# Lesson 2: Causes of Death

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## 2.1 Age-Specific Death Rate (ASDR)

Formula 1 (1)

Example

A hypothetical country reported the following data:

• Number of deaths in the age group 50-55 in 1998 = 1513
• Estimated 1998 mid-year population in the age group 50-55 = 146,605

The age-specific death rate for the age group 50-55 in 1998 is calculated using formula (1) above as:

#### Notation

In this lesson we will denote the age-specific death rate as:

= age-specific death rate for the age group (x,  x + n)

Note the subscripts in the notation: x stands for the beginning age of the age group and n stands for the length of the age interval.

Using this notation, the age-specific death rate for the age group 50-55 is

#### Effect of the Multiplier

Note that the age-specific death rate in formula (1) has multiplier 1000. The resulting rate is interpreted as number of deaths in a year per 1000 people in the age group.

In the computation of life table quantities, the rates are usually expressed as deaths in a year per person in the age group. This means that the rate will not be multiplied by 1000 as in formula (1).

## 2.2 Age-Cause-Specific Death Rate (ACSDRate)

Formula (2)

 Example In the hypothetical country considered in the previous example, the number of deaths in the age group 50-55 due to cardiovascular disease in 1998 is reported to be 345. Using formula (2), one can calculate the age-cause-specific death rate for cardiovascular disease for the age group as:

Notation for age-cause-specific death rate

As in age-specific death rate, use the following notation:

= age-cause-specific death rate in the age interval (x, x + n)
due to a specific cause

Note that a specific cause is denoted as  .

## 2.3 Age-Cause-Specific Death Ratio (ACSDRatio)

Formula (3)

 Example In the hypothetical country referred to in the two previous examples, there were 1513 deaths in the age group 50-55 in 1998. Among these deaths, 345 were due to cardiovascular disease. The age-cause-specific death ratio for cardiovascular deaths in the age group 50-55 is calculated using formula (3) as: This ratio indicates that in 1998 for the hypothetical country considered, 22.8% of all deaths in the age group 50-55 were due to cardiovascular disease.

Notation for age-cause-specific death ratio:

cause-specific death ratio for disease   in the age interval (x, x + n)

#### Exercise 3

Question 1

If last year a region in your country had an age-specific death rate of 4.4 per 1000 people in the age group 20-24, and the mid-year population for that group was 50,000, how many deaths occurred in that group last year?

1. 440
2. 220
3. 50
4. 500

Question 2

If half of the deaths in Question 1 were due to a deadly epidemic, what is the age-cause-specific death rate (ACSDRate) for that epidemic?

1. 5.0
2. 1.1
3. 50.0
4. 2.2

Question 3

If 11 of the deaths in Question 1 were due to dysentery, what is the age-cause-specific death ratio (ACSDRatio) for dysentery?

1. 5.0%
2. 15.0%
3. 2.2%
4. 11.0%

2.4 Relationships among ASDR, ACSDRate, and ACSDRatio

#### Age-Specific Death Rate and Age-Cause-Specific Death Rate

Recall that total number of deaths in an age group is the sum of deaths due to each cause. Suppose there are rcauses of death operating in a population. Then in a specific age group:

Total deaths in the age interval = deaths due to cause 1 + deaths due to cause 2 +...+ deaths due to cause r.

When we divide both sides of the above equation by the mid-year population of the age group we get:

The equation above shows that the age-specific death rate is equal to the sum of the age-cause-specific death rates in that age interval.

In the notations given above, this relation can be expressed as:

#### Age-Specific Death Rate, Age-Cause-Specific Death Rate, and Age-Cause-Specific Death Ratio

Remember that the age-cause-specific death ratio is defined as the percentage of deaths due to a particular cause among all deaths in the age interval. This ratio can also be expressed as the ratio of an age-cause-specific death rate and the age-specific death rate:

Because both age-specific death rate and age-cause-specific death rate have mid-year population as the denominator, the ratio on the right-hand side reduces to the ratio of the age-cause-specific death rate to total deaths in the age interval.

When published reports provide the age-specific death rate and the age-cause-specific death rate, you can use those numbers to obtain the age-cause-specific death ratio.

In the notations introduced above:

Age-cause-specific death ratio

Also note that the age-cause-specific death rate can be obtained from the age-specific death rate by multiplying the age-specific death rate by the corresponding age-cause-specific death ratio:

#### Cautionary Note

The advantage of the age-cause-specific death ratio is that it does not require knowledge of the mid-year population in computing it. Therefore, it is often seen as a measure of relative significance of causes of death across subgroups of a population. The age-cause-specific death rate is considered a measure of occurrence of death and is used to compute relative risk of death from a specific cause .

However, one needs to be careful in interpreting the age-cause-specific death ratio and age-cause-specific death rate. The following hypothetical example for cancer mortality will illustrate this point. In a hypothetical country, age-specific death rates and age-cause-specific death ratios for cancer death for the age groups 55-64 and 65-74 in a given year are as follows:

Age Group 55-64 65-74 Table 2.4.1: Hypothetical Rates vs. Ratios Cause-Specific DeathRate per 100,000 people (Cancer) 448.4 871.6 Cause-Specific Death Ratio (Cancer) 38.0 33.0

The data show that while the incidence of death from cancer is higher in the 65-74 age group than in the 55-64 age group, the ratio of cancer deaths relative to other cause-specific death ratios is smaller in that group. These data show that the cause-specific death rate is not always a good indicator of relative risk and in order to identify causes of death in specific subgroups as priorities for research or prevention, it is necessary to examine both the ratio and rate of occurrence.

#### Exercise 4

This is an open-ended question to stimulate thinking. Write down your own answer before you look at the answer key.

Assume you are presenting your research to government officials to help them determine the number one reason a child might not survive its first year of life. In this lesson, you have learned about three different summary measures describing causes of death. Which of these measures would you focus on in your presentation and why?

## 2.5 An Example with Real Data

In this section we look at data from Costa Rican males in 1960 and learn to compute age-cause-specific death rates and age-cause-specific death ratios.

The basic data needed to compute the age-cause-specific death rates and age-cause-specific death ratios are the mid-year population and the number of deaths by cause in specific age groups.

The data presented below are also available to download as a single zip file so students may examine and work with the data in their own spreadsheet software.

Age Interval Mid-YearPopulation Deaths Diarrhea Cancer CVD* Other Causes Table 2.5.1: Deaths by Cause and Mid-Year Population: 1960 Costa Rican Males <1 year 29,780 2,235 538 2 17 1,678 1-4 93,280 654 140 13 8 493 5-9 83,036 142 10 8 0 124 10-14 68,192 87 1 5 4 77 15-19 55,985 72 2 4 4 62 20-24 48188 87 0 6 7 74 25-29 40,996 67 0 7 4 56 30-34 35,390 70 2 4 6 58 35-39 28,499 86 2 10 10 64 40-44 23,319 103 1 23 13 66 45-49 21,074 136 0 20 28 88 50-54 17,231 159 3 46 33 77 55-59 13,098 176 2 55 44 75 60-64 9,858 233 4 74 64 91 65-69 6,772 246 3 62 78 103 70-74 4,747 246 5 47 95 99 75-79 2,878 220 3 44 69 104 80-84 1,250 169 5 23 62 79 85+ 457 154 5 13 55 81 *CVD = Cardiovascular Disease Source: Preston, et al. (1972)

#### Age-Cause-Specific Death Rates

Data in Table 2.5.1 can be used to compute the age-cause-specific death rates by simply dividing the number of deaths by cause in a particular age group by the corresponding mid-year population and multiplying by 1000. The resulting calculations are given in Table 2.5.2.

Age Interval All Causes Diarrhea Cancer CVD Other Causes Table 2.5.2: Age-Cause-Specific Death Rates: 1960 Costa Rican Males <1 year 75.05037 18.06582 0.06716 0.57085 56.34654 1-4 7.01115 1.50086 0.13937 0.08576 5.28516 5-9 1.71010 0.12043 0.09634 0.00000 1.49333 10-14 1.27581 0.01466 0.07332 0.05866 1.12916 15-19 1.28606 0.03572 0.07145 0.07145 1.10744 20-24 1.80543 0.00000 0.12451 0.14526 1.53565 25-29 1.63431 0.00000 0.17075 0.09757 1.36599 30-34 1.97796 0.05651 0.11303 0.16954 1.63888 35-39 3.01765 0.07018 0.35089 0.35089 2.24569 40-44 4.41700 0.04288 0.98632 0.55749 2.83031 45-49 6.45345 0.00000 0.94904 1.32865 4.17576 50-54 9.22755 0.17410 2.66961 1.91515 4.46869 55-59 13.43717 0.15270 4.19911 3.35929 5.72607 60-64 23.63563 0.40576 7.50659 6.49219 9.23108 65-69 36.32605 0.44300 9.15535 11.51802 15.20969 70-74 51.82220 1.05330 9.90099 20.01264 20.85528 75-79 76.44197 1.04239 15.28839 23.97498 36.13621 80-84 135.20000 4.00000 18.40000 49.60000 63.20000 85+ 336.98031 10.94092 28.44639 120.35011 177.24289

Figure 2.5.1 below shows the age patterns of mortality in the population. Note that it is a U-shaped (or J-shaped) curve with high infant mortality and high death rates at older ages.

Figure 2.5.1: Mortality Pattern across the Life Span (All Causes): 1960 Costa Rican Males

Figures 2.5.2 - 2.5.4 below show the age pattern of mortality for various causes in the population. Note the difference in the shape of the curves. The curves for cancer and CVD mortality show a steady increase with age. The diarrhea mortality is very high among the youngest and oldest groups.

Figure 2.5.2: Cancer Mortality Pattern across the Life Span: 1960 Costa Rican Males

Figure 2.5.3: Diarrhea Mortality Pattern across the Life Span: 1960 Costa Rican Males

Figure 2.5.4: CVD Mortality Pattern across the Life Span: 1960 Costa Rican Males

#### Age-Cause-Specific Death Ratios

We use the data in Table 2.5.1 to compute the age-specific death ratios. They are computed by dividing the number of deaths due to a specific cause by the total deaths in the same interval (and multiplying by 100). Table 2.5.3 shows the computed age-cause-specific death ratios for 1960 Costa Rican males.

Age Interval Diarrhea Cancer CVD Other Causes Table 2.5.3: Age-Cause-Specific Death Ratios: 1960 Costa Rican Males <1 year 24.07159 0.08949 0.76063 75.07830 1-4 21.40673 1.98777 1.22324 75.38226 5-9 7.04225 5.63380 0.00000 87.32394 10-14 1.14943 5.74713 4.59770 88.50575 15-19 2.77778 5.55556 5.55556 86.11111 20-24 0.00000 6.89655 8.04598 85.05747 25-29 0.00000 10.44776 5.97015 83.58209 30-34 2.85714 5.71429 8.57143 82.85714 35-39 2.32558 11.62791 11.62791 74.41860 40-44 0.97087 22.33010 12.62136 64.07767 45-49 0.00000 14.70588 20.58824 64.70588 50-54 1.88679 28.93082 20.75472 48.42767 55-59 1.13636 31.25000 25.00000 42.61364 60-64 1.71674 31.75966 27.46781 39.05579 65-69 1.21951 25.20325 31.70732 41.86992 70-74 2.03252 19.10569 38.61789 40.24390 75-79 1.36364 20.00000 31.36364 47.27273 80-84 2.95858 13.60947 36.68639 46.74556 85+ 3.24675 8.44156 35.71429 52.59740

Table 2.5.3 shows the relative significance of various diseases at specific age intervals. It clearly shows that among children, diarrhea is the leading cause of death, while among the elderly, deaths by cardiovascular disease are most common.

#### Exercise 5

Note to students: This exercise is lengthy but essential to the mastery of these concepts. Work through these examples on your own. Just reading this material will not be enough. Good luck!

Use the data on "Age-Specific Deaths by Cause for 1960 Costa Rican Females."

1. Compute age-specific death rates (overall and for each cause).
2. Compute age-specific death ratios (for each cause).
3. Draw graphs of age-specific death rates and age-cause-specific death rates.
4. Describe the age patterns of mortality (overall and for each cause).
5. Describe the relative significance of the three causes of death in two age intervals: 1-4 and 85+.

Age Interval Mid-YearPopulation Deaths Diarrhea Cancer CVD Table 2.5.4, Exercise 5: Age-Specific Deaths by Cause: 1960 Costa Rican Females <1 year 28661 1834 476 5 11 1-4 90412 695 158 6 12 5-9 80892 136 12 3 8 10-14 66080 63 33 3 5 15-19 54702 46 11 1 6 20-24 48077 61 10 11 7 25-29 43331 76 0 6 11 30-34 37918 86 1 10 16 35-39 29771 82 0 18 12 40-44 23843 70 2 17 11 45-49 21554 100 0 36 24 50-54 17493 122 2 42 28 55-59 13065 137 1 47 45 60-64 9906 186 2 55 64 65-69 6848 197 3 49 67 70-74 4742 219 5 46 66 75-79 2819 191 5 27 61 80-84 1242 165 4 23 53 85+ 806 255 4 1 90

After you have completed the exercise, compare your calculations, graphs, and descriptions to the answer key below.

### Exercise 3

Question 1

If last year a region in your country had an age-specific death rate of 4.4 per 1000 people in the age group 20-24, and the mid-year population for that group was 50,000, how many deaths occurred in that group last year?

B. 220, calculated as follows (solving for X, the number of deaths):

 ASDR(20-24) = (X / 50,000) * 1000 = 4.4 = 1000X / 50,000 = 4.4 = X / 50 = 4.4 = X = 4.4 * 50 = X = 220

### Exercise 3

Question 2

If half of the deaths in Question 1 were due to a deadly epidemic, what is the age-cause-specific death rate (ACSDRate) for that epidemic?

B. 2.2. Just as 220 deaths produced an ASDR(20-24) of 4.4, then the 110 deaths due to the epidemic yield an age-cause-specific death rate of 2.2 (half of 4.4).

### Exercise 3

Question 3

If 11 of the deaths in Question 1 were due to dysentery, what is the age-cause-specific death ratio (ACSDRatio) for dysentery?

A. 5.0%. The age-cause-specific death ratio is the percentage of all the deaths were due to a particular cause. If 11 out of the 220 deaths were due to dysentery, then 5% (11/220 = .05) of the deaths were due to dysentery.

### Exercise 4

Assume you are presenting your research to government officials to help them determine the number one reason a child might not survive its first year of life. In this lesson, you have learned about three different summary measures describing causes of death. Which of these measures would you focus on in your presentation and why?

Answer: The age-cause-specific death rate (ACSDRate) for all the major causes would reveal which cause is producing the most deaths; this is an acceptable answer.

The best answer would be the age-cause-specific death ratios (ACSDRatios) for all the major causes. Not only would ACSDRatios demonstrate (in easy-to-understand percentages) which cause is number one, they would also show the significance of the number one cause in relation to other causes.

The age-specific death rate (ASDR) for age group 0-1 measures overall infant mortality from all causes. ASDR would not distinguish among causes of death; therefore it is not a correct answer.

### Exercise 5

1. Compute age-specific death rates (overall and for each cause).
2. Compute age-specific death ratios (for each cause).
3. Draw graphs of age-specific death rates and age-cause-specific death rates.
4. Describe the age patterns of mortality (overall and for each cause)
5. Describe the relative significance of the three causes of death in two age intervals: 1-4 and 85+.

1. Compute age-specific death rates (overall and for each cause).

Age Interval All Causes Diarrhea Cancer CVD Exercise 5, Answer Key: Age-Cause-Specific Death Rates: 1960 Costa Rican Females <1 year 63.98939 16.60793 0.17445 0.38380 1-4 7.68703 1.74756 0.06636 0.13273 5-9 1.68125 0.14835 0.03709 0.09890 10-14 0.95339 0.49939 0.04540 0.07567 15-19 0.84092 0.20109 0.01828 0.10969 20-24 1.26880 0.20800 0.22880 0.14560 25-29 1.75394 0.00000 0.13847 0.25386 30-34 2.26805 0.02637 0.26373 0.42196 35-39 2.75436 0.00000 0.60462 0.40308 40-44 2.93587 0.08388 0.71300 0.46135 45-49 4.63951 0.00000 1.67022 1.11348 50-54 6.97422 0.11433 2.40096 1.60064 55-59 10.48603 0.07654 3.59740 3.44432 60-64 18.77650 0.20190 5.55219 6.46073 65-69 28.76752 0.43808 7.15537 9.78388 70-74 46.18305 1.05441 9.70055 13.91818 75-79 67.75452 1.77368 9.57786 21.63888 80-84 132.85024 3.22061 18.51852 42.67311 85+ 316.37717 4.96278 1.24069 111.66253

2. Compute age-specific death ratios (for each cause).

Age Interval Diarrhea Cancer CVD All Other Causes Exercise 5, Answer Key: Age-Cause-Specific Death Ratios: 1960 Costa Rican Females <1 year 25.95420 0.27263 0.59978 73.17339 1-4 22.73381 0.86331 1.72662 74.67626 5-9 8.82353 2.20588 5.88235 83.08824 10-14 52.38095 4.76190 7.93651 34.92063 15-19 23.91304 2.17391 13.04348 60.86957 20-24 16.39344 18.03279 11.47541 54.09836 25-29 0.00000 7.89474 14.47368 77.63158 30-34 1.16279 11.62791 18.60465 68.60465 35-39 0.00000 21.95122 14.63415 63.41463 40-44 2.85714 24.28571 15.71429 57.14286 45-49 0.00000 36.00000 24.00000 40.00000 50-54 1.63934 34.42623 22.95082 40.98361 55-59 0.72993 34.30657 32.84672 32.11679 60-64 1.07527 29.56989 34.40860 34.94624 65-69 1.52284 24.87310 34.01015 39.59391 70-74 2.28311 21.00457 30.13699 46.57534 75-79 2.61780 14.13613 31.93717 51.30890 80-84 2.42424 13.93939 32.12121 51.51515 85+ 1.56863 0.39216 35.29412 62.74510

3. Draw graphs of age-specific death rates and age-cause-specific death rates.

Mortality Pattern across the Life Span (All Causes): 1960 Costa Rican Females

Diarrhea Mortality Pattern across the Life Span: 1960 Costa Rican Females

Cancer Mortality Pattern across the Life Span: 1960 Costa Rican Females

CVD Mortality Pattern across the Life Span: 1960 Costa Rican Females

4. Describe the age patterns of mortality (overall and for each cause).

Overall mortality is high for children under 5 years old, low and flat from age 5 up to about age 45, and steadily increasing after that.

The highest mortality from diarrhea is that of children under 1 year old. Mortality from diarrhea remains very low from age 5 through age 69, then slowly increases.

Mortality from cancer is low until about age 30 when it starts rising. It increases sharply until age 84, when there is a sharp decline.

Mortality from CVD is low and flat until about age 45 and then it rises steadily and increases sharply at age 85.

5. Describe the relative significance of the three causes of death in two age intervals: 1-4 and 85+.

It helps to look at this graph of age-cause-specific death ratios:

Comparison of Age-Cause-Specific Death Ratios across the Life Span: 1960 Costa Rican Females

In the 1-4 age group, diarrhea is the most significant cause of death. In the 85+ group, CVD is by far the most significant.

Lesson 3: Life Tables

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