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# Calculating beneficiary numbers of SAM/MAM using prevalence

This question was posted the Assessment and Surveillance forum area and has 3 replies. You can also reply via email – be sure to leave the subject unchanged.

### Rogers Wanyama

Emergency Nutrition Specialist

Normal user

20 Jan 2011, 05:17

Hi Annonymous 169
A similar question was posted in 2009. Log to the link below.
http://www.en-net.org.uk/question/157.aspx
Hope it helps
Thanks
Rogers

### Anonymous 81

Public Health Nutritionist

Normal user

20 Jan 2011, 07:53

Dear Annonymous 169

http://www.en-net.org.uk/question/212.aspx

Cheers
Kiross

### Mark Myatt

Consultant Epideomiologist

Frequent user

20 Jan 2011, 09:54

Others have pointed out:

http://www.en-net.org.uk/question/157.aspx

and:

http://www.en-net.org.uk/question/212.aspx

One approach is to use the formula:

EXPECTED = POP * U5% * EP% * CFI

where:

POP = Total population
U5% = Percentage of total population age 6-59 months
EP% = Estimated prevalence
CFI = Correction factor to estimate incidence from prevalence

The value of CFI is uncertain (see the links above). A CFI of 2.0 (in this formula) is broadly in-line with published estimates. This level of CFI is used for SAM. I do not think we have a good idea of the value of CFI for MAM (so I would use 2.0).

The problem with:

EXPECTED = POP * U5% * EP% * CFI

is that it takes a "fairy tale" view of programming in the sense that it assumes a coverage proportion of 100%. I have looked at coverage of TFC, OTP (in both CTC and CMAM guises) and SFP and have never seen coverage above 89%. Here are some rules of thumb for different program types:

TFC : Typical range 0.5 - 5% (maximum seen is c. 30%)
OTP : Typical range 20% - 80% (minimum 8%, maximum 89%)
SFP : Typical range 5% - 20% (limited data available)

We have to face it ... most programs achieve coverage below SPHERE minimum standards.

The point is that we need to account for coverage in the formula:

EXPECTED = POP * U5% * EP% * CFI * COVERAGE

Using your data and assuming the program will hit the SPHERE minimum of 50% we have:

EXPECTED = POP * U5% * EP% * CFI * COVERAGE
EXPECTED = 450000 * 20% * (3.1 / 100) * 2.0 * (50 / 100)
EXPECTED = 2790

Another approach is to use the formula:

EXPECTED = POP * U5% * EP% + (POP * U5% * EP% * CFI)

That is prevalent cases + incidence cases.

A value of 1.6 is used for CFI (this is a published estimate). This level of CFI is used for SAM. I do not think we have a good idea of the value of CFI for MAM (so I would use 1.6).

This formula also fails to account for coverage. A better formula is:

EXPECTED = POP * U5% * EP% * IC + (POP * U5% * EP% * CFI * AC)

where:

IC : Initial phase coverage (often low)
AC : Achieved coverage (i.e. after the first few months)

It is sensible to use:

IC = AC / 2

as the average between starting at zero and achieving 50% some time later.

AC = 50%

and:

IC = 50% / 2 = 25%

we get:

EXPECTED = 450000 * 0.2 * 0.031 * 0.25 + 450000 * 0.2 * 0.031 * 1.6 * 0.5
EXPECTED = 2930

The two methods give similar answers.

You have to be aware that there are big sources of error in both of these approaches:

POP : Subject to secular change but also displacement and migration
U5% : Subject to secular change &c. and public health shocks
CFI : An informed guess base on limited data
EP% : For SAM this will be very imprecise (e.g. 1.15%, 95% CI = 0.38%; 2.57%).

And COVERAGE is not known. We have to be realistic about what we will achieve. I'm sure that the agencies that "achieve" 8% coverage started out thinking they would get 80% coverage.

BEWARE : You need to use EP% for your program admission criteria. If you use MUAC then EP% is for the MUAC case-definition not the W/H case-definition.

So ... a short answer ... there is no really correct way. There are different ways of getting an informed guess which, given the same assumptions, give roughly the same answers.

I hope this helps.