Does anyone have an idea on why sample size calculation for U5DR in SMART survey is based on expected CDR and not expected U5DR ? 

My question is similar that of op if I understand the op correctly which is why I didn't want to create a new thread for this. 

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.

@Mark thanks for the response that is quite insightful. 

@Mark I am not sure but is there any paper or material you are aware for the justification of the units for the expression of death rate. It is common practice to express death rate in 10000/day my guess is that this is just a norm. Am I right? 

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.

Dear Kelvin:

The convention of expressing mortality rates as a number of deaths per 10,000 population per day was started several decades ago by Mike Toole and others. It was recommended only for, and is used almost exclusively in, acute humanitarian emergencies. This mortality rate format can be used for the population as a whole or for a specific age groups, such as children less than 5 years of age. In acute emergencies, the recommendation is to set up an active surveillance system for mortality so that the number of deaths can be compiled in the very short term, often every day. This is done because mortality rates may fluctuate rapidly, and programmers need immediate data to judge the short-term effectiveness of their programs. As such, it does not make much sense to calculate such a short-term mortality rate as deaths per population per year, although such a calculation would be entirely valid and arithmetically equivalent to calculating a rate per day. But it might look funny to calculate the death rate every day which uses such a long time denominator. 

Which population constant to use in a death rate depends on what death rate is being calculated. Generally, we like to have death rates in the single or double digits. So if we are calculating a cause-specific mortality rate for a relatively rare disease, we don't really want to present a cause-specific mortality rate of 0.006 deaths / 1000 / year. Instead, by increasing the population constant to 1 million, we could present a rate of 6 deaths / 1,000,000 / year which may be a bit more intuitively understandable. On the other hand, a mortality rate for a more common disease of 8,928 deaths / 1,000,000 / year also looks funny; 8.9 deaths / 1000 / year is better. But of course all these rates are arithmetically interchangeable, and they are all entirely correct.

Although your question did not directly pertain to this topic, I cannot pass up the opportunity to address the confusion between age-specific mortality rates and cumulative risk of death before the 5th birthday. UNICEF predominantly uses a mortality measure in young children which is the proportion of a hypothetical cohort of 1000 live-born newborns who die before their 5th birthday. Although this is not really a mortality rate (the denominator does not reflect the population at risk throughout the five-year time period), UNICEF insists on calling it "under-5 mortality rate", thus causing confusion with the age-specific mortality rate in children under 5 years of age. An age-specific mortality rate is the number of deaths in a given age group divided by the number of individuals in that age group per unit time; for example, 2.3 deaths in children under 5 / 1000 children under 5 / year. This is a very different number from the UNICEF cumulative risk of death before the 5th birthday. I cannot count the number of times I've seen an age-specific mortality rate for children under 5 derived from a population-based survey compared to the cumulative risk of death before the 5th birthday presented in UNICEF's State of the World's Children. Of course the latter is much higher, so survey managers fallaciously conclude that mortality has declined substantially (a quite unbelievably) in their surveyed population.

Okay, I hope this provides some additional clarification.

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?

The FANTA Profiles tool has an excel spreadsheet that looks at mortality:

Project, USAID’s FANTA. “Manual for Country-Level Nutrition Advocacy Using PROFILES and Nutrition Costing.” Food and Nutrition Technical Assistance III Project, April 2018. https://www.advancingnutrition.org/sites/default/files/2020-03/nutrition-advocacy-profiles-manual-apr2018.pdf.