Standardized Mortality Ratio (SMR) Calculation

The Standardized Mortality Ratio (SMR) compares the observed deaths in a specific group (hazardous industry workers) to the deaths expected based on the national death rates for similar age groups.

The formula for SMR is:

$ SMR = \frac{\text{Total Observed Deaths}}{\text{Total Expected Deaths}} \times 100 $

Step 1: Calculate Expected Deaths

Calculate the expected number of deaths for each age group based on the national death rate and the worker population.

• Age 25-34: Expected Deaths = $ (3000 \times \frac{2.0}{1000}) = 6 $
• Age 35-44: Expected Deaths = $ (2000 \times \frac{3.5}{1000}) = 7 $
• Age 45-54: Expected Deaths = $ (2000 \times \frac{6.0}{1000}) = 12 $

Step 2: Sum Total Expected Deaths

Add the expected deaths from all age groups:

Total Expected Deaths = $ 6 + 7 + 12 = 25 $

Step 3: Sum Total Observed Deaths

Add the observed deaths reported for the hazardous industry workers from the table:

Total Observed Deaths = $ 8 + 9 + 13 = 30 $

Step 4: Calculate SMR

Apply the SMR formula using the calculated totals:

$ SMR = \frac{30}{25} \times 100 $

$ SMR = 1.2 \times 100 $

$ SMR = 120 $

Conclusion

The Standardized Mortality Ratio (SMR) for the hazardous industry workers, compared to the national population, is 120.