Severely malnourished children with a low weight-for-height have a higher mortality than those with a low mid-upper-arm-circumference: I. Empirical data demonstrates Simpson's paradox.

Background: According to WHO childhood severe acute malnutrition (SAM) is diagnosed when the weight-for-height Z-score (WHZ) is <-3Z of the WHO standards, the mid-upper-arm circumference (MUAC) is < 115 mm, there is nutritional oedema or any combination of these parameters. Recently there has been a move to eliminate WHZ as a diagnostic criterion on the assertion that children meeting the WHZ criterion are healthy, that MUAC is universally a superior prognostic indicator of mortality and that adding WHZ to the assessment does not improve the prediction; these assertions have lead to a controversy concerning the role of WHZ in the diagnosis of SAM.

Methods: We examined the mortality experience of 76,887 6-60 month old severely malnourished children admitted for treatment to in-patient, out-patient or supplementary feeding facilities in 18 African countries, of whom 3588 died. They were divided into 7 different diagnostic categories for analysis of mortality rates by comparison of case fatality rates, relative risk of death and meta-analysis of the difference between children admitted using MUAC and WHZ criteria.

Results: The mortality rate was higher in those children fulfilling the WHO WHZ criterion than the MUAC criterion. This was the case for younger as well as older children and in all regions except for marasmic children in East Africa. Those fulfilling both criteria had a higher mortality. Nutritional oedema increased the risk of death. Having oedema and a low WHZ dramatically increased the mortality rate whereas addition of the MUAC criterion to either oedema-alone or oedema plus a low WHZ did not further increase the mortality rate. The data were subject to extreme confounding giving Simpson's paradox, which reversed the apparent mortality rates when children fulfilling both WHZ and MUAC criteria were included in the estimation of the risk of death of those fulfilling either the WHZ or MUAC criteria alone.

Conclusions: Children with a low WHZ, but a MUAC above the SAM cut-off point are at high risk of death. Simpson's paradox due to confounding from oedema and mathematical coupling may make previous statistical analyses which failed to distinguish the diagnostic groups an unreliable guide to policy. WHZ needs to be retained as an independent criterion for diagnosis of SAM and methods found to identify those children with a low WHZ, but not a low MUAC, in the community.