Skip to main content

Table 3 The effect of mathematical coupling on the interpretation of CFR and possibility of Simpson’s paradox

From: Severely malnourished children with a low weight-for-height have similar mortality to those with a low mid-upper-arm-circumference: II. Systematic literature review and meta-analysis

Study Author & year Single deficits alone    Single and both deficits    Difference WHZ-MUAC
S-whz S-muac S-whz v S-muac All-whz All-muac All-whz v All-muac S-whz-S-muac All-whz-All-muac Effect on CFR
CFR CFR χ2 Fisher Cramer CFR CFR χ2 Fisher Cramer
% % p p   % % p p     
1 Aguayo 2015 0.23 0.23 nc (0.96) 0.00 0.58 0.61 0.81 nc 0.00 −0.01 −0.04 >All
2 Grellety 2012 1.69 1.20 nc 0.73 0.02 3.03 2.83 0.88 0.880 0.01 0.50 0.20 >S
3 Grellety 2015 0.87 4.76 nc (0.19) 0.05 1.79 3.76 0.002 nc 0.06 −3.89 −1.97 >S
4 Isanaka 2015 0.57 0.43 nc (0.68) 0.01 0.61 0.54 0.77 nc 0.01 0.14 0.08 >S
5 Lowlaavar 2016 6.43 0.00 nc 0.14 0.10 9.13 10.99 0.61 0.607 0.03 6.43 −1.86 Reverse
6 LaCourse 2014 6.90 5.88 nc 0.83 0.02 6.67 5.95 nc 0.860 0.01 1.01 0.71 >S
7 Olofin 2016 15.52 13.25 0.52 0.52 0.03 28.52 19.51 0.002 nc 0.10 2.27 9.01 >All
8 Berkley 2005 10.11 10.94 0.74 0.74 0.01 19.97 19.01 0.63 nc 0.01 −0.83 0.96 Reverse
9 Chiabi 2017 4.35 14.29 nc 0.31 0.17 22.35 25.30 0.65 0.659 0.03 −9.94 −2.95 >S
10 Sachdeva 2016 7.89 20.00 0.004 0.005 0.17 11.83 18.72 0.021 0.023 0.09 −12.11 −6.89 >S
  1. S-whz WHZ below cut off point with MUAC above cut-off point as defined in the paper, S-muac MUAC below cut off point with WHZ above cut-off point as defined in the paper, All-whz WHZ below the cut-off point, with MUAC either above or below the cut-off point as defined in the paper, All-muac MUAC below the cut-off point, WHZ either above or below the cut-off as defined in the paper, S-whz–S-muac (single deficit) WHZ minus MUAC CFR, All-whz – All-muac (combined deficits) WHZ minus MUAC CFR, CFR Case Fatality Rate in percentage; χ2 significance of Chi-squared analysis of MUAC against WHZ CFRs; Fisher Fisher’s exact test, two-sided mid P-value (values in parentheses are approximate as one cell number too large); Cramer Cramer’s V of association between variables; “>All” the difference in CFRs between WHZ and MUAC is greater with All-whz/muac; “>S” the difference is greater with S-whz/muac; “Reverse” the direction of the change is reversed (Simpson’s paradox), negative numbers WHZ < MUAC, positive numbers WHZ > MUAC. Significant differences are shown in bold script