How to calculate the death rate(the fatality rate)

[Jun Choi]

Hi all,

I'm interested in the Serious Accidents Punishment Act's impact on industrial accidents in South Korea.
However, I had a problem calculating the death rate for the given data.

My data does not have the total number of workers, which is about 19,000,000 in South Korea.
What I know only in data is the number of injured workers, which is about 108,379.

Then, given the situation, how should I calculate the death rate next?

I calculated the death variable in Stata as follows:
The death variable would be 1 if the worker died while working.
The death variable would be 0 if the worker did not die while working.


. tab death

death | Freq. Percent Cum.
------------+-----------------------------------
0 | 106,317 98.10 98.10
1 | 2,062 1.90 100.00
------------+-----------------------------------
Total | 108,379 100.00

. save "/Users/mac/Desktop/acc/2020.dta", replace
file /Users/mac/Desktop/acc/2020.dta saved

Thank you for your help in advance.
Jun

[Clyde Schechter]

The use of the term "death rate" should be avoided because the term is ambiguous. There are numerous epidemiologic statistics that include death in the numerator, and the term "death rate" is often used indiscriminately to refer to any of them, often without even providing any context to help understand which is meant.

In the title of your post you also refer to "fatality rate." The case fatality probability of a disease or condition is defined as the number of deaths among people with the disease or condition divided by the number of people with the condition. So, in the table you show, there are a total of 108,379 people with the condition occupational injuries, of whom 2,062 died. So the case fatality probability is 1.90%. Now, there are other considerations that may apply here: was the period of follow-up of the people with occupational injuries long enough that we can reasonably believe that all of the people who would ultimately die of the condition were found and included in the study. Also, if, instead of just the totals, we had information about how long each person survived until either dying or reaching the end of the study's observation period, it might be more informative to do a full-blown survival analysis instead of just calculating a summary figure. But given the data you show, calculating the case fatality rate is straightforward.

Notice that, so far, I have made no mention of the total number of workers. The total number of workers has nothing to do with the fatality probability. It is, however, the all-important denominator for the mortality probability. The mortality probability from a condition is defined as the number of people dying from the condition divided by the total number of people who are at risk for developing the condition. So it is impossible to calculate a mortality probability for occupational injuries without knowing the total number of workers.

I have avoided using the term "rate" here because an epidemiological rate must also include a unit of time in the denominator, i.e., so many deaths per year (or per month, or whatever). As the data you describe has no time variables, it is impossible to calculate rates in this sense, and only probabilities are available.

[Jun Choi]

First of all, thank you very much for your help.




I am trying to research an MA course’s thesis in economics, which is especially labor economics.

What I am trying to use the term might be ambiguous for the readers who read my paper. Then, what should I use the term dead industrial accidents instead of the death rate? Is it appropriate to use the mortality rate per 10,000 workers due to industrial accidents while working at the workplace?




There is data I have, which is from 2017 to 2022. I want to find out the mortality rate from 2017 to 2022 in South Korea. Sorry for not being mentioned about the time period. I forgot what I should mention regarding the time needed to calculate.




Is it possible to use this method using the observation by increasing manually as follows? I think that the mean value seems appropriate for me, which is about 1.08, however, the standard deviation looks like it is abnormally not feasible, which is about 104.2.

Please refer to the codes I used.

. set obs 18,974,513 
Number of observations (_N) was 108,379, now 18,974,513.

. gen death = 0

. replace death = 1 if v12 == 31
(882 real changes made)

. replace death = 1 if v12 == 32
(1,180 real changes made)

. tab death

      death |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 | 18,972,451       99.99       99.99
          1 |      2,062        0.01      100.00
------------+-----------------------------------
      Total | 18,974,513      100.00

. gen total_worker = 1

. tab total_worker

total_worke |
          r |      Freq.     Percent        Cum.
------------+-----------------------------------
          1 | 18,974,513      100.00      100.00
------------+-----------------------------------
      Total | 18,974,513      100.00

. gen mortality_rate = (death/total_worker)*10000

. sum mortality_rate

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
mortality_~e | 18,974,513    1.086721    104.2402          0      10000

Thank you for your suggestions, and assist again,

Jun

[Clyde Schechter]

If the total number of workers is 18,974,513 and over a six year period there were 2,062 deaths from industrial accidents, then the industrial accident mortality rate (and that is what you should call it) calculation begins with:

. cii proportions 18974513 2062

                                                            Binomial exact   
    Variable |        Obs  Proportion    Std. err.       [95% conf. interval]
-------------+---------------------------------------------------------------
             | 18,974,513    .0001087    2.39e-06         .000104    .0001135

Now, that is per worker per 6 years. It is more conventional to present such results in units like per 10,000 workers per year. To do that we have to multiply by 10,000 and then divide by 6. So that gives us 0.18 per 10,000 workers per year, 95% CI 0.17, 0.19. If you wish to also report the standard error (not standard deviation) it is similarly multiplied by 10,000 and divided by 6, giving a result of 0.004.

That is the best that can be done with aggregate data like this. A more subtle analysis would take into account that the number of workers fluctuates as people enter and leave the work force, and would calculate the denominator not as the total number of workers, which is some sort of average over the 6 year period, but as the total number of person-days of workforce participation.

[Jun Choi]

Dear Clyde,

Thank you very much for your help again!
I was able to calculate the correct death rate and injury rate for your assistance.

Also, I apologize for the late reply...

Jun