UK FHS
Historical sociology
(2014+)
Quantitative Data Analysis II.
Direct standardization of
incidence ratios
Crude rates adjusted to standardized rates
of a phenomenon
Jiří Šafr
jiri.safr(AT)seznam.cz
updated 30/12/2014
Standardization of incidence ratios
(intensity indicators)
• Many social phenomenon change depending on
the structural conditions (age, gender,
environment, institutional conditions, etc.).
• The calculated intensity indicator (ratio) is
therefore not only the degree of intensity of the
phenomenon, but also reflects the structure of
the file that is its bearer.
standardization
Purpose of standardization of ratios
• Comparing rates of a specific phenomenon (mortality,
self-destructiveness, natality, divorce rate, employment
rate etc.) in two or more different areas / populations
(defined by period of time or geographically).
• Simple comparison between crude rates might be
misleading because crude rates are not very informative
about the phenomenon since there is a possibility of
different frequency distributions in unlike populations in
focus.
• → Standardization for the characteristic(s) responsible
for the differences in comparison is necessary =
removing the distorting effect of other confounding
factors, such as age. → standardized rates adjusted to take into
account differences in these confounding factors to provide a less distorted comparison.
• This method has a long tradition in demographic,
epidemiologic and public health research.
Standardization of intensity
indicators
• If we want to juxtapose intensity indicators,
whose size is related to a specific structural
arrangement, we must "cleanse" the impact of
this structural factor.
• We do this by standardizing
- direct
- indirect
E.g. eliminate the effect of age structure
→ comparisons between different populations
Direct standardization
• DSR is simply a weighted proportion (or mean) of event rate for a
study population, using the group/stratum sizes of a reference
population as the weighting scheme.
• Standardized (= adjusted) rate is summary index measure only
for the purpose of comparison because its extent has no intrinsic
value.
• The choice of a reference / standard population is essential. It
must be related to the population under study naturally.
• We use as the standard the population structure, which we consider
"normal" variation of the variable that affects the intensity of the
examined phenomenon.
• On this standard structure we apply individual partial indicators of
intensity, i.e. the indicators calculated for those groups that
correspond to the sorting standard population.
• The resulting standardized indicator represents the overall
intensity of the investigated phenomenon, which would be
reached in the population, if the structural arrangement would
conform to the standard structure.
Example of direct standardization: Suicidal rates of
men in Czechoslovakia in 1950‘s and 1960‘s
• Specific crude mortality rates (per 100 000 men) for the
period 1949/1950 and 1960/1961 show that in all age
categories, except the oldest, men's suicides increased.
160,000
140,000
120,000
100,000
1949/1950
80,000
1960/1961
60,000
40,000
20,000
0,000
15—19 20—29 30—39 40—49 50—59 60—69 70—79
80+
• However, we can also see that suicide rate increases with age
in general (in both periods of time it is the highest among the oldest groups).
• And moreover the Czech population grew older between 1950
to 1960.
→ We need to standardize suicidal rate – adjust for age
structure changes
Source: [Lamser, Růžička 1970: 201-202]
Direct standardization example: Suicidal rates of men in
Czechoslovakia 1949/1950 and 1960/1961
Age
15—19
20—29
30—39
40—49
50—59
60—69
70—79
80+
Total
Standard population
(age structure of male
population in CSSR 1. 3.
1950)
0,0974
0,3039
0,1582
0,1872
0,1247
0,0785
0,041
0,009
1,000
Mortality rate for suicide
Standardized mortality
(annual average)
rate for suicide
age specific crude rates
1949/1950
1960/1961 1949/1950 1960/1961
deaths per 100,000 men of that age
12,509
18,691
27,703
39,600
44,924
52,092
74,741
143,244
32,833
Global rates: Crude rates: 1950‘s
13,059
26,483
32,494
48,049
55,089
60,706
80,358
124,814
42,046
1960‘s
The standard is the age structure in 1950.
For the first row: 0,0974 * 13,059 = 1,272 (and so on)
Rows add up.
We compare crude with standardized (adjusted) rate ratio.
1,218
5,680
4,383
7,413
5,602
4,089
3,064
1,289
32,738
1,272
8,048
5,141
8,995
6,870
4,765
3,295
1,123
39,509
Standardized rate
Comparing 1960‘s
crude and standardized rate ratio,
the difference is 2.537
Source: [Lamser, Růžička 1970: 201-202]
Example of direct standardization (suicide rate):
procedure and interpretation
Steps of direct standardization:
• As the standard we use age structure from 1950's (ratio Px)
However, it could be the other period if we had relative frequencies for age groups in 1960‘s or arbitrary external population (the Standard).
• Multiplying each specific crude mortality rates (qx) in 1960‘s (column 2) by
corresponding specific relative frequencies of age groups (Px) for each
cohort from 1950’s (column 3) brings ratios of suicides per 100,000 men (column
5 and 6 of the table).
• These numbers refer to the population which will have age composition
of the standard P (here 1950’s).
• We count up all specific rates to get the total – global standardised rate
for 1960‘s.
Both rates are now comparable: crude rate for 1949/1950 with standardised
for 1960/1961. The difference between suicidality of Czechoslovak men in
the period 1950‘s to 1960‘s is in fact not so great as it seems from the
original crude (non-standardized) rates.
• In the 1960/1961 period, the mortality rate for suicides was 42.046 (per 100
000 men) → crude rate ratio, however with no changes in the age
structure only 39.509 → standardised (adjusted) rate ratio.
• The difference 2.537 (= 42.046 - 39.509) is caused by the change of the age
structure, i.e. increasing the proportion of older men.
(Please note, in the book on p. 202, there is quoted erroneously 3.537)
Source: [Lamser, Růžička 1970: 201-202]
Choice of standard
• When we choose the standard, we make sure that the chosen
standard structure or standard intensity expresses a certain
state, which we consider under the given conditions "normal".
• E.g. factor affecting the rate (intensity of the phenomenon) is age
• We choose as the standard superior structure for both
compared populations
e.g. for comparison between districts → structure of the region;
between regions → nationwide structure, etc.
• When we do not have the data (i.e. specific ratios), we use the sum
or average of the structural configuration of the two (or more)
populations being compared.
• It is not appropriate if one of the compared populations is much
larger than the other (e.g. a district with 70 thousand residents and
county-region with 1.5 mil. inhabitants).
Standardization using the sum or average would be reflected in
practically the same result as if we had chosen as the standard the
larger of the two populations.
• In international comparisons → Hypothetical age structure (as a
combination of actual age structures of the populations; provided by
World Health Organization, WHO)
[Lamser, Růžička 1970: 201-202]
International Standard Population
Distribution (percent)
Age
group
Segi (“world”)
standard
Scandinavian
(“European”) standard
WHO World
Standard*
New WHO World
Population Standard
[Ahmad et al. 2001] is
especially defined to reflect
the average age structure of
the world’s population
expected over the next
generation, from the year
2000 to 2025.
0-4
12.00
8.00
8.86
5-9
10.00
7.00
8.69
10-14
9.00
7.00
8.60
15-19
9.00
7.00
8.47
20-24
8.00
7.00
8.22
25-29
8.00
7.00
7.93
30-34
6.00
7.00
7.61
35-39
6.00
7.00
7.15
40-44
6.00
7.00
6.59
45-49
6.00
7.00
6.04
50-54
5.00
7.00
5.37
55-59
4.00
6.00
4.55
60-64
4.00
5.00
3.72
65-69
3.00
4.00
2.96
Age
group
70-74
2.00
3.00
2.21
85-89
0.44
75-79
1.00
2.00
1.52
90-94
0.15
80-84
0.50
1.00
0.91
95-99
0.04
85+ *
0.50
1.00
0.63
100+
0.005
Total
100.00
100.00
100.00
* For purposes of comparison, the new WHO Standard age group 85+ is an aggregate of the age
groups 85-89, 90-94, 95-99 and 100+ (for these groups see **).
WHO World
Standard**
Source: [Ahmad et al. 2001: 10]
Advantages and disadvantages of
direct standardization
Advantages:
• Direct standardization is simple and easy to understand
its outcome.
Disadvantages:
• We need to know the actual composition of the
population but the evidence we need is often difficult to
obtain. → specific rates of phenomenon under the study
(rates sorted by the structural factor).
• There is very strong effect of random fluctuations of the
indicator.
• Such random fluctuations occur very often in small
samples. Thereafter their seriousness increases when
such intensity is applied within selected standard
population.
Indirect standardization
It is useful when the specific rates (e.g. by age) for the population
being studied are not known however the total number of events is
known. So only the data on total number of observed events is
necessary. The specific numbers of event cases (e.g. age) are not
required. It is suitable when populations are small (so the number
of events are also small).
We will omit it; see e.g. [Lamser, Růžička 1970: 202-205]
But we will pay a great attention to application of direct
standardization to contingency table
(i.e. elaboration where relation between two variables is
adjusted for the effect of third variable); see presentation
Direct standardization in contingency table at
http://metodykv.wz.cz/QDA2_crosstab_standardiz.ppt
References
• Ahmad B. O., C. Boschi-Pinto, A. D. Lopez, Ch. J. L. Murray, L. Lozano,
M. Inoue. 2001. Age Standardization Of Rates: A New WHO Standard.
GPE Discussion Paper Series: No. 31. EIP/GPE/EBD, World Health
Organization. Available at http://www.who.int/healthinfo/paper31.pdf
• Lamser, V. , L. Růžička. 1970. Základy statistiky pro sociology. Praha
: Svoboda.
• Rosenberg, Morris. 1962. „Test Factor Standardization as a Method of
Interpretation“. Social Forces 41 (1): 53-61.
• Curtin L. R., Klein R. J. 1995. „Direct Standardization (Age-Adjusted
Death Rates)“. Centres for Disease Control and Prevention: Healthy
People 2000: Statistical Notes 1995 (6). Available at
www.cdc.gov/nchs/data/statnt/statnt06rv.pdf .
• LaMorte, W. W. 2014. Standardized Rates of Disease. Boston
University School of Public Health. Available at
http://sphweb.bumc.bu.edu/otlt/MPHModules/EP/EP713_StandardizedRates/index.html