Measures of Mortality Part 2 2/6/2015

Outline: Standardization Direct adjusted rates Indirect adjusted rates

Standardization A principal role in demography is to compare the mortality between two or more populations. The comparison of crude mortality rates is misleading. 2/6/2015

If the populations being compared differ greatly with respect to , for example, age or sex, that will affect the overall rate of morbidity or mortality. 2/6/2015

For example, age is an important determinant of mortality. An older population will have a higher overall mortality rate than a younger population. As a result, variations in age will complicate any comparison between two or more populations that have different age structures. 2/6/2015

This is achieved by using methods of standardization. One way to overcome this problem is to combine category specific rates into a single summary rate that has been adjusted to take into account its age structure. This is achieved by using methods of standardization. 2/6/2015

Methods of Standardization There are two methods of standardization commonly used: 1- Direct method 2- Indirect method 2/6/2015

Direct Adjusted Rates Requires a standard population, to which the estimated 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 population

How to calculate standardized crude death rate? 1- Select a standard population, whose age distribution will be the standard for comparison. 2- calculate age specific death rate for the two populations (A and B). 2/6/2015

3- Calculate the expected number of deaths that would occur in a year if the standard population experienced the age-specific death rates (ASDR) of populations A and B. 4- Multiply each age group in the standard population by the corresponding ASDR for populations A and B. 2/6/2015

6- To calculate the age-standardized crude rate for each population: 5- Add the columns of the expected deaths for the two populations (A & B) to obtain the total expected deaths in the standard population. 6- To calculate the age-standardized crude rate for each population: Divide the total expected deaths for each population by total standard population. 2/6/2015

Population, Deaths, and Death Rate by Community and by Age Community B Age (year) 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 10 0.5 15 – 34 6,000 6 35,000 35 35 – 54 13,000 52 4.0 17,000 85 5.0 55 – 64 7,000 105 8,000 160 Over 64 1,600 80.0 15,000 1,350 90.0 All ages 50,000 1,781 35.6 100,000 1,740 17.4 Death Rate (per 1000) 2/6/2015

Age – adjusted death rate (per 1000) (years) Standard population Death rate in A (per 1,000) Expected deaths at A’s rate in B 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 41 41.0 35 – 54 30,000 4.0 120 5.0 150.0 55 – 64 15,000 225 300.0 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) 22.0 25.0 2/6/2015

x 1000 Calculation of standardized death rate Total standard population = 150,000 Expected deaths for pop A = 3299 Standardized death rate for pop A = Expected deaths pop A x 1000 Total standard population 2/6/2015

standardized death rate for pop A: 3299 x 1000 = 21.99 per 1000 150,000 The result indicates that pop A crude death rate would be 21.99/1000 if it has the same age structure as the standard population which far less than the observed crude death rate 35.6/1000. 2/6/2015

standardized death rate for pop B: Total standard population = 150,000 Expected deaths for pop B = 3,772.5 2/6/2015

Standardized death rate for pop B = Expected deaths pop A x 1000 Total standard population 3,772.5 x 1000 = 25.15 per 1000 150,000 2/6/2015

The result indicates that pop B crude death rate would be 25 The result indicates that pop B crude death rate would be 25.15/1000 if it has the same age structure as the standard population which far more than the observed crude death rate 17.4/1000. 2/6/2015

The result indicates that pop A crude death rate would be 21 The result indicates that pop A crude death rate would be 21.99/1000 if it has the same age structure as the standard population which far less than the observed crude death rate 35.6/1000. 2/6/2015

This ratio is called the Comparative Mortality Ratio (CMR). We can calculate: The ratio of the directly standardized rates to provide a single summary measure of the difference in mortality between the two populations. This ratio is called the Comparative Mortality Ratio (CMR). 2/6/2015

Comparative Mortality Ratio (CMR) calculated by dividing the overall age adjusted rate in country B by that of A. In our example: Comparative Mortality Ratio (CMR) = 25.15/21.99 = 1.14 2/6/2015

This CMR is interpreted as: after controlling for the affects of age, the mortality in Country B is 14% higher than in country A. 2/6/2015

Example 2: Table 2 presents crude mortality data for two populations (countries A and B). The overall crude mortality rate is higher for country A (10.5 deaths per 1,000 person years) 2/6/2015

compared with country B (7 deaths per 1,000 person years). Notice the ASDRs rates being higher among all age-groups in country B. For example, 18% of the population in country A are aged over 60 years compared with 6% in country B. 2/6/2015

Table 2. Crude mortality rates stratified by age for two populations (country a, B). Country B Age group # deaths/ 1000 Pop (M) in millions Death rate # deaths Pop Death rate/ 0 - 29 7,000 6 1.2 6,300 1,500,000 4.2 30 - 59 20,000 5.5 3.6 3,000 550,000 60+ 120,000 2.5 48 6,000 50 Total 147,000 14 10.5 15,300 2,170,000 7

Country A has a much older population than country B. The reason for the difference between the crude mortality rates between country A and country B is that these two populations have markedly different age-structures. Country A has a much older population than country B. 2/6/2015

Table 3. Standard population Age group Pop 0 - 29 100,000 30 - 59 65,000 60+ 20,000 Total 185,000 2/6/2015

Age (years) Standard population Death rate in A (per 1,000) Expected deaths at A’s rate in B B’s rate 0 - 29 100,000 1.2 120 4.2 420 30 - 59 65,000 3.6 234 5.5 357.5 60+ 20,000 48 960 50 1,000 Total 185,000 10.5 1,314 7 1,777.5 2/6/2015

x 1000 Calculation of standardized death rate Total standard population = 185,000 Expected deaths for pop A = 1314 Standardized death rate for pop A = Expected deaths pop A x 1000 Total standard population 2/6/2015

1314 x 1000 = 7.1 per 1000 185,000 standardized death rate for pop A: The result indicates that pop A crude death rate would be 7.1/1000 if it has the same age structure as the standard population which is less than the observed crude death rate 10.5/1000. 2/6/2015

x 1000 Calculation of standardized death rate Total standard population = 185,000 Expected deaths for pop A = 1777.5 Standardized death rate for pop B = Expected deaths pop A x 1000 Total standard population 2/6/2015

standardized death rate for pop B: 1777.5 x 1000 = 9.6 per 1000 185,000 The result indicates that pop A crude death rate would be 9.6/1000 if it has the same age structure as the standard population which is more than the observed crude death rate 7/1000. 2/6/2015

We can calculate the Comparative Mortality Ratio (CMR) as: = 9.6/7.1 = 1.35 2/6/2015

CMR is interpreted as: After controlling for the affects of age, the mortality in Country B is 35% higher than in country A. 2/6/2015

Indirect Adjustment of Rates Used if age-specific rates cannot be estimated.

Indirect Adjustment of Rates Based on applying the age-specific rates of the standard population to the population of interest to determine the number of “expected” deaths. Steps in calculation: 1- Choose standard population and list its age-specific death rate. 2/6/2015

Suppose we selected population B as the standard population. List ASDR for population B. List the age distribution of the pop A in the next column. Calculate expected deaths for pop A by multiplying each age group by the corresponding ASDR for the standard population. 2/6/2015

Sum the column of the expected deaths. This total shows the number of deaths that would occur if population A experienced the ASDR of pop B. Calculate the standardized mortality ratio as: 2/6/2015

____________________ Standardized Mortality Ratio(SMR)= Total observed deaths In population (A) ____________________ Total expected deaths in a population (A) 2/6/2015

Standard death rate pop B Expected deaths in A at standard rates Age (years) Standard death rate pop B (per 1,000) Total population A Expected deaths in A at standard rates Observed Deaths A Under 1 20.0 1,000 15 1 – 14 0.5 3,000 1.5 3 15 – 34 1.0 6,000 6.0 6 35 – 54 5.0 13,000 65.0 52 55 – 64 7,000 140.0 105 Over 64 90.0 20,000 1,800.0 1,600 Total 17.4 50,000 2,032.5 1,781 2/6/2015

SMRA = 1781 / 2032.5 = 0.876 The result shows that the observed deaths in A were 12% lower than they would have been if A ASDR were the same as those of pop B. 2/6/2015

Standardized Mortality Ratio The ratio is exactly 1 if the observed and expected deaths are the same. If the SMR is greater than 1, more deaths have occurred than anticipated. If SMR is less than 1, fewer deaths have occurred than anticipated. 2/6/2015

Example 2: Table 2 presents crude mortality data for two populations (countries A and B). The overall crude mortality rate is higher for country A (10.5 deaths per 1,000 person years) 2/6/2015

compared with country B (7 deaths per 1,000 person years). Notice the ASDRs rates being higher among all age-groups in country B. For example, 18% of the population in country A are aged over 60 years compared with 6% in country B. 2/6/2015

Table 2. Crude mortality rates stratified by age for two populations (country a, B). Country B Age group # deaths/ 1000 Pop (M) Death rate # deaths Pop Death rate/ 0 - 29 7,000 6 1.2 6,300 1,500,000 4.2 30 - 59 20,000 5.5 3.6 3,000 550,000 60+ 120,000 2.5 48 6,000 50 Total 147,000 14 10.5 15,300 2,170,000 7

Country A has a much older population than country B. The reason for the difference between the crude mortality rates between country A and country B is that these two populations have markedly different age-structures. Country A has a much older population than country B. 2/6/2015

Table 3. Standard population Age group Pop 0 - 29 100,000 30 - 59 65,000 60+ 20,000 Total 185,000 2/6/2015

Total expected deaths (E) 9,540 Table 3. Number of expected deaths if the population B had the same age-specific mortality rates as Country A. Country B Expected deaths 0 - 29 0.0012 x 1,500,000 = 1,800 30 - 59 0.0036 x 550,000 = 1,980 60+ 0.048 x 120,000 = 5,760 Total expected deaths (E) 9,540 Total observed deaths (O) 15,300 Standardized Mortality Ratio (O/E) x 100 160 2/6/2015

An overall summary measure can then be calculated, that is, the standardized mortality ratio (SMR), which is the ratio of the observed number of deaths to the expected number of deaths. 2/6/2015

SMR = Observed number of deaths (O) X 100% Expected number of deaths (E) SMR = 160 = 1.6 X 100 = 160 100 This means: The number of observed deaths in Country B is 60% higher than the number we would expect if Country B had the same mortality experience as Country A. 2/6/2015