18 Discussion 



usual curves of mortality seen in nearly any disease. Obviously 

 therefore, even in these age-independent causes of death, the aged 

 do not profit from improved conditions. 



Sacher: Your analysis of the curve of deaths into three components. 

 Dr. Benjamin, implies the hypothesis that the population is divided 

 into three mutually exclusive sub-groups, each of which is subject 

 to just one of the three modes of death. An alternative hypothesis 

 is that each individual in the population is subject to all three risks. 

 On this basis one should consider, for each individual at each age, the 

 joint probability of dying of these diseases. The basic actuarial func- 

 tion for the discussion of mortality on this probability model is there- 

 fore the rate of mortality function rather than the curve of deaths, 

 for in this model it is the contingent probabilities, the mortality 

 rates, that combine additively. The multiple risk model seems to me 

 to conform better to our intuitive judgments about the nature of the 

 mortality process. The same data that you analysed in terms of the 

 rate of the curve of deaths can be analysed in terms of the rate of 

 mortality function. The conclusion reached is that one component, 

 identifiable with mortality from infectious disease, has decreased 

 markedly, whereas the component identifiable with mortality from 

 degenerative disease (your senescent mortality) has changed very 

 little. The changes in mortality over a period of a century were 

 assignable primarily to the progressive change in numerical value of 

 two parameters (Sacher, unpublished). 



Gerking: What did you really mean by saying theoretical life- 

 tables are never actually reproduced. Dr. Benjamin ? 



Benjamin: A life-table is made up of a large number of genera- 

 tions, and people who are dying at the older ages have been born a 

 long while earlier, so that it is only a model. You could construct a 

 generation life-table in which you had only the mortality appro- 

 priate to people born at one particular time, but of course it would 

 take a long while to accumulate this data because you would need to 

 follow a generation right through. So the life-table, which is based 

 on a short period of observation, is actually never reproduced 

 because the environmental conditions are changing all the time. The 

 actuary in normal practice merely uses the life-table as a model to 

 indicate the variation of mortality from age to age, to obtain a basis 

 for his calculations ; he makes no claim that it will be reproduced in 

 the future. 



I agree with Sacher that you would have to use rates if you were 

 applying probabilistic theory because that is more fundamental, 

 but it did seem to me to be easier to look at this from the point of 

 view of lifespans by stretching out the curve of deaths. If you did 



