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Table 1 Simple example of ten hypothetical death records with four possible causes of death labelled A, B, C and D. The example shows the calculation of weights using the data driven and arbitrary methods, and the comparison of the methods

From: A new data driven method for summarising multiple cause of death data

I: Ten hypothetical death records

Record ID

UCoD

CCoDs

1

A

 

2

A

A

3

A

B

4

A

B C

5

A

A C

6

B

A D

7

B

C D

8

C

A C A

9

D

B C

10

D

A B C

II: Data driven weights

Step 1: Calculate of the number of CCoDs associated with each UCoD, across all 10 records divided by the frequency of the UCoD, but this is zero if the CCoD is the same as the UCoD

UCoD

Frequency of UCoD

CCoD

  

A

B

C

D

A

5

0/5

2/5

2/5

0/5

B

2

1/2

0/2

1/2

2/2

C

1

1/1

0/1

0/1

0/1

D

2

1/2

2/2

2/2

0/2

Step 2: Calculation of data driven weights for each cause

For each CCoD that is different from the UCoD, weight = (number from Step 1)/(number of CCoDs in record) (that are not the same as the UCoD)

For UCoD, weight = 1 – sum of weights for CCoDs

Record ID

UCoD

CCoDs

# of CCoDs

Data driven weights for each cause

    

A

B

C

D

1

A

 

0

1

0

0

0

2

A

A

0

1

0

0

0

3

A

B

1

1-(2/5) = 3/5

(2/5)/1 = 2/5

0

0

4

A

B C

2

1-(1/5)-(1/5) = 3/5

(2/5)/2 = 1/5

(2/5)/2 = 1/5

0

5

A

A C

1

1-(2/5) = 3/5

0

(2/5)/1 = 2/5

0

6

B

A D

2

(1/2)/2 = 1/4

1-(1/4)-(1/2) = 1/4

0

(2/2)/2 = 1/2

7

B

C D

2

0

1-(1/4)-(1/2) = 1/4

(1/2)/2 = 1/4

(2/2)/2 = 1/2

8

C

A C A

1

(1/1)/1 = 1

0

1–1 = 0

0

9

D

B C

2

0

(2/2)/2 = 1/2

(2/2)/2 = 1/2

1-(1/2)-(1/2) = 0

10

D

A B C

3

(1/2)/3 = 1/6

(2/2)/3 = 1/3

(2/2)/3 = 1/3

1-(1/6)-(1/3)-(1/3) = 1/6

III. Arbitrary weights, if UCoD has weight p = 1/2 and there is equal allocation across all unique CCoDs

Record ID

UCoD

CCoDs

Arbitrary weights for each cause of death

   

A

B

C

D

1

A

 

1

0

0

0

2

A

A

1

0

0

0

3

A

B

1/2

1/2

0

0

4

A

B C

1/2

1/4

1/4

0

5

A

A C

1/2

0

1/2

0

6

B

A D

1/4

1/2

0

1/4

7

B

C D

0

1/2

1/4

1/4

8

C

A C A

1/2

0

1/2

0

9

D

B C

0

1/4

1/4

1/2

10

D

A B C

1/6

1/6

1/6

1/2

IV: Comparison of contributions of causes of death

 

A

B

C

D

UCoD only

50.00%

20.00%

10.00%

20.00%

Data driven weights

52.17%

19.33%

16.83%

11.67%

Arbitrary weights, with p = 1/2

44.17%

21.67%

19.17%

15.00%