Confusion over CDR and U5DR sample size calculation

I was around at the time and cannot exactly recall why crude mortality rate was preferred to the under five years mortality rate. It does seem a rather odd decision given that SMART's anthropometry component concentrates on children under five year of age. I think the decision may have been based on sample size issues with U5MR requiring a larger number of households than CMR. There was also some confusion about terminology and denominators used for U5MR (See the 2006 SMART Methodology manual) and benchmark values for U5MR were not, at the time, well established (they were based on doubling the CMR thresholds).

A rationale for estimating under five years mortality rather than all-age mortality is that the under five years population is an early warning (sentinel) population (i.e. mortality is likely to rise in this population before it rises in the general population). Also, under five years mortality is less influenced than CMR by the age structure of the population. Different age structures can make comparisons between different populations meaningless without standardising for age (e.g. developed countries may have higher CMRs than developing countries because they have a higher proportion of elderly persons in their population). Standardisation is likely to require the collection of additional demographic data in emergency situations.

As SMART was being developed, I worked with Save the Children UK and proposed a method for estimating U5MR adapted from, the widely used "previous birth history" method. This was presented in Field Exchange 17 (see pages 13 - 16. Woody's commentary is more than fair).

This covers some aspects of sample size calculations for rates. The sample size calculator and rate calculation spreadsheet presented in the article are now available from here.

I hope this is of some use to someone.

I think that this is only a matter of convenience. We really need a standard way to express mortality rates so that they can be compared against thresholds, between populations, and between time periods for the same population.

A number of standard formats are used:

deaths / 1,000 population / year : This is most often used to express mortality in stable populations. We often see "1,000 populations" replaced by "per 1,000 live births" in U5MR estimates.

deaths / 10,000 population / day : This is what we are used to in humanitarian populations when we expect mortality to be high and changing rapidly.

deaths / 1,000 / month : Not in common use but may be seen in stable camp settings (i.e. after the immediate crisis has passed).

Other demoninators are used. For COVID we often see 100,000 in the denominator:

    Population New York City as of 1st May =  8,398,748
    Estimate count of COVID deaths as of 1st May = 23,430

That is 23430 / 8398748 * 100 = 0.2789702% dead from COVID. This might be expressed as:

    0.002789702 * 100000 = 279 / 100,000

I have seen this expressed as deaths / million population.

Using these standard formats makes it easy to compare rates. If we did not have these standard formats we'd have to work raw counts. For example. what is the proper interpretation of thes two rates?

    (1) 271 deaths in 158,934 persons over 13 days

    (2) 445 deaths in 72,072 persons over 47 days

We have all the data we need but the true relation is that the two rates are similar to each other is not obvious at first glance:

    (1) 271 / 158934 * 10000 / 13 = 1.31 / 10000 / day

    (2) 445 / 72072 * 10000 / 47 = 1.31 / 10000 / day

The standard formats also makes it quite easy to convert between formats. So that (e.g.):

    1.31 / 10,000 / day
    
is the same mortality rate (risk of death) as:
    
    (1.31 * 365) / (10000 / 1000) = 47.8 / 1,000 / year

Moving between with 100,000; 10,000, and 1,000 is simple. Moving between follow-up periods is less straightforward arithmetic. No problem with a calculator / software and taking care to keep track of time.

I hope this is of some help.

Woody,

Thanks for this most informative reply.

Multiple meanings for U5MR are confusing. Do you have a good way of converting between rates using the deaths / 1000 live births denominator and deaths / 10,000 children age < 5 years? I have used a rather rough and ready method to do this. This divides the UNICEF U5MR by 5000 to give the proportion of children aged under five years that die each year. Multiplying by 10000 and dividing by 365 should give deaths / 10000 / day. This is very rough and ready - lots of somewhat silly assumptions - and the "deaths / 10000 / day" does not fit well with an estimate of average mortality over a five year period.

BTW ... I do not think we even need a dedicated "mortality survey" to estimate UNICEF's U5MR statistic. I think we can do this using survey data that can be used to describe the age distribution of the population (e.g. SMART survey data on ages of children) and then fit a regression model:

    log(n) = a + b * t

where n is the number at each age and t is age. We could do this with age-groups. The absolute value of the stimate of b would be an estimate of the mortality rate.

I think this should work for under fives.

What do you think?