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

Quantitative Data Analysis II.

UK FHSHistorical sociology

(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.

• 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]

0,000

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

15—19 20—29 30—39 40—49 50—59 60—69 70—79 80+

1949/1950

1960/1961

Direct standardization example: Suicidal rates of men in Czechoslovakia 1949/1950 and 1960/1961

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.

Comparing 1960‘scrude and standardized rate ratio,

the difference is 2.537

Source: [Lamser, Růžička 1970: 201-202]

Crude rates: 1950‘s 1960‘s Standardized rateGlobal rates:

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 populationse.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*

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 70-74 2.00 3.00 2.21 75-79 1.00 2.00 1.52 80-84 0.50 1.00 0.91 85+ * 0.50 1.00 0.63 Total 100.00 100.00 100.00

Source: [Ahmad et al. 2001: 10] * 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 **).

Age group

WHO World Standard**

85-89 0.44

90-94 0.15

95-99 0.04

100+ 0.005

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.

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 standardizationIt 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/MPH-Modules/EP/EP713_StandardizedRates/index.html