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Table 5 The effect of group combination on the proportion of deaths identified by X or Y criteria

From: 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

  Total Dead CFR CFR X deaths Y deaths
# # % X/Y % %
Scenario A
X 500 0 0.0    
Y 1500 30 2.0 0.0   
Both X & Y 500 30 6.0    
Total 2500 60 2.4    
All-X 1000 30 3.0   50%  
All- Y 2000 60 3.0 1.0   100%
Scenario B
X 500 6 1.2    
Y 1500 30 2.0 0.6   
Both X & Y 500 30 6.0    
Total 2500 66 2.6    
All- X 1000 36 3.6   55%  
All- Y 2000 60 3.0 1.2   91%
Scenario C
X 500 10 2.0    
Y 1500 30 2.0 1.0   
Both X & Y 500 30 6.0    
Total 2500 70 2.8    
All- X 1000 40 4.0   57%  
All- Y 2000 60 3.0 1.3   86%
  1. In Scenario A, X does not have any mortality by itself, but when the subjects with both criteria are included X and Y appear to have the same mortality rate. Using only criterion X would select those children with zero mortality and those with both X and Y criteria and miss all the deaths related to criterion Y
  2. In Scenario B, there is a lower mortality with criterion X, however when the subjects fulfilling both criteria are included the relative case fatality rates are reversed so it appears now that X is a superior diagnostic parameter than Y. Yet its use only identifies 55% of the deaths
  3. In Scenario C, both X and Y have the same mortality rates but when the subjects with both criteria are included Y appears to be a superior diagnostic criterion. Yet this only leads to identification of 57% of deaths
  4. The columns % deaths shows the percentage of all deaths that would occur in children with criterion X or criterion Y as the single diagnostic tool. Criterion Y identifies more deaths than criterion X, but when the children with both criteria are included criterion X appears to have a higher case fatality rate