Vol. 8 No. 1 Printed in Great Britain
International Journal of Epidemiology © Oxford University Press 1979
A Note on Wong's Competing Risk Model GBERRY 1
Wong (1) proposed a method of adjusting the number of deaths due to other causes if one particular cause of death was eliminated. This method was novel because it took relative susceptibility into account and did not assume independence between competing causes of death. However the aspect of the method with which I am concerned does not concern this point and therefore I will discuss it in terms of independent effects (in Wong's notation
of the equation for d'n , but his approach is similar to that of Kimball (2) which was criticised by several writers (3, 4, 5). It effectively assumes that the deaths from R2 all occurred at the beginning of the time interval before there had been any deaths from Rt or R3, or that all the deaths occurred at the same time. Either assumption seems unrealistic and can be avoided by assuming instead that those who died of R2 survived, on average, for half of the interval. In the absence of any contrary information this seems the most reasonable assumption to make, and it is impossible to proceed without making some assumption. Since those who died of R2 had not died of R\ ot R3 during the part of the interval before they died of R2, then the elimination of R2 would put them at additional risk of dying from R\ or /? 3 for only the part of the interval remaining after they would otherwise have died of R2. This leads to
S,,=l).
Wong defined du, dn, dl3 as the number of deaths from causes R\, R2, R3 in the first interval and /j as the number of people alive at the start of the interval. d'n and d\-$ were defined as the additional number of deaths from causes R\ and R$ if R2 were eliminated. He argued that since dti died of R{ out of /1 — d\i who had not died of R2 then d
du =dn x
n
/, -dn
d
d'u =dn x
and therefore qu ,2 , the partial crude probability of dying from Rt, with R2 eliminated, is given by dn +d'n
,2 11'
0i-dn'2) q 11.2 ~
as suggested by Cornfield (6). Another way of comparing these 2 approaches is in terms of the death rates. Defining m l t as the average death rate from R j in the first interval then with R2 present we have 2dn m n -
Wong obtained a slightly different expression for
International Journal of Epidemiology © Oxford University Press 1979
A Note on Wong's Competing Risk Model GBERRY 1
Wong (1) proposed a method of adjusting the number of deaths due to other causes if one particular cause of death was eliminated. This method was novel because it took relative susceptibility into account and did not assume independence between competing causes of death. However the aspect of the method with which I am concerned does not concern this point and therefore I will discuss it in terms of independent effects (in Wong's notation
of the equation for d'n , but his approach is similar to that of Kimball (2) which was criticised by several writers (3, 4, 5). It effectively assumes that the deaths from R2 all occurred at the beginning of the time interval before there had been any deaths from Rt or R3, or that all the deaths occurred at the same time. Either assumption seems unrealistic and can be avoided by assuming instead that those who died of R2 survived, on average, for half of the interval. In the absence of any contrary information this seems the most reasonable assumption to make, and it is impossible to proceed without making some assumption. Since those who died of R2 had not died of R\ ot R3 during the part of the interval before they died of R2, then the elimination of R2 would put them at additional risk of dying from R\ or /? 3 for only the part of the interval remaining after they would otherwise have died of R2. This leads to
S,,=l).
Wong defined du, dn, dl3 as the number of deaths from causes R\, R2, R3 in the first interval and /j as the number of people alive at the start of the interval. d'n and d\-$ were defined as the additional number of deaths from causes R\ and R$ if R2 were eliminated. He argued that since dti died of R{ out of /1 — d\i who had not died of R2 then d
du =dn x
n
/, -dn
d
d'u =dn x
and therefore qu ,2 , the partial crude probability of dying from Rt, with R2 eliminated, is given by dn +d'n
,2 11'
0i-dn'2) q 11.2 ~
as suggested by Cornfield (6). Another way of comparing these 2 approaches is in terms of the death rates. Defining m l t as the average death rate from R j in the first interval then with R2 present we have 2dn m n -
Wong obtained a slightly different expression for
