Standardization of rates by Dr. Basil Tumaini, presented during the residency at Muhimbili University of Health and Allied Sciences, Epidemiology class

1. Rate
Standardization
Dr. Basil Tumaini
MMED Resident
Muhimbili University of Health and Allied Sciences

2. Outline
 Definition of terms
 Types of rates
 The role of confounding and the rationale for
standardisation
 Direct and indirect standardisation
 Discussion

3. Rate
 Defined as special form of proportion that includes a
specification of time.
 Most commonly used in epidemiology because it most
clearly expresses probability or risk of diseases or
other events in defined population over a specified
period of time.

4. Calculation Of Rates
Rate = Number of events in a specified time period
Population at risk of these events in a specified time period
X k
k is used to denote the units of population such as per
1,000 or per 100,000 depending on convention and
convenience
9,981 deaths in Arusha in 2000
951,270 total population in Arusha 2000
= 10.49 per 1,000
or 1049 per 100,000

5. Types of Rates
 3 major types:
 Crude rates
 Specific rates (age-specific, e.g., infant
mortality rate)
 Adjusted rates

6. Crude Rates
 Are summary statistics that ignore heterogeneity of
the population under investigation
 Example: Crude mortality rate:
Total deaths in 2003 x 1,000 = T.Z. death rate
Estimated T.Z. pop in 2003*

7. Crude Rates
Number of new cases
in a specified year
---------------------------------- x 1000
Number of individuals
in the population
in the specified year
Number of deaths
in a specified year
-------------------------------- x 1000
Number of individuals
in the population
in the specified year
Crude mortality rate =
Crude incidence rate =

8. Crude Rates
Advantages
• Actual Summary rates
• Easy calculation for international comparisons
Disadvantages
Since population varies in composition (e.g., age)
differences in crude rates difficult to interpret

9. Specific Rates
Stratifies populations into more homogeneous
groups (strata) based on the demographic
characteristic thought to be related to the
outcome of interest (e.g. age-specific, sex-
specific, race-specific)

10. Example
Total # of deaths in 2003 among
persons age less than 1 year x 1,000 = 2003 infant mortality rate
Number of live births during 2003

11. Age-Specific Mortality Rate
• Provides a broader view of mortality for sub-groups
stratified by age
• Numerator and denominator are limited to a specific age
group
• Comparable across populations

12. Age-Specific Mortality Rate
Number of deaths among
persons aged 0-14 in a given
year
Aged 0 –14 = _________________________  100000
years
Total number of persons
aged 0-14 in the same
year

13. Age-Specific Incidence Rate
Number of new cases among
persons aged 0-14 in a given
year
Aged 0 –14 = _________________________  100000
years
Total number of persons
aged 0-14 in the same
year

14. Age specific TB incidence rates / 1000 person /
year, among migrant and native populations
0.00
1.00
2.00
3.00
4.00
0-4 5-14 15-44 45-64 65+
TBIncidenceRate
Age group
Native population TB Incidence rate
/ 1000
Imigran TB Incidence rate / 1000

15. Adjusting (Standardizing) Rates
 Allows comparisons of rates between populations that
differ by variables that can influence the rate (e.g., age)
Two methods:
 Direct method
 Indirect method

16. Adjusted Rates
Advantages
 Summary statement
 Differences in group composition “removed” hence allow
unbiased comparison
Disadvantages
 Fictional rates
 Absolute magnitude dependent on standard population
chosen
 Opposing trends in subgroups masked

17. Rate of Disease
Is a basic measure of disease occurrence because it most
clearly expresses probability or risk of disease1 in a defined
population2 over a period of time3
 Incidence rate
 Mortality rate

18. Crude TB incidence rates in native and immigrant
populations
Male pop.
(thousands)
TB Cases TB Incidence rate
/ 1000
Male pop.
(thousands)
TB Cases TB Incidence rate
/ 1000
Total 21300 19380 0.91 175 148 0.84
Native poulation Immigrant

19. Age specific TB incidence rates in native and immigrant
population
Male pop.
(thousands)
TB Cases TB Incidence rate /
1000
Male pop.
(thousands)
TB Cases TB Incidence rate /
1000
0-4 1917 1150 0.60 28 30 1.07
5-14 2556 186 0.07 33 6 0.18
15-44 6816 1686 0.25 91 44 0.48
45-64 6177 7358 1.19 36 14 0.38
65+ 3834 9000 2.35 32 9 0.28
Total 21300 19380 0.91 220 103 0.47
Age
Native poulation Immigrant

20. Age specific TB incidence rates / 1000 person / year, among
migrant and native populations
0.00
1.00
2.00
3.00
4.00
0-4 5-14 15-44 45-64 65+
Age group
TBIncidenceRate
Native population TB Incidence
rate / 1000
Imigran TB Incidence rate / 1000

21. Why is the discrepancy?
Native population relative age
structure
8%
19%
Immigrant population relative
age structureAge
group
(y)
0-49%
5-14
16%
5%
100%
12%
100%
52%
Total
45-64
15-4432%
29%
18% 65+

22. Problems with Crude Rates
♦ Crude rates may obscure the fact that subgroups of the
population exhibit significant differences in risk
♦ Before making any conclusion, we need to compare age
specific rates for these two populations; all age specific
rates for Immigrants are higher than those for Natives.
♦ Since rates change dramatically with age, differences in
age distributions between populations need to be
accounted for before attempting to compare their risks

23. (Population: native or
immigrant)
Confounding
Tb incidence
(Age structure)
Observed association
True associationUnobserved association

24. Standardization of Rates
• Also referred to as adjusting rates
•Used to reduce distortion in comparisons between crude
rates
•Permits comparison of event occurrence in two or more
study groups which are adjusted for differences in the
variable of interest of the groups

25. So why standardise rates?
 To facilitate comparison between two or more
different populations (geographical areas, different
hospital populations, experimental groups
 That differ in composition e.g. age or sex distribution
 In this case crude rates may be misleading

26. How or why?
 Taking an example of CMR, risk of dying
depends very much on age
 Age specific death rates are high for infants
and very old people and low for middle age
groups*
 So CMR and overall incidence rates will
depend on age composition of the
population concerned.

27. Direct standardization
 Applied when variable-specific rates from
each of the populations under study are
applied to the standard population
 The outcome comprise the variable-adjusted
rates
 Examples: age-sex adjusted mortality,
morbidity or fertility rates

28. Direct Adjustments of Rates
 Requires a standard population, to which the study
population’s variable-specific (e.g. age-specific) rates can be
applied
 Choice of the standard population may affect the
magnitude of the age-adjusted rates, but not the ranking of
the populations

29. Procedure for
direct standardization

30. 1. Define standard population
 both combined,
 bigger of the two,
 national or
 international

31. Community A Community B
STANDARD (both
combined)
Age (year) Population Population Population
Under 1 1,000 5,000 1,000 + 5,000 = 6,000
1 – 14 3,000 20,000
15 – 34 6,000 35,000
35 – 54 13,000 17,000
55 – 64 7,000 8,000
Over 64 20,000 15,000
All ages 50,000 100,000
Defining the standard population

32. 2. Obtain the number of cases or deaths
we would expect in the standard population
 Apply the age (or other category) specific
rates of the index population to the numbers
in each age group of the standard population
 Obtain the number of cases or deaths we
would expect in the standard population if
the index rates applied to the standard
population

33. Community A Community B
Age
(year)
Population Deaths Death Rate
(per 1000)
Population Deaths Death Rate
(per 1000)
Under 1 1,000 15 15/1000 x
1000 =15.0
5,000 100 100/5000 x
1000 = 20.0
1 – 14 3,000 3 3/3000 x
1000=1.0
20,000 35
15 – 34 6,000 6 35,000 35
35 – 54 13,000 52 17,000 85
55 – 64 7,000 105 8,000 160
Over 64 20,000 1,600 15,000 1,350
All ages 50,000 1,781 35.6 100,000 1,740 17.4
Calculating age-specific death rates of
each study population

34. Expected number of cases or deaths in the standard population
Age
(years)
Standard
population
Death rate
in A
(per 1,000)
Expected
deaths at
A’s rate
Death rate
in B
(per 1,000)
Expected
deaths at
B’s rate
Under 1 6,000 15.0 15/1000 x
6,000
= 90
20.0 20/1000 x
6,000 = 120.0
1 – 14 23,000 1.0 0.5
15 – 34 41,000 1.0 1.0
35 – 54 30,000 4.0 5.0
55 – 64 15,000 15.0 20.0
Over 64 35,000 80.0 90.0
Total 150,000 35,6 17.4
Age –
adjusted
death rate
(per 1000)

35. 3. Obtain the total number of
expected cases or deaths
 Add the expected cases or deaths over the
age groups
 The total number of expected cases or
deaths is obtained

36. Total number of expected cases or deaths
Age
(years)
Standard
population
Death rate
in A
(per 1,000)
Expected
deaths at
A’s rate
Death rate
in B
(per 1,000)
Expected
deaths at
B’s rate
Under 1 6,000 15.0 90 20.0 120.0
1 – 14 23,000 1.0 23 0.5 11.5
15 – 34 41,000 1.0 41 1.0 41.0
35 – 54 30,000 4.0 120 5.0 150.0
55 – 64 15,000 15.0 225 20.0 300.0
Over 64 35,000 80.0 2,800 90.0 3,150
Total 150,000 35,6
3,299 17.4
3,772.5*
Age –
adjusted
death rate
(per 1000)

37. 4. Obtain variable-standardized rate
 Divide the total expected cases or deaths by
the total standard population
 A standardised rate is obtained.
 In our example, an age-adjusted death rate is
obtained

38. Age-adjusted death rates
Age
(years)
Standard
population
Death
rate
in A
(per
1,000)
Expected
deaths at
A’s rate
Death rate
in B
(per 1,000)
Expected
deaths at
B’s rate
Under 1 6,000 15.0 90 20.0 120.0
1 – 14 23,000 1.0 23 0.5 11.5
15 – 34 41,000 1.0 41 1.0 41.0
35 – 54 30,000 4.0 120 5.0 150.0
55 – 64 15,000 15.0 225 20.0 300.0
Over 64 35,000 80.0 2,800 90.0 3,150
Total 150,000 35,6 3,299 17.4 3,772.5
Age –
adjusted
death rate
(per 1000)
3299/150000 x
1000 =
22.0
3772.5/150000 x
1000 =
25.0

39. Community A Community B
Age
(year)
Population Deaths Death Rate
(per 1000)
Population Deaths Death Rate
(per 1000)
Under 1 1,000 15 15.0 5,000 100 20.0
1 – 14 3,000 3 1.0 20,000 35 1.0
15 – 34 6,000 6 1.0 35,000 35 1.0
35 – 54 13,000 52 4.0 17,000 85 5.0
55 – 64 7,000 105 15.0 8,000 160 20.0
Over 64 20,000 1,600 80.0 15,000 1,350 90.0
All ages 50,000 1,781 35.6 100,000 1,740 17.4
Unadjusted rates

40.  In studies of morbidity standardized
rate my be: prevalence or incidence
rate
 In studies of mortality it will be
standardized mortality rate.

41. SUMMARY:
Direct standardization
 Requires stratum specific (e.g. age-specific) rates in the
index populations
 The number of cases observed in the study population
should be large enough to give meaningful stratum-specific
rates necessary for direct standardization

42. Indirect standardization of rates
 Variable-specific rates from the standard population
are treated to the study populations to give the
standardized rates
 Involves the use of known specific rates applied to the
actual (observed) population characteristic of interest
being compared to generate expected events

43. Indirect standardization is used when
 Age-specific death rates for the index population are
unknown
 The index populations or number of deaths are too small
for calculating stable age-specific rates
 It has been called ‘the mirror image of the direct
method’

44. Standardized incidence ratio
 Obtained when observed events are divided by the
expected events
 In case of death it will be the standardized mortality
ratio (SMR)
 SMR = Observed events in the index population
Expected events from the standard rates
SMR = Total observed deaths in a population
Expected deaths in a population

45. Procedure for
indirect standardization

46. Define the set of standard
variable-specific rates
Example: a set of standard age specific rates

47. 1. Apply the standard age specific rates to the population in the
corresponding age group of the index population to get the
expected number of cases or deaths in each group
2. Add the expected cases or deaths over the age groups
3. Divide the total observed cases or deaths by the total expected
to get (SMR)
4. The crude rate in the standard population multiplied by the
SMR gives the standardized rate in the index population.

48. Population of Community A by Age
and Standard Death Rates
Age
(years)
Population
in A
Standard
death rate
(per 1,000)
Under 1 1,000 20.0
1 – 14 3,000 0.5
15 – 34 6,000 1.0
35 – 54 13,000 5.0
55 – 64 7,000 20.0
Over 64 20,000 90.0
Total 50,000 17.4
Assume that the age-specific death rates in population B
are the standard

49. Population and Expected Deaths of
Community A by Age
Age
(years)
Population
in A
Standard death
rate
(per 1,000)
Expected
deaths in A at
standard rates
Under 1 1,000 20.0 20.0
1 – 14 3,000 0.5 1.5
15 – 34 6,000 1.0 6.0
35 – 54 13,000 5.0 65.0
55 – 64 7,000 20.0 140.0
Over 64 20,000 90.0 1,800.0
Total 50,000 17.4 2,032.5
SMRA = 1781 / 2032.5 = 0.876
SMRB = 1.0

50. Standardized Mortality Ratio
If the SMR is greater than 1,
more deaths have occurred
than anticipated
If the SMR is less than 1,
fewer deaths have occurred
than anticipated