# How to convert DHS under five mortality rate to SMART under 5 mortality estimate?

This question was posted the Assessment and Surveillance forum area and has 5 replies.

### Anonymous 29900

student

Normal user

22 Feb 2019, 01:37

Is there anyway of converting DHS reported under 5 mortality estimates to SMART survey under 5 mortality estimates?

For instance a DHS report stated that the under 5 mortality (5q0) as 58 per 1000 live birth. How can I directly convert it to SMART survey scale of per 10,000/day ?

I am aware that the DHS is probability of dying before the age of 5, while the estimate from SMART surveys is just a rate.

Thanks in advance

### Mark Myatt

Consultant Epidemiologist

Frequent user

25 Feb 2019, 10:26

This is a bit of a tricky thing to do. The are a number of methodological differences (as you note). Both meths can estimate U5MR. The "SMART" method looks at mortality over a short period of time prior to the survey (usually less than three months). THe "DHS" method estimates mortality over a longer period. The "SMART" method presents an average mortality over a short period. The "DHS" method presents an average mortality over a much longer period. Both methods present lagged estimates but the lag is longer in "DHS" compared to SMART. This means that the "DHS" estimate will not fully reflect recent levels of mortality. This is what the "SMART" estimate is for. The "DHS" method can be thought of as providing a development indicator. The "SMART" method provides a emergency indicator.

Conversion can be useful if you want to treat U5MR as a background "pre-emergency" mortality rate. Conversion is not difficult if you keep track of the two denominators (persons and time). You can express U5MR as an annual mortality risk by dividing by 5. Using your 58 / 1,000 / day figure:

58 / 5 = 11.6 / 1,000 / year

multiplying by 10 will give this as a rate per 10,000 per year:

11.6 * 10 = 116 / 10,000 / year

dividing by 365 will give a rate per 10,000 per day:

116 / 365 = 0.32 / 10,000 / day

You can compare this to the "SMART" estimate to make an estimate of excess mortality. If (e.g.) the "SMART" estimate is 0.83 / 10,000 day then you can see that there has been a recent:

0.83 / 0.32 = 2.59

fold increase in mortality.

I hope this is of some use.

### Bradley A. Woodruff

Self-employed

Technical expert

25 Feb 2019, 17:50

Dear Anonymous 29900:

The short answer to your question about converting between the DHS measure of child mortality and the SMART measure of child mortality is no, there is no easy way to convert between these two different measures of child mortality. The DHS measure, which is the same used by UNICEF in MICS surveys, is not an incidence rate. It is a cumulative incidence. It measures the cumulative risk of death for a hypothetical cohort of live-born children during their first 5 years of life. Another way to say this is: by the time a child reaches their fifth birthday, what is the total cumulative likelihood that that child will be dead.

The usual mortality rates, such as that recommended by SMART and the age-specific death rates derived from vital statistics data, are measures of the risk of death at a point in time. These rates are the number of eligible children who die during a given period of time period divided by the number of eligible children. The time period can be a day (used in acute emergencies), a month (sometimes used in relatively stable displaced populations), or year (used in most vital statistics analyses). The number of eligible persons is usually the average of the population at the beginning of the time period and the population at the end of the time period.

Unfortunately, the same term has been applied to these two very different measures of child mortality; that is, under-5 mortality rate. Let's stop this usage. The actual numbers produced by these different measures are very different. Perhaps we should call them the "cumulative under-5 mortality risk" (the DHS/UNICEF measure) and the "age-specific mortality rate for children less than 5 years of age" (the vital statistics/SMART measure). Because the DHS/UNICEF cumulative under-5 mortality risk measures the 5-year cumulative risk of death, it is often more than 5 times higher than the 1-year age-specific mortality rate for children under 5. So if you cite an cumulative under-5 mortality risk without giving the units, a person thinking of age-specific mortality rate will freak out. This has happened many times and just leads to confusion and inappropriate reaction. But the mathematical relationship between the two measures is not a constant, so purely mathematical conversion is impossible.

The discrepancy between these measures comes from the denominator. In a true mortality incidence rate, a person who dies is removed from the denominator after he/she dies. This is done by recognizing that the size of the population changes during the time period of concern. Thus, the denominator is the average size of the population denominator during this time period. So, for example, there are 1000 children born on the same day. Five years later, 400 of these children have died. The cumulative under-5 mortality risk is 400/1000 or 0.4 or 40%. But the age-specific mortality rate during this period would be 400/([1000+600]/2), or 0.5 or 50%. This is because the denominator for the cumulative under-5 mortality risk remains 1000 (the original 1000 live births), but the denominator for the age-specific mortality rate is only 800 (the average of the starting population of 1000 and the ending population of 600). As a result, the discrepancy between the cumulative under-5 mortality risk and the age-specific mortality rate increases with increasing child mortality.

And, as Mark has pointed out, the cumulative under-5 mortality risk, as measured in DHS and MICS, averages out child mortality for the prior 5 years, whereas the age-specific mortality rate often measures more recent mortality. For example, in a SMART survey with a recall period of 75 days, the measure of child mortality applies to the most recent 75 days.

I've created a small spreadsheet which takes estimates of infant mortality and the cumulative under-5 mortality risk from MICS or DHS reports and calculates three age-specific mortality rates for children less than 5. No guarantees are implied, and I would love to hear about any mistakes found or improvements made by users.

https://www.dropbox.com/sh/letqzpemaymvzx6/AACPM1RFkAQXnlSYENMYQmxYa?dl=0

### Mark Myatt

Consultant Epidemiologist

Frequent user

26 Feb 2019, 09:26

Woody,

Thanks for that very thorough answer and for the calculator. I think it would be useful if you could give a worked example of the use of the calculator.

### Tanny

stundent

Normal user

13 Sep 2019, 11:20

@Bradley I came across this page while looking for solution to similar questions. I click on the link you provided but it is no longer available. Can you by any chance repost the link to the excel sheet ? Thanks in advance.

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