Determine number of Children treated for period longer than two months in OTP

This will depend on what is included in the district report. I am often frustrated by these reports and have usually addressed such questions by pulling data from OTP registers and OTP beneficiary record cards that fit with the required analysis. In one case (Nigeria) we pulled about 100,000 OTP beneficiary records cards. It was quite an effort but is is do-able. It will not always  be practical if you want o look at a particular district.

If you have mean LOS with a standard deivation then you could use a PROBIT type estimator (not hard to do ... ask here if you need an example) to estimate the proportion with LOS > 2 months but you'd also want to be able to have this data for Uncomplicated SAM cases. You could work with expectations of proportions with uncomplicated SAM and adjust estimates accordingly but this might yield only very approximate results which may be inaccurate if the model used does not match will with reality.

I find the monthly reports tend to be tailored to simple program monitoring indicators and many of these were decided when we had little experience with CTC/CMAM programming.

If you have mean and standard deviation for length of stay then it is quite simple to estimate the proportion of cases with LOS > 2 months uisng the "probit" approach. For example, if:

    mean LOS = 46.22 days
    SD LOS = 22.66 days

We can use the normal distribution to calculate the probability thatany simple LOS is > 61 (c. 2 months) in R:

    pnorm(q = 61, mean = 46.22, sd = 22.66, lower.tail = FALSE)

gives p = 0.2571197 .. so LOS > 61 days like in 25.71% of cases.

In Excel:

    =1-NORM.DIST(61,46.22,22.66,TRUE)
    
gives 0.257119741 which is also 25.71%

You can convert this to number sof children by calculation 25.17% of admissions.

This assumes that LOS is normally distributed.

I you cannot find the SD for LOS then you can make rough guesses using the minimum and maximum values with "range rules" such as:

    mean(x) = min(x) + ((max(x) - min(x)) / 2

    sd(x) = ((max(x) - min(x)) / 4

PRIBIT estimates using mean and sd derived from these rules-of-thumb will be very approximate.

I think one problem is that we do not really know the data to hand is for "uncomplicated cases" only. Maybe needed > 2 months to recover suggests a complication of some kind.

This may take you nowhere!