We will build our skill set for using the indirect age adjustment methodology with an example. First an introduction to the methodology. The standardized mortality ratio is the result you get when you apply the indirect age adjustment method to mortality data. This indirect method is used less frequently than the direct age adjustment method we've just learned. But this method is more commonly used in occupational and environmental studies. This approach is very useful when the age-specific number of deaths are small. This was the case among our age groups of Hispanic males and females in our example. So, we will apply the indirect age adjustment method to build our skills. Finally, the standardized mortality ratio is a measure of risk, because it directly measures the difference between the probability of death in the population of interest and the standard population. So, this approach is being used more frequently in studies of health inequalities. As a quick side note, we're going to start calling the population of interest the study population. Because that label is a bit easier to apply. The standardized mortality ratio, or SMR, is calculated as the number of observed deaths divided by the number of expected deaths, times 100. Although the numerator of this ratio is an observed number. The denominator takes a bit more calculation. The denominator is an estimate as the sum of the age specific death rates in the standard population multiplied by the age specific population counts in the study population. The interpretation of the SMR is as follows. If the SMR is greater than 100 that means the number of observed deaths is greater than what would be expected if the study population had the same probability of dying as the standard population. In other words, the study population has a greater risk of death compared to the standard population. If the SMR is equal to 100, that means the number of observed deaths is the same as what would be expected if the study population had the same probability of dying as a standard population. In other words the study population has the same risk of death compared with the standard population. And finally, if the SMR is less than 100, that means the number of observed deaths is less that what we would expect, if the study population had the same probability of dying as the standard population. In other words, the study population has less risk of death compared with the standard population. We also have to be a bit careful about interpreting the magnitude of the SMR. For example, an SMR of 278 can be interpreted as 178% increase in the risk of death, remembering that 100% would mean equal risk. We could interpret the 278 as a 2.78 fold increase in the risk of death in the study population compared with the standard population. Using the term risk is shorthand for the more lengthy interpretation in the first two bullets. More specifically than number of observed deaths in the study population is 178% higher than what would be expected if the study population had the same probability of dying as the standard population. Let's go back to our example. Please go to the indirect MRs tab in the spreadsheet. Because there were not more than 25 deaths in each age group among our Hispanic males and females. We will compare mortality in Hispanics with whites using indirect age adjustment. You will notice in the table that we have linked to the crude mortality rates for whites, as calculated in the direct MRs tab. We have also linked to the total number of Hispanics in the population located in the direct MRs tab. It should be noted, however, that we do not have to apply the direct age adjustment methodology prior to the indirect age adjustment methodology. On the contrary, typically only one age adjustment approach is used. But the crude mortality rates in population estimates were located in the direct MRs tab. So, we will use them to avoid data entry errors and save time on re-entering the data. Calculate the expected deaths by multiplying the crude mortality rate by the Hispanic population. Be sure you divide the crude mortality rate by 1000, so it is the crude mortality rate per one person. This is important to get the correct estimate of the expected deaths. Take a minute to do this for the overall comparison of mortality rates in Hispanics and whites, as well as in the sex stratified tables. Click continue when you are ready. If you have applied the formula correctly, you will have the same results as showed here. I want to draw your attention to the total number of expected deaths. This was automatically summed in your spreadsheet because I programmed the cell to do so. This estimate is what is needed for the SMR formula. This estimate can be interpreted as the expected number of in the Hispanic population if the Hispanic population had the same probability of death as the white population. To complete our estimate of the SMR, we divide the number of observed deaths in the Hispanic population by the number of deaths we would expect if Hispanics had the same probability of dying as whites. The number of observed deaths in Hispanic comes from the direct MRs tab. We see that the SMR is 45 which can be interpreted as a 55% decrease in the risk of death in Hispanics compared to whites. It's a decrease in the risk because 45 is less than 100. If you go on to calculate the SMRs from blacks compared with whites you would get this results. The SMRs can be summarize as Hispanics have a lower risk of death compared to whites. Black men have a higher risk of death compared to white men. Black women have the same risk of death as compared to white women. This example points out the importance of not only age adjustment, but also stratification by sex. A quick side note. There is a straightforward formula for calculating a 95% confidence interval for the standardized mortality ratios, or SMRs, which is shown here in this slide. Going back to our example of comparing Hispanics to whites, we can estimate a lower limit of 42 and an upper limit of 48 using the formulas seen here, ll is lower limit, ul is upper limit. Because our 95% confidence interval does not include 100, we can conclude that the SMR is statistically significantly different from 100. Signaling a statistically significant decrease in the risk of death among Hispanics compared to whites. A few technical notes on indirect age adjustment. First, these rations compare the study population to a standard population. It would be inappropriate to ratio two SMRs. For example, it would be inappropriate to ratio the SMR for Hispanic compared to white to the SMR for black compared to white. However, if SMRs have the same standard population like whites in Maryland, then you can compare the SMRs to make decision about priorities, policies, and programs. But again they should not be set ratio to each other in a statistical sense. The second and third technical notes are the same warnings we learned about in the technical notes for direct age adjustment. Namely, it's not meaningful to age-adjust data for small age ranges, and if the mortality rates do not have a consistent relationship over time you should not age-adjust but rather explore that relationship of age and mortality over time. A final word on age adjustment, there are many ways to adjust per age or other important variables. You can always stratify your analysis or look at subgroups which we did in our example when we stratified by sex. We can use the direct or indirect standardization methods which we just described and practiced. Life tables and multi-variables statistical analyses are also methods that can be employed. We won't cover these approaches in depth in the course, but we hope you have gained a solid understanding of direct and indirect age adjustment. And you are familiar with the spreadsheet tool provided. Let's take a break.
