Skip to main content

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