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Standardizing RatesNam Bains
October 15th, 2007Statistics and Analysis in Public Health
APHEO
Acknowledgements
Sue BondyBrenda ColemanMary-Anne Pietrusiak
Overview
What and why Choice of standard population Age vs. age/sex vs. sex-specific Small numbers How many age groups? Variance formulae
What is standardization?
A procedure that adjusts for differences in population structure and provides a single summary measure for the comparison of populations.
Typically used to adjust for age and sex
Direct: Rates in study population (PHU) are applied to a standard population distribution (Canada).
Indirect: Uses rates from a standard population (Ontario) to derive expected number of events in a study population (PHU).
Why standardize?
Examining crude rates alone can be misleading if underlying populations are different (age-specific rates are better)
But Cumbersome to compare age-specific
rates especially when doing large number of comparisons
Crude vs. age-standardized morality rate (Brant PHU, all causes)
650
700
750
800
850
900
950
1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
rate
r pe
r 10
0,00
0 crude
SRATE
Crude vs. age-standardized morality rate (Toronto PHU, respiratory disease)
40
45
50
55
60
65
70
75
80
1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999
rate
per
100
,000
crude
SRATE
Age-standardization: Sample calculation
Sum
Standard Population
deaths population Crude Rate (Canada 1991) Expected deathsAge Groups d i p i r i = d i /p i P i D i = r i * P i
0-10 5 20,000 0.0002500 4,000,000 1000.010-19 10 15,000 0.0006667 4,000,000 2666.720-29 10 15,000 0.0006667 4,600,000 3066.730-39 10 20,000 0.0005000 4,900,000 2450.040-49 20 16,000 0.0012500 3,800,000 4750.050-59 20 11,000 0.0018182 2,600,000 4727.360-69 20 9,000 0.0022222 2,300,000 5111.170+ 40 9,000 0.0044444 2,100,000 9333.3
Sum 135 115,000 28,300,000 33,105117.3913 116.98
Study Population (PHU)
Rate (per 100,000)
Age-standardization: Sample calculation II
Study Population (PHU) Standard Population
(Canada 1991) Crude Rate Expected
deaths # deaths population
Age Groups di pi Pi
Weight = Wi=
(Pi) /∑ (Pi) ri = di/ pi Di = ri * Wi
0-10 5 20,000 4,000,000 0.1413 0.000250 0.000035
10-19 10 15,000 4,000,000 0.1413 0.000667 0.000094
20-29 10 15,000 4,600,000 0.1625 0.000667 0.000108
30-39 10 20,000 4,900,000 0.1731 0.000500 0.000087
40-49 20 16,000 3,800,000 0.1343 0.001250 0.000168
50-59 20 11,000 2,600,000 0.0919 0.001818 0.000167
60-69 20 9,000 2,300,000 0.0813 0.002222 0.000181
70+ 40 9,000 2,100,000 0.0742 0.004444 0.000330
Sum 135 115,000 28,300,000 1.00 0.001174 0.001170
Rate per 100,000 117.39 116.98
4,000,000 / 28,300,000 = 0.1413
Choice of standard population
0-45-9
10-14
15-19
20-24
25-29
30-34
35-39
40-44
45-49
50-54
55-59
60-64
65-69
70-74
75-79
80-84
85+
World ('Segi')WHO World
EuropeanCanada 1991
USA 1940USA 2000
-
2,000
4,000
6,000
8,000
10,000
12,000
-
2,000
4,000
6,000
8,000
10,000
12,000
-
2,000
4,000
6,000
8,000
10,000
12,000
USA 1940
Canada 1991
World “Segi”
USA 2000
European WHO World
Different standard populations
Ontario cancer mortality rates calculated using different standard populations
0
10
20
30
40
50
60
Lung 30.8 50.3 45.1 30.9 46.7
Female breast 9.8 16.1 13.9 9.8 14.6
Colon 9.2 17.2 14.7 9.5 14.8
Pancreas 5.3 9.6 8.3 5.3 8.3
Prostate 5.3 12.4 10.0 5.6 9.5
1940 US 2000 US 1991 Canada World European
Choice of standard population: considerations
When several different populations are being compared, a ‘pooled’ standard minimizes the variance of the adjusted rates
In examining trends, an appropriate standard is one that reflects the average structure of the population over the time period
The standard should be similar to the population of interest
It should not change frequently (all historic data would need to be recomputed)
It should be used consistently to ensure comparability of rates
Choi, 1999. Am J Epi
Suggested standard population Standard population, Canada 1991 Population Numbers % of Total
Age (years) Version 1 Version 2 Version 1 Version 2 <1 year 401,731 403,061 1.43% 1.43% 1 – 4 1,551,438 1,550,285 5.52% 5.51% 5 – 9 1,952,910 1,953,045 6.95% 6.95% 10 -14 1,912,988 1,913,115 6.80% 6.80% 15 - 19 1,925,926 1,926,090 6.85% 6.85% 20 - 24 2,108,995 2,109,452 7.50% 7.50% 25 - 29 2,528,685 2,529,239 8.99% 8.99% 30 - 34 2,597,980 2,598,289 9.24% 9.24% 35 - 39 2,344,684 2,344,872 8.34% 8.34% 40 - 44 2,138,771 2,138,891 7.61% 7.61% 45 - 49 1,674,125 1,674,153 5.95% 5.95%
50 - 54 1,339,856 1,339,902 4.77% 4.76% 55 - 59 1,238,381 1,238,441 4.40% 4.40% 60 - 64 1,190,172 1,190,217 4.23% 4.23% 65 - 69 1,084,556 1,084,588 3.86% 3.86% 70 - 74 834,014 834,024 2.97% 2.97% 75 - 79 622,230 622,221 2.21% 2.21% 80 - 84 382,310 382,303 1.36% 1.36% 85 - 89 192,414 192,410 0.68% 0.68% 90 + 95,466 95,467 0.34% 0.34%Total 28,117,632 28,120,065 1 1
Age versus Age/Sex
Adjusts for underlying differences in age and sex distribution simultaneously
Disadvantage with so many stratum, numbers are spread thin Rates are NOT COMPARABLE to those that are age-
standardized
female male female male FEMALE MALE
Age Groups d if d im p if p im P iF P iM
[d i(m)/pi(m)*P i(m)]+
[di(f)/pi(f)*P i(f)]
0-10 1 4 9,500 10,500 1,800,000 2,200,000 1027.610-19 4 6 7,000 8,000 1,800,000 2,200,000 2678.620-29 3 7 7,000 8,000 2,000,000 2,600,000 3132.130-39 3 7 9,500 10,500 2,400,000 2,500,000 2424.640-49 8 12 7,500 8,500 1,700,000 2,100,000 4778.050-59 12 8 5,000 6,000 1,300,000 1,300,000 4853.360-69 12 8 5,000 4,000 1,200,000 1,100,000 5080.070+ 25 15 5,000 4,000 1,300,000 800,000 9500.0
Sum 68 67 55,500 59,500 13,500,000 14,800,000 33,474118.28
Expected deaths
Study Population (PHU)
Rate (per 100,000)
Population# deathsStandard Population -
Canada 1991
(1
* 1,800,000 ) + (
4 *
2,200,000 ) = 1027.6 9,500 10,500
Age/sex standardization: Sample calculation
Age-standardized rates≠
Age/sex standardized rates≠
Sex-specific age standardized rates (Rates for females standardized to the Female Standard population
orRate for males standardized to the Male Standard population)
How many age categories?
Lots (detailed age groups)• better control of the effect of any differences in
age distributions but,• lots of strata means there might not be enough
events (larger variance)
Fewer (broad groups)• will produce less precise adjustment• broad groups (i.e., 65+) will not be sensitive to
changes in age-specific rates within that group
Other considerations• availability of data (i.e., CCHS)
Age categories
US NCI (19) M & M (13) US NCHS (11)<1 <1 <1
1- 4 1- 4 1- 4
5 - 9 5 - 95 - 14
10 - 14 10 - 14
15 - 19 15 - 19 15 - 24
20 - 24 20 - 24
25 - 29 25 - 34 25 - 34
30 - 34
35 - 39 35 - 44 35 - 44
40 - 44
45 - 49 45 - 54 45 - 54
50 - 54
55 - 59 55 - 64 55 - 64
60 - 64
65 - 69 65 - 74 65 - 74
70 - 74
75 - 79 75 - 84 75 - 84
80 - 84
85+ 85+ 85+
All cause age-standardized mortality rate, per 100,000 population, Elgin St. Thomas PHU, 2001
619.5 624.8 624.6 621.6 622.2 646.1 630.5500
520
540
560
580
600
620
640
660
680
700
19 13 11 9 8 7 5
# of Age Groups
All cause age-specific mortality rates, Ontario 2001
1
10
100
1000
10000
Age group
rate
per
10,
000
popl
atio
n
Small numbers age-standardized rates based on a small number
of events will be unstable and exhibit large amount of random variation
NCHS cutoff: 25 events 10-24: Calculate SMR (indirect) or crude rate <10: conduct case reviews
Variance estimates “There are a few in public health who believe that confidence
intervals should not be used around estimates derived from 'population' statistics such as the death rate in a given population, because they believe there is no statistical uncertainty in such estimates. This belief is contrary to the statistical theory underlying confidence intervals, and the biological and random processes governing the occurrence of events such as deaths and illnesses.”
Washington State Dept. of HealthGuidelines for using confidence intervals for public health assessment
Vital or administrative data are not subject to sampling
error, but can be affected by errors in the registration process or incomplete registration. Also, for the purposes of analytic work, the events that occur can be thought of as one of a series of possible results that could have arisen under the same circumstances (i.e., subject to random variation).
Curtin LR, Klein RJ. 1995. NCHS.
Variance estimates Based on binomial distribution
Spiegelman, Lilienfeld NCHS, Statistics Canada (for vital events) Not great when <100 events
Based on Poisson distribution Based on Gamma distribution
Better for small numbers Based on Chi-square
SeerStat With adjustment for non-independent events
Carriere & Roos, Stukel
∑
Pi ∑Pi
ri (1-ri) pi
2
*
Pi = Standard Population in age strata iri = age-specific rate for study populationpi = Study population in age strata i
Based on Binomial distribution
Based on Poisson approximation
∑
Pi ∑Pi
ri
di
2
*
Pi = Standard Population in age strata iri = age-specific rate for study populationdi = number of deaths in Study population in age strata i
2
Based on Poisson approximation
∑
Pi ∑Pi
di
pi
2
*
Pi = Standard Population in age strata ipi = Study population in age strata idi = number of deaths in Study population in age strata i
2
Other issues
How to treat cells with 0 values
When NOT to standardize When age-specific rates are not constant over time
(i.e., not moving in parallel), the comparison of age-standardized rates over that time period is not valid
The choice of standard population could affect the results in these cases
Next steps…
Finish report and sample calculations Add recommendations / best practices Incorporate recommendations into Core
Indicators for Public Health
Standardizing RatesNam Bains
Project Lead, Health System Intelligence Project (HSIP)
