Hi Alexander,
LOS is usually expressed in days.
Weight gain is normally calculated as discharge weight minus admission weight (usually expressed in grammes). For oedema cases we can use the 'minimum weight' which is the weight after oedema has resolved; (discharge weight - minimum weight).
The rate of weight gain is expressed in g / kg / day. Thus the rate of weight gain would be:
(Discharge weight - Admission weight in g) / admission weight in kg / LOS in days
The rate of weight gain for an individual child would consider the admission weight in SC and discharge weight in OTP for the purposes of calculation. The whole episode is considered a continuum of care.
It should be noted that the discharge criteria from SC to OTP for children aged 6 - 59 months do not consider any weight criteria for children. Discharge is based on appetite, clinical status and evidence of decreasing oedema. During SC it is typical for a child to be treated with F75 milk and (in some cases) F100 (at 130 kcal / kg / day). Weight gain is not the aim of treatment in Phase 1 and only small weight gains may be observed in transition phase (or weight loss with any reduction in oedema) prior to transfer to OTP. It is of little use to calculate the rate of weight gain for a child for SC alone.
However if the child is recovered in the inpatient setting then we can calculate the rate of weight gain for the whole treatment episode in the same way as above (using admission weight or minimum weight for marasmus or oedema cases respectively).
For a community based programme minimum rates of weight gain should be greater than 5 g / kg / day
For inpatient care the minimum rate of weight gain should be equal or greater than 8g / kg / day
It should also be noted that we would normally only calculate and report the rate of weight gain for recovered cases (not for other treatment outcomes).
The updated SPHERE guidelines (2011) continue to recommend the average weight gain of marasmus and oedema cases be calculated separately. However references to standards for rates weight gain appear to have been removed (perhaps others can enlighten this). The minimum rates of weight gain indicated above were previously used as a sphere standard (for inpatient) or as a commonly accepted operational standard (for OTP). However they may still act as useful (albeit debatable) benchmarks for your study.
There are currently no recommendations regarding MUAC gain although some studies have reported observed rates of MUAC gain. It has been suggested that changes in MUAC are too small from week to week to be accurately captured. This may change in the future wit the development of more reliable methods to measure MUAC.
Your last question is a little more complex but I would ask the question as to why you are interested in the 15% weight gain criterion as a benchmark for your study? This criterion has fallen into disuse following the findings of researchers and updated WHO guidelines (2013) recommending that this criterion is no longer used. With fixed discharge cut offs using WFH or MUAC criteria we see that the child will generally stay in the programme longer in proportion to the degree of malnutrition on admission (the more severely malnourished they are, the longer they stay). There are articles / publications which suggest that the rate of weight gain or MUAC gain during recovery reach an asymptote and then decrease but the trajectory of weight gain (or MUAC gain) appears to differ between individual children.
I hope this helps
Paul