SMRs, PMRs and Survival Measures Principles of Epidemiology Lecture 3 Dona SchneiderDona Schneider, PhD, MPH, FACE

SMRs, PMRs and

Survival Measures

Principles of Epidemiology

Lecture 3Dona Schneider, PhD, MPH, FACE

Epidemiology (Schneider)

REVIEW: Adjusted Rates are Created Through Standardization

Standardization:

The process by which you derive a

summary figure to compare health

outcomes of groups

The process can be used for mortality,

natality, or morbidity data


Standardization Examples

Direct Method requires

Age-specific rates in the sample population

The age of each case

The population-at-risk for each age group in the sample

Age structure (percentage of cases in each age group)

of a standard population

Summary figure is an AGE-ADJUSTED RATE


Standardization: Age Adjustment (cont.)

Indirect method requires

Age structure of the sample population at risk

Total cases in the sample population (not ages of cases)

Age-specific rates for a standard population

Summary figure is a STANDARDIZED MORTALITY RATIO (SMR)


Indirect Standardization Instead of a standard population structure, you utilize

a standard rate to adjust your sample

Indirect standardization does not require that you know the stratum-specific rates of your cases

The summary measure is the SMR or standardized mortality/morbidity ratio

SMR = Observed X 100

Expected


Indirect Standardization (cont.)

An SMR of 100 or 100% means no

difference between the number of

outcomes in the sample population and

that which would be expected in the

standard population


Total expected deaths per year: 2,083

(3) = (1) X (2)(2)(1)

1,27522,95355,56555-64

5648,21268,68745-54

1742,86860,83835-44

591,59437,03025-34

111,3837,98920-24

Expected Number of Deaths for Farmers and

Farm Managers per 1,000,000

Standard Death Rates per 1,000,000 (All Causes of Death)

Number of Farmers and Farm Managers

(Census, 1951)Age Group

Example: SMR for Male Farmers, England and Wales, 1951

Total observed deaths per year: 1,464

SMR = 1,464 X 100 = 70.3%

2,083

In 1951, male farmers in England and

Wales had a mortality rate 30 percent

lower than the comparably-aged

general population.


SMR = Observed / Expected X 100

SMR (for 20–59 yr olds) = 436 / 181.09 X 100 = 241%

436181.09Totals

11231.9675.2342,49455-59

(4)(3) = (1) X (2)(2)(1)

17458.3256.82102,64945-54

9850.5533.96148,87035-44

2217.4121.5480,84530-34

2013.7116.1285,07725-29

109.1412.2674,59820-24

Observed Deaths from TBC in White Miners

Expected Deaths From TBC in White Miners if They Had the Same Risk as the General Population

Death Rate (per 100,000) for TBC in Males in the General Population

Estimated Population of White MinersAge

(yr)

SMR for Tuberculosis for White Miners Ages 20 to 59 Years,

United States, 1950


In the United States in 1950, white miners

ages 20 to 59 years died of tuberculosis

almost 2.5 times as often as comparably-aged

males in the general population


Individuals in a cohort may contribute different amounts of risk due to length of exposure (person-years)

Calculation of stratum or age-specific and total SMRs

SMR = O/E X100 = 179/88.15 X 100 = 203%

88.15

24.38

46.50

14.27

3.00

(4) = (2) X (3)

Exp

Study Cohort

2.03 179Total

1.9725.09754870-79

2.1112.43,7509860-69

1.896.12,3402750-59

2.002.51,200640-49

(1) / (4)(3)(2)(1)

SMR =

Reference Population

Rate per 1,000

Person-Years in TOTAL cohort

Number or outdomes of

interest (Obs)Age

(yr)


Workers in this cohort were twice as likely to have the outcome of interest as the

general population

Those ages 60-69 had the highest age-specific SMR

Those ages 50-59 had the lowest age-specific SMR


SMR’s (con’t) Sometimes exposures change over time and

individuals may have different amounts of exposure when they are in a cohort over multiple years

Example: Over a period of years, the manufacturing process of product X changed. The occupational

cohort involved in the processes had 58 deaths (we do not know their ages). Was this more or less than would be expected in the general population?

Stratify the cohort by known exposure periods


9.5450.92,09855-64

6.7432.01,55255-64

4.7409.41,14455-64

0.111.254415-24

.0617.53,70225-34

1.944.24,38235-44

4.7157.72,96845-54

1958-1963

0.010.3415-24

0.418.82,20625-34

2.246.34,73735-44

6.8164.14,11445-54

42.9TOTAL

SMR = observed/expected x 100% = 58 / 42.9 x 100% = 135%

1953-1957

1948-1952

3.1150.82,02845-54

1.544.53,27535-44

0.617.73,42325-34

0.19.91,25015-24

Exp. Cancer Deaths

US White Male CA Deaths (per 100,000)

Person-years in Cohort

Age Group


Persons in this cohort had the outcome

35% more often than would be expected in

the general population.

We could not calculate age-specific SMRs

without the ages of the cases.

If we have the ages of cases:

Epidemiology (Schneider) SMR = Obs / Exp X 100 = 15 / 12.9 X 100 = 116%

Exp = 12.92.60.90.930-34

1.52.31.725-29

0.30.91.8Age 20-24

Expected deaths = population rates x person-years / 1000

1.71.81.930-34

1.51.51.725-29

1.61.81.8Age 20-24

Population rates(per 1,000)

Obs = 1521030-34

24325-29

012Age 20-24

Observed Deaths

150050050030-34

10001500100025-29

2005001000Age 20-24

1980-841975-791970-74Person-years


From these data you can compute

A total SMR (116%)

Age-specific SMRs (age 20-25, SMR = 100%)

Time period SMRs (1970-1974, SMR = 114%)

Age-specific and time period SMRs (age 20-24,

1970-74, SMR = 111%)


SMRs

Expect a Healthy worker effect Occupational studies should have SMRs < 100

Workers tend to be healthier than the general population which comprises both healthy and unhealthy individuals

You cannot compare SMRs between studies -- only to the standard population


Comparison of Rates

Hides subgroup differencesPermits group comparison

Magnitude depends on population standardControls confounders

Fictional rateProvides a summary figureAdjusted

No summary figureProvides detailed

information

Cumbersome if there are many subgroups

Controls for homogeneous

subgroupsSpecific

Readily calculable

Difficult to interpret because of differences in population structures

Actual Summary ratesCrude

DisadvantagesAdvantages


In Summary:

One type of rate is not necessarily more important than another. Which you choose depends on the information sought.

Crude rates are often used to estimate the burden of disease and to plan health services.

To compare rates among subpopulations or for various causes, specific rates are preferred.

To compare the health of entire populations, adjusted rates are preferred because they allow for comparison of populations with different demographic structures.


CDC Wonder

http://wonder.cdc.gov/


Additional Outcome Measures

Proportionate Mortality Ratio

Proportionate Mortality Rate

Case Fatality Rate

Years of Potential Life Lost

Measures of Survival


Additional Outcome Measures

Proportionate Mortality Ratio

The ratio of observed/expected deaths (in terms of proportions of deaths in the standard population) x 100

PMRs are explained similarly to SMRs

100% = no difference between groups


Computing a PMR

All Deaths 1950-54 1955-59 1960-64

20-24 10 5 2

25-29 10 15 10

30-34 5 5 15

Cancer Deaths20-24 2 1 0

25-29 3 4 2 observed30-34 0 1 2 =15Population Proportion of Cancer Deaths

20-24 0.07 0.07 0.07

25-29 0.09 0.10 0.10

30-34 0.11 0.12 0.12

Expected deaths due to cancer = Population proportion x all deaths in sample20-24 0.7 0.4 0.1

25-29 0.9 1.5 1.0 expected30-34 0.6 0.6 1.8 =7.6

PMR = Observed/Expected x 100 = (15/7.6) x 100 = 197%


PMR = 197%

The study population has twice the proportion

of cancer deaths as the standard population.


CHD Proportionate Mortality RateFigure 3-19. Deaths from heart disease as a percent of deaths from all causes, by age group, United States, 1986.

0%

20%

40%

60%

80%

100%

AllAges

<1 1-4 5-14 15-24 25-34 35-44 45-54 55-64 65-74 75-84 85+

Pe

rce

nt

of

All

De

ath

s

Heart Disease All Other Causes


2.71.52,211Diabetes mellitus9

5.43.04,449

Chronic liver disease and cirrhosis7

4.12.33,343Cerebrovascular diseases8

14.98.312,281Suicide6

100147,750All causes

2.71.52,203Pneumonia and influenza10

15.0 8.412,372Homicide and legal

intervention5

19.210.715,822Diseases of the heart4

26.414.721,747HIV infection3

27.015.022,228Malignant neoplasms2

32.218.026,526Accidents and adverse effects

1

Cause-specific death rate per 100,000

Proportionate mortality rate (%)

NumberCause of DeathRank

Order

Ten Leading Causes of Death, 25-44 Years, All Races, Both Sexes, United States, 1991 (Population 82,438,000)


Comparing Mortality and Case-Fatality Rates

Assume a 1995 population of 100,000 people where 20 contract disease X and 18 people die from the disease. One remains stricken and one recovers. What is the mortality rate and what is the case-fatality rate for disease X?

Mortality rate from disease X18 / 100,000 = .00018 = .018%

Case-fatality rate from disease X18 / 20 = .9 = 90%


Years of Potential Life Lost Death occurring in a particular individual at an

early age results in a greater loss of that

individual’s productivity than if that same

individual lived to an average life span.

By convention, YPLL (or PYLL) is based on a life

expectancy of 75 years

YPLL can be calculated for individual or group data


Example: Individual data method A person who died at age 20 would contribute 55

potential years of life lost (75-20=55 YPLL)

Deaths in individuals 75 years or older are

excluded

The rate is obtained by dividing total potential

years of life lost by the total population less than

75 years of age.


*excluded

YPLL from Disease X = 169.5 / 4 = 42.4 per person

169.5xxxSum

15605

xx85*4

60153

20552

74.56 months1

YPLL Contributed (75-age)

Age at Death (Years)

Individual


Example: Age Group MethodIn a population of 12,975,615, what is the rate of YPLL for 2000?

1. Obtain the ages at the time of death for each case (column 1)Exclude those over age 75

2. Calculate the mean age for each age group (column 2)

3. Subtract the mean age from 75 (column 3)

4. Calculate stratum-specific YPLL by multiplying column 1 by column 3

5. Sum the stratum-specific YPLL

6. Divide by the total population for the ages selected

Epidemiology (Schneider) Rate of YPLL per 1,000 persons = 93,234.0/12,975,615 = 7.2 per 1,000 in 2000

6412.537.537.517135-39

xxx

2.5

7.5

12.5

17.5

22.5

27.5

32.5

42.5

47.5

52.5

57.5

62.5

67.5

72.0

74.5

Age 75-mean(3)

93,234.0xxxxxx

175.072.57070-74

480.067.56465-69

1075.062.58660-64

1487.557.58555-59

1912.552.58550-54

3190.047.511645-49

4257.542.513140-44

10327.532.524330-34

14630.027.530825-29

21525.022.541020-24

18112.517.531515-19

4000.012.56410-14

3510.07.5525-9

2016.03.0281-4

298.00.54<1

YPPL(1)x(3)

Mean Age at Death(2)

# Deaths(1)Age


Measuring Survival

Five-year survival

Not a magical number

May be subject to LEAD TIME BIAS

Cannot evaluate new therapies


Measuring Survival (cont.)

Life Tables (assume no change in treatment over the time of observation) Used to calculate probability of surviving fixed

segments of time

Allow each case to contribute to data analysis regardless of the time segment in which they are enrolled

The probability of surviving 5 years is the product of surviving each year (p.89)


Measuring Survival (cont.) Kaplan-Meier

Time periods are not predetermined but are

set by the death or diagnosis of a case

Withdrawls and those lost to follow-up are

removed from the analysis

Typically used for small numbers of cases



Median Survival

The time that half the population survives

Not effected by outliers like the mean

Can calculate the median survival time

when half rather than all the cases die



Relative survival rate

Compares survival from a given disease to a

comparable group who do not have the

disease

Relative Survival Rate (%) = Observed/Expected x 100

Documents

SMRs, PMRs and Survival Measures Principles of Epidemiology Lecture 3 Dona SchneiderDona Schneider, PhD, MPH, FACE