There are several resources available online which are more targeted at hospitals, but the principles apply to an OTP setting. For example: https://apps.who.int/iris/bitstream/handle/10665/279755/9789241515184-eng.pdf

Key things to focus on are procedures for recognition ans referral of a sick child, including whether staff are trained in this (e,g, ETAT) and issues around continuity of care/relationships between the OTP and medical services;  and what were the barriers faced by mothers/carers/famiilies in accessing care. Typically the highest risk children are those with the least access for reasons of geography, finances, and gender related societal factors like decision making and access to resources.

A difficult problem with no easy solution.

I think the following may need some attention ...

(1) Early case identification. If you can do something at admission (i.e. predict a negative outcome with a useful degree of confidence) then you can tailor treatment to avoid a negative outcome or to "watch-list" child ro detect non-response or a deterioration. This requires considerable data. Data analysis techniques and tools for (e.g.) machine learning have advanced making it possible to develop powerful predictive models).

(2) Inter-provider interface could be an issue. Overcoming this will requie investigating the interface and taking improving measures. Multisectoral UNO such as UNICET or UNHCR involved in and funsi=ding many interventions should be able to help you improve interfaces between disparta care-providers. Interface audits might prove useful to help identify, document, and address interface related barriers. I'd be tempted to treat each death of the sort you descrie s sa "critical incident" trigreing an audit.

(3) You could consider expanding the care portfolio. Specialist support units such as inpatient care or stabilisation centers (SC) have been a common part of CMAM programming since it was introduced. If you go this route you need to be sure that you pay attention to case identification issues so that sicking children do not languish in basic CMAM care. Referral between OTP and SC should not be an issue if they are part of the same program.

(4) Coverage is very important to the success of CMAM programming. If you can identify and recruit cassa early in the disease episode then treatment is likely to be more effect and in-care mortality should drop. Good coverage assessment methods are available that can help identify barriers to coverage. You might wat to consider using the "Family MUAC" approach developed by ALIMA to improve timeliness of admission.

(5) I think Jay is correct when he suggests looking at "the barriers faced by mothers/carers/famiilies in accessing care" since it may be possible to address some of these with (e/g/) help with travel or help with costs.

I hope this is of some use.