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% |