SMRs, PMRs and Survival Measures

1
SMRs, PMRs and Survival Measures

• Principles of Epidemiology
• Lecture 3
• Dona Schneider, PhD, MPH, FACE

2
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

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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

4
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)

5
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

6
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

7

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

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
(3) (1) X (2)
(2)
(1)
11
1,383
7,989
20-24
59
1,594
37,030
25-34
174
2,868
60,838
35-44
564
8,212
68,687
45-54
1,275
22,953
55,565
55-64

• Total expected deaths per year 2,083
  

SMR 1,464 X 100 70.3 2,083

Total observed deaths per year 1,464
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In 1951, male farmers in England and Wales had a
mortality rate 30 percent lower than the
comparably-aged general population.
9
SMR for Tuberculosis for White Miners Ages 20 to
59 Years, United States, 1950
Expected Deaths From TBC in White Miners if They
Had the Same Risk as the General Population
Observed Deaths from TBC in White Miners
Death Rate (per 100,000) for TBC in Males in the
General Population
Estimated Population of White Miners
Age (yr)
(4)
(3) (1) X (2)
(2)
(1)
10
9.14
12.26
74,598
20-24
20
13.71
16.12
85,077
25-29
22
17.41
21.54
80,845
30-34
98
50.55
33.96
148,870
35-44
174
58.32
56.82
102,649
45-54
112
31.96
75.23
42,494
55-59
181.09
Totals
436
SMR Observed / Expected X 100 SMR (for 2059 yr
olds) 436 / 181.09 X 100 241


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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
11

• 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
Study Cohort
Reference Population Rate per 1,000
Person-Years in TOTAL cohort
Number or outdomes of interest (Obs)
Exp
Age (yr)
SMR
(1) / (4)
(4) (2) X (3)
(3)
(2)
(1)
3.00
2.00
2.5
1,200
6
40-49
14.27
1.89
6.1
2,340
27
50-59
46.50
2.11
12.4
3,750
98
60-69
70-79
24.38
1.97
25.0
975
48
88.15
2.03

179
Total
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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

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SMRs (cont)

• 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

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Exp. Cancer Deaths
US White Male CA Deaths (per 100,000)
Person-years in Cohort
Age Group
1948-1952
0.1
9.9
1,250
15-24
0.6
17.7
3,423
25-34
1.5
44.5
3,275
35-44
3.1
150.8
2,028
45-54
4.7
409.4
1,144
55-64
1953-1957
0.1
11.2
544
15-24
.06
17.5
3,702
25-34
1.9
44.2
4,382
35-44
4.7
157.7
2,968
45-54
6.7
432.0
1,552
55-64
1958-1963
0.0
10.3
4
15-24
0.4
18.8
2,206
25-34
2.2
46.3
4,737
35-44
6.8
164.1
4,114
45-54
9.5
450.9
2,098
55-64
42.9
TOTAL
SMR observed/expected x 100 58 / 42.9 x 100
135
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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
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1980-84
1975-79
1970-74
Person-years
200
500
1000
Age 20-24
1000
1500
1000
25-29
1500
500
500
30-34
Observed Deaths
0
1
2
Age 20-24
2
4
3
25-29
S Obs 15
2
1
0
30-34
Population rates(per 1,000)
1.6
1.8
1.8
Age 20-24
1.5
1.5
1.7
25-29
1.7
1.8
1.9
30-34
Expected deaths population rates x
person-years / 1000
0.3
0.9
1.8
Age 20-24
1.5
2.3
1.7
25-29
S Exp 12.9
2.6
0.9
0.9
30-34
SMR S Obs / S Exp X 100 15 / 12.9 X 100 116
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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)

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SMRs

• Expect a Healthy worker effect
• Occupational studies should have SMRs lt 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

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Comparison of Rates
Disadvantages
Advantages
Actual Summary rates
Difficult to interpret because of differences in
population structures
Crude
Readily calculable
Controls for homogeneous subgroups
Cumbersome if there are many subgroups
Specific
No summary figure
Provides detailed information
Fictional rate
Provides a summary figure
Adjusted
Magnitude depends on population standard
Controls confounders
Hides subgroup differences
Permits group comparison
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• 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.

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CDC Wonder

• http//wonder.cdc.gov/

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Additional Outcome Measures

• Proportionate Mortality Ratio
• Proportionate Mortality Rate
• Case Fatality Rate
• Years of Potential Life Lost
• Measures of Survival

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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

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Computing a PMR
All Deaths
Cancer Deaths
observed
expected
PMR Observed/Expected x 100 (15/7.6) x 100
197
25
PMR 197The study population has twice the
proportion of cancer deaths as the standard
population.
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CHD Proportionate Mortality Rate
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Ten Leading Causes of Death, 25-44 Years, All
Races, Both Sexes, United States, 1991
(Population 82,438,000)
Number
Cause of Death
Proportionate mortality rate ()
Rank Order
Cause-specific death rate per 100,000
32.2
18.0
26,526
1
Accidents and adverse effects
27.0
15.0
22,228
Malignant neoplasms
2
26.4
14.7
21,747
HIV infection
3
Diseases of the heart
19.2
10.7
15,822
4
Homicide and legal intervention
5
15.0
8.4
12,372
14.9
8.3
12,281
Suicide
6
Chronic liver disease and cirrhosis
7
5.4
3.0
4,449
4.1
8
Cerebrovascular diseases
2.3
3,343
2.7
1.5
2,211
Diabetes mellitus
9
2.7
1.5
2,203
10
Pneumonia and influenza
All causes
147,750
100
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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 X
• 18 / 100,000 .00018 .018
• Case-fatality rate from disease X
• 18 / 20 .9 90

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Years of Potential Life Lost

• Death occurring in a particular individual at an
  early age results in a greater loss of that
  individuals 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

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Example Individual data method

• A person who died at age 20 would contribute 55
  potential years of life lost (75-2055 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.

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YPLL Contributed (75-age)
Age at Death (Years)
Individual
74.5
6 months
1
20
55
2
60
15
3
xx
85
4
15
60
5
169.5
xxx
Sum
excluded   YPLL from Disease X 169.5 / 4
42.4 per person
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Example Age Group MethodIn a population of
12,975,615, what is the rate of YPLL for 2000?

• Obtain the ages at the time of death for each
  case (column 1)
• Exclude those over age 75
• Calculate the mean age for each age group (column
  2)
• Subtract the mean age from 75 (column 3)
• Calculate stratum-specific YPLL by multiplying
  column 1 by column 3
• Sum the stratum-specific YPLL
• Divide by the total population for the ages
  selected

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Age 75-mean(3)
YPPL(1)x(3)
Mean Age at Death(2)
Deaths(1)
Age
74.5
298.0
0.5
4
lt1
72.0
2016.0
3.0
28
1-4
67.5
3510.0
7.5
52
5-9
62.5
4000.0
12.5
64
10-14
57.5
18112.5
17.5
315
15-19
52.5
21525.0
22.5
410
20-24
47.5
14630.0
27.5
308
25-29
42.5
10327.5
32.5
243
30-34
6412.5
37.5
37.5
171
35-39
32.5
4257.5
42.5
131
40-44
27.5
3190.0
47.5
116
45-49
22.5
1912.5
52.5
85
50-54
17.5
1487.5
57.5
85
55-59
12.5
1075.0
62.5
86
60-64
7.5
480.0
67.5
64
65-69
2.5
175.0
72.5
70
70-74
xxx
xxx
xxx
93,234.0
Rate of YPLL per 1,000 persons
93,234.0/12,975,615 7.2 per 1,000 in 2000
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Measuring Survival

• Five-year survival
• Not a magical number
• May be subject to LEAD TIME BIAS
• Cannot evaluate new therapies

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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)

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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

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Measuring Survival (cont.)

• 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

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Measuring Survival (cont.)

• 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