# Caseload calculations (incidence rate)

This question was posted the Prevention and treatment of severe acute malnutrition forum area and has 16 replies. You can also reply via email – be sure to leave the subject unchanged.

### Sarah Butler

Director, Emergency Nutrition, Save the Children

Normal user

18 Aug 2011, 13:37

I'm currently training some folks on how to calculate expected CMAM caseload using the (prevalence + incidence) * coverage equation. I'm having difficulty explaining to my team the calculation for incidence. We get stuck on this bit: "Incidence = prevalence / duration of illness (with duration of SAM illness estimated at 7.5 months or 7.5/12); therefore, incidence = prevalence x 12/7.5 or prevalence x 1.6." (FANTA generic CMAM guidelines) Does anyone have a citation for where we've gotten the duration of SAM as being 7.5 months? How about a simple way to explain the various numerators and denominators of this equation? If the program duration is only 6 months, can the equation be calculated as prevalence * 6/7.5? Thank you.

### Rogers Wanyama

Emergency Nutrition Specialist

Normal user

18 Aug 2011, 15:19

Have a look at the links below :

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

Garenne M,Willie D, Maire B, et al. Incidence and duration of severe wasting in two African populations. Public Health Nutr. 2009;12(11):1974–1982.

Thanks

### Mark Myatt

Consultant Epideomiologist

Frequent user

18 Aug 2011, 15:33

The 7 - 8 months duration is based on analysis of data from DRC and Senegal and is presented in:

Garenne M, et al., Incidence and duration of severe wasting in two African populations, Public Health Nutrition,

2009;12(11):1974–1982

The method is based on incidence being approximately equal to prevalence/average duration. This is outlined in:

MacMahon B, Pugh TF, Epidemiology Principles and Methods, Boston, MA, USA, Little Brown & Company, 1970

And:

Miettinen O, Estimability and estimation in case-referent studies, American Journal of Epidemiology, 1976;103(2):226–235

Have you tried the leaky water tank analogy (incidence = water in, recovery + death = leaks, prevalence is what is left in the tank).

### Tamsin Walters

en-net moderator

Forum moderator

18 Aug 2011, 19:01

*From Ijaz Habib:*

HI....the 7.5months disease duration represents the average duration in which an untreated severe acute malnourished child would either spontaneously recover or die. it is product of research study mentioned by my brother Rogers.

The most recent study done by Sheila Isanaka*, Rebecca F. Grais, Andre´ Briend, and Francesco Checchi and published in March 2011 reflects comparatively less disease duration i.e. 75-81days on w/h zscore or 101-116 on muac for untreated MAM cases. The disease duration for SAM is 45days based on z-score.

The reduced disease duration means more case load. We are still adhering to the 7.5months disease duration due to nutritional supplies limit from donor.

I wish the technical leads Andre Briend and Mark Myatt may comment on it for further clarification.

regards

ijaz habib

### Rogers Wanyama

Emergency Nutrition Specialist

Normal user

19 Aug 2011, 01:11

Hi

As stated above,the study by Garenne et al led to an average duration of 7.5 months resulting to a conversion factor of 1.6 which is think is the one mostly applied. A recent study by Isanaka et al suggests a shorter duration of SAM hence a higher coefficient should be used.

How are we able to estimate disease burden bearing in mind prevalence (derived from surveys) usually have a large C.I (If am not wrong). Do these coefficients apply in all contexts (Including emergency contexts)?

Thanks

### André BRIEND

Frequent user

19 Aug 2011, 07:48

Dear Ijaz,

I don’t have much to add to this discussion which comes back regularly in this forum, which shows it is not a settled issue. Maybe I should stress that the conversion prevalence incidence using the average duration of untreated SAM is applicable only when the prevalence survey is done in a population where there is no SAM programme in place. Also, it assumes that the situation is stable (i.e. constant incidence). If the survey is done during a crisis or an emergency which is not expected to last for long, it is likely that the incidence will decrease over time once the crisis is over. Your conservative attitude of sticking to the commonly used 1.6 coefficient (assuming a 7.5 months duration) looks reasonable to me. Ideally, these coefficients should be validated by analysing past data and examining the relationship between initial surveys and case load. As mentioned before in this forum, this is currently attempted by Nancy Dale in collaboration with HNTS (Claudine Prudhon, in WHO Geneva). NGOs who have data that could be used for this analysis should be encouraged to get in touch with them.

### Mark Myatt

Consultant Epideomiologist

Frequent user

19 Aug 2011, 11:08

I also have little to add. André is correct ... the average duration approach only works for constant incidence. I think that this almost never applies to wasting in the contexts we usually work in. At best this is a "rough and ready" method but it is all we have at present. The 1.6 value with some estimate of coverage has been used for some time and seems to work (in the sense that no-one has reported gross failure of the method using this value).

I must say that the revised estimates of duration of a SAM episode (45 days) seem a little odd to me. I'm not yet convinced that this is a sound estimate. This is just my opinion and nothing else.

### Anonymous 2411

INGO

Normal user

17 May 2016, 20:58

Hi there,

Does any one has a reference in calculating SAM case load for a period of 6 months?

Is it worth considering the incidence for short period?

The UNICEF SAM programme guidance document 2015 is defining incidence on page 57 as below and doubting whether to consider or not the incidence when estimating the case load for 6 months.

Incidence: The occurrence of new cases of children 6-59 months with SAM in a population over a specific time period (usually a year).

### Anonymous 730

Nutrition and Food Security Officer

Normal user

17 May 2016, 21:01

For 6 months,you would simply do the whole calculation as indicated above then divide the final result by 2.

### Anonymous 2411

INGO

Normal user

17 May 2016, 23:01

Anonymous 730 Thank you for your prompt feedback.Just to get more clarification, do we need to divide by 2 the expected incidence only and keep the same prevalence estimate? My concern is, if we divide the total annual estimate by 2 to get the 6 months estimate, is it not going to affect the prevalent cases that one can find them at any given time?

### Paul

Technical expert

18 May 2016, 04:38

Hi Anonymous,

Firstly I would refer you back to the previous posts on the calculation of incidence above. Any estimate will be context dependent and is a "rough and ready" estimate of caseload.

There are some things you may want to consider when calculating incidence.

- Which year / month / area did you get your prevalence estimate from?

The prevalence of acute malnutrition will show seasonal fluctuation. Was the prevalence estimate from your area (e.g. was it national / regional or local)? During which season was it done? When would the prevalence would be expected to be higher or lower? You could develop a seasonal calendar (e.g. see the SQUEAC manual) using secondary data and in collaboration with the community to identify the usual fluctuations you might expect in your locality.

- The incidence calculation is a 'rule of thumb' and again will vary according to context but as Andre has mentioned earlier it is based on a stable incidence which may not apply to your area.

- What is the purpose of your estimate? If it is to calculate caseload in order to arrange the appropriate logistics then you can adapt those inputs as you go depending on how adaptable your logistic supply chain is. You may also wish to estimate the programme coverage you expect to achieve in order not to over estimate your supply need.

**You should not under any circumstances use the caseload estimate to then an indirectly estimate your programme coverage**

- In practical terms you can 'fudge' the estimate. Your prevalence estimate will usually come with 95% CI intervals. If you think that the period over which your programme will operate will not cover any peak of malnutrition then you could estimate the prevalence to be somewhere (e.g. the midpoint) between the stated prevalence and the lower 95% CI or if you think it may be higher you could use the upper 95% CI. Then apply the 1.6 'fudge factor' (which gives the caseload for 12 months) and divide by 2 (for 6 months). Don't consider your estimates to be anything more than an educated guess.

- At the beginning of your programme (if it is new) you are likely to find more cases. The caseload will continue to rise for the first 3 months, especially if you have a good outreach programme, and then stabilise or possibly fall (as long as there is no developing crisis). In terms of logistics it is probably worth 'front-loading' your programme and reduce inputs as things progress if required. You can also expect a higher referral rate to inpatient at first but this should also fall over time if your case finding efforts are effective.

Please also see:

http://www.cmamforum.org/Pool/Resources/caseloadCMAM-June-2012(1).pdf

### Mark Myatt

Consultant Epideomiologist

Frequent user

18 May 2016, 08:48

I think Paul has summarised the issues quite well.

Anonymous : You are right. The formula is:

caseload = prevalence + K * prevalence

Since prevalence does not depend of K and prevalent cases will need treatment immediately.

For 6 months you would dived K by 12/6:

caseload = prevalence + (K/2) * prevalence

About five years ago (see above) I wrote:

The 1.6 value with some estimate of coverage has been used for some time and seems to work (in the sense that no-one has reported gross failure of the method using this value).

This is no longer true. For example, a CMAM program in a large West African country reported that:

12 month caseload = prevalence + 1.6 * prevalence

resulted in a gross underestimate of caseload even at moderate levels of coverage. A little high-school algebra together with estimates of population, prevalence, and coverage were used to adjust "K" in the formula:

12 month caseload = population * prevalence * K * coverage

to match the observed caseload. This yielded a value of K = 7.5.

There has been considerable recent work on the average duration of an untreated SAM episode in order to find suitable values for K. This has found that K could range between 1.2 and 16.4 depending upon location. This data is in the process of being published. I will report back when these are published.

The available evidence indicates that a single value for K does not exist. There is a need to use a local value for K.

I think the only thing to do is to choose a known local K. If there is no known local K then we can pick a value that seems appropriate (e.g. in Southern Niger K hae been estimated to be K = 9 so we might use K = 9 for a program in Northern Nigeria) and then calibrate K using estimates of population, prevalence, coverage, and known caseload.

Note that K is also used in the single coverage estimator.

I hope this is of some use.

### Shewangizaw SA Ashenafi

Nutrition program manager

Normal user

18 May 2016, 11:42

In addition please the below link and read, i hope it will helps

http://www.cmamforum.org/Pool/Resources/caseloadCMAM-June-2012(1).

Regards!!!

### Anonymous 2411

INGO

Normal user

18 May 2016, 14:10

Dear Mark, Paul and Shewangizaw , thanks a lot . I really appreciate your input.

Best regards,

### Nitush Fikir

Nutritionist

Normal user

5 Jan 2017, 12:34

Dear Mark,

Thank you for your technical guidance above.

1. I’m a bit confused by “For 6 months you would divide K by 12/6”

caseload = prevalence + (K/2) * prevalence

In the absence of known K, should we still apply the formula K=1 + (t/7.5), in which case K=1.8 for 6 months programme. If we use K/2, it gives K=1.3 (because when we apply K=1+(t/7.5) formula for 12 months programme, K=2.6)

Please kindly further explain the K values for the 6 months period.

2. I couldn’t also understand how K=7.5 is calculated for the below formula.

12 month caseload = population * prevalence * K * coverage

to match the observed caseload. This yielded a value of K = 7.5.

Please kindly further explain this.

3. As per your guidance above (“e.g. in Southern Niger K have been estimated to be K = 9”)

I look forward for the published articles but was the K in Nigeria estimated based on the observed caseload? If so, could it be due to underestimation of population number, new population influx in the area, under or over estimation of the prevalence of malnutrition etc…

4. Finally, can we still use the average duration of 7.5 months used to calculate the correction factor in the caseload calculation formula = N * P * K * C where K=1+(t/7.5) in the absence of known local K.

Greatly appreciate your help and guidance on this

### Mark Myatt

Consultant Epideomiologist

Frequent user

6 Jan 2017, 10:35

(1) It is me that was confused ("lazy thinking" might be the better term for it). You have this right. The caseload prediction formula:

caseload = N * P * K * C

has:

K = 1 + (t / 7.5) = 2.6

This uses the estimate of the average duration of an untreated SAM episode (i.e. 7.5 months) from two African populations from a study published in 2009 using older data. All times should be expressed in the same units. For one year (twelve months) we have:

K = 1 + (12 / 7.5) = 2.6

For six months we have:

K = 1 + (6 / 7.5) = 1.8

Recent work indicates that the value of K varies between locations. It seems that K = 2.6 will often be an underestimate.

(2) Here is a worked example ...

The program estimated caseload to be:

Estimated caseload (E) = 58,000

The program admitted:

Caseload (L) = 84,000

We have:

L = CNP(K + 1) = 84,000

where:

L = Observed caseload N = Population P = Prevalence K = Incidence (expressed as a correction to prevalene)

The process to get at a new K is:

L = CNP(K + 1) K + 1 = L / CNP K = (L / CNP) - 1

With some numbers:

C = 50% (0.5) N = 1,000,000 P = 2% (0.02) L = 84,000 CNP(K + 1) = 84000 0.5 * 1000000 * 0.02 * (K + 1) = 84000 10000 * (K + 1) = 84000 K + 1 = 84000 / 10000 K = (84000 / 10000) - 1 K = 7.4

Another (simpler) way of expressing this is:

New.K = (Observed caseload / Expected caseload) - 1

This holds if we don't expect a change in coverage. We can include a change in coverage using something like:

New.K = ((new coverage / old coverage) * observed caseload) / expected coverage) - 1

This is a way of calibrating K from program experience.

(3) This article and this article might be of use. The is a "current topic" in our field and other reports are in press. An international technical working group is being established.

(4) Use what is appropriate. The example above is ... "The available evidence indicates that a single value for K does not exist. There is a need to use a local value for K. I think the only thing to do is to choose a known local K. If there is no known local K then we can pick a value that seems appropriate (e.g. in Southern Niger K hae been estimated to be K = 9 so we might use K = 9 for a program in Northern Nigeria) and then calibrate K using estimates of population, prevalence, coverage, and known caseload". In the absence of useful information then the default value (2.6) could be used.

I hope this is of some use.

### Nitsuh Fikir

Public Health

Normal user

6 Jan 2017, 14:30

Dear Mark,

It's very helpful. Thank you very much for your detailed explanation. I'll read the links you've provided, and more on the subject.