In: Statistics and Probability
. Below are some crude cause-specific mortality rates from the two studies. Crude mortality rate per 100,000 person-years 1988-1993 2003-2008 Drug Overdose 80.7 242.1 Substance Use Disorder 54.8 109.5 HIV Disease 280.0 84.0 Using both relative and absolute measures of association, compare the three cause-specific mortality rates for the 2003-2008 and 1988-1993 study populations. Use the 1988-1993 study population as the referent group. State in words your interpretation of each of these measures. 4. Do the demographic characteristics of the two study populations influence your interpretation of these crude measures of association? Why or why no
Introduction:
The crude mortality rate (CMR) given here may be considered as the incidence rate of mortality or death, per 100,000 population members, in a given year, due to a particular cause. Here, the period 1988-1993 is the reference period.
An absolute measure of association is the rate difference (RD), which is obtained by subtracting the risk in the reference period, from the risk in the later period. In this case, it can be obtained by subtracting the CMR due to a particular cause for the reference period (1988-1993), from the CMR for that cause in 2003-2008. For example, for Drug Overdose, RD = 161.4 (= 242.1 – 80.7).
A relative measure of association is the relative risk (RR), which can be obtained by dividing the risk in the current period, by the risk in the reference period. In this case, the CMR in 2003-2008 can be divided by the CMR in 1988-1993, to obtain the relative risk. For example, for Drug Overdose, RR = 3 (= 242.1/80.7).
The above measures can be interpreted as follows:
RD:
For Drug Overdose: There is an increase in the risk of death by 161.4 deaths per 100,000 persons in the population, from 1988-1993 to 2003-2008, due to drug overdose.
For Substance use disorder: There is an increase in the risk of death by 54.7 deaths per 100,000 persons in the population, from 1988-1993 to 2003-2008, due to substance use disorder.
For HIV disease: There is a decrease in the risk of death by 196 deaths per 100,000 persons in the population, from 1988-1993 to 2003-2008, due to HIV disease.
RR:
For Drug Overdose: The risk of death due to drug overdose has increased by 3 times, from 1988-1993 to 2003-2008.
For Substance Use Disorder: The risk of death due to substance use disorder has increased by 1.9982, or approximately, 2 times, from 1988-1993 to 2003-2008.
For HIV Disease: The risk of death due to HIV disease has increased by 0.3 times, that is, decreased by 3.33 times from 1988-1993 to 2003-2008.
Explanation:
In the given information, only the crude mortality rates are mentioned. No information is given regarding the other demographic characteristics of the populations during the two periods, such as the age distributions, sex distributions, etc. It is possible that the overall age of the population has increased from 1988-1993 to 2003-2008, making the increased death rates more likely, as an older population is bound to have higher number of deaths than a younger population, in general. The increased crude mortality rates due to drug overdose and substance use disorder may be due to prolonged abuses of drugs and other toxic substances over the years; the decreased death rate due to HIV may be because of the advances in treatments for HIV.