 126 101.7
Change from using the year 1940 population to the year 2000 population as the standard
12
Population Pyramids for the 1940 and 2000 US Populations Expressed as a Percent of Total Population
13
Crude and Age- Adjusted Death Rates: US, 1930– 1997, Based on the Year 1940 Standard
14
Crude and Age- Adjusted Death Rates: US, 1960– 2000, Based on the Year 2000 Standard
15
Crude rate = unadjusted rate
16
Indirect age adjustment
17
“The number of deaths occurring in a given population (occupation) expressed as the percentage of the number of deaths that might have been expected to occur if the given population (occupation) had experienced within each age group the same rate as that of the standard population.”
Standardized Mortality Ratio (SMR)
18
Standardized Mortality Ratio: Indirect Age Adjustment
n SMR =
19
Observed number of deaths per year
Expected number of deaths per year
Standardized Incidence Ratio
n SIR =
20
Observed number of new cases per year
Expected number of new cases per year
Calculation of a Standardized Mortality Ratio (SMR)
n In a population of 534,533 White male miners, there were 436 deaths from tuberculosis (TB) in 1950
n Is this mortality experience from TB greater than, less than, or about the same as that which you would expect in White males of the same ages in the general population?
21
Calculation of a Standardized Mortality Ratio (SMR)
n SMR =
n SMR =
22
Observed deaths for an occupation-age-sex-race group
Expected deaths for an occupation-age-sex-race group
Observed deaths for 20–59-year–old White male miners
Expected deaths for 20–59-year–old White male miners
Computation of an SMR for Tuberculosis (TB), all Forms, for White Miners Ages 20–59 Years, US, 1950
Source: adapted from (1963). Vital Statistics—Special Reports, DHEW. 23
Age (years)
Estimated population of White miners
(1)
Death rate per 100,000 for TB for males in general
population (2)
Expected deaths from TB in White miners if they had the same risk as general population
(3) = (1) x (2)
Observed deaths from TB in White
miners (4)
20–24 74,598 12.26 9.14 10
25–29 85,077 16.12 13.71 20
30–34 80,845 21.54 17.41 22
35–44 148,870 33.96 50.00 98
45–54 102,649 56.82 58.32 174
55–59 42,494 75.23 31.96 112
Computation of an SMR for Tuberculosis (TB), all Forms, for White Miners Ages 20–59 Years, US, 1950
Source: adapted from (1963). Vital Statistics—Special Reports, DHEW. 24
Age (years)
Estimated population of White miners
(1)
Death rate per 100,000 for TB for males in general
population (2)
Expected deaths from TB in White miners if they had the same risk as general population
(3) = (1) x (2)
Observed deaths from TB in White
miners (4)
20–24 74,598 12.26 9.14 10
25–29 85,077 16.12 13.71 20
30–34 80,845 21.54 17.41 22
35–44 148,870 33.96 50.00 98
45–54 102,649 56.82 58.32 174
55–59 42,494 75.23 31.96 112
181.09 436
n SMR =
n SMR (for 20–59 years old) = = 241
Computation of an SMR for Tuberculosis (TB), all Forms, for White Miners Ages 20–59 Years, US, 1950
25 Source: adapted from (1963). Vital Statistics—Special Reports, DHEW.
Observed deaths for an occupation-cause-race group
Expected deaths for an occupation-cause-race group
436
181.09
x 100
SMR of Lung Cancer by Arsenic Concentration in the Air
Source: (2008). Environ Health Prev Med;13:207–18. 26
The material in this video is subject to the copyright of the owners of the material and is being provided for educational purposes under rules of fair use for registered students in this course only. No additional copies of the copyrighted work may be made or distributed.
Putting it all Together: Measures of Disease and Mortality
Section D
n Prevalence
n Incidence u Cumulative incidence u Incidence rate
n Prevalence = Incidence x duration of disease
Key Points from the Past Two Lectures: Indices of Mortality
n Prevalence
n Incidence u Cumulative incidence u Incidence rate
n Prevalence = Incidence x duration of disease
Key Points from the Past Two Lectures: Indices of Mortality
existing cases → burden of disease
New cases → risk of disease
n Mortality rate u Crude u Cause-specific
n To compare two populations u Direct adjustment u Indirect adjustment (SMR, SIR)
Key Points from the Past Two Lectures: Indices of Mortality
n Mortality rate u Crude u Cause-specific
n To compare two populations u Direct adjustment u Indirect adjustment (SMR, SIR)
Key Points from the Past Two Lectures: Indices of Mortality
Adjusted rates are useful for comparing populations but are not the true rates
Adjusted rates are dependent on the standard population used for the adjustment (e.g., 1940 vs. 2000)
n Case fatality
n Five-year survival
n Observed survival u Proportion (closed cohort) u If not everyone is followed for the entire study period:
• Life tables • Kaplan-Meier
n Median survival time
n Relative survival
Key Points from the Past Two Lectures: Expressing Prognosis
6
n Case fatality
n Five-year survival
n Observed survival u Proportion (closed cohort) u If not everyone is followed for the entire study period:
• Life tables → time intervals determined by investigator • Kaplan-Meier → time depends on when events occur
n Median survival time
n Relative survival
Key Points from the Past Two Lectures: Expressing Prognosis
7
n For example, incidence rate, mortality rate
n For example, cumulative incidence, case fatality
Key Points from the Past Two Lectures: Rates vs. Proportions
8
n For example, survival to first myocardial infarction
n For example, survival to delivery in a population of pregnant women
Key Points from the Past Two Lectures: Survival Doesn’t Have to Mean Death
9
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Lecture Evaluation
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