cases of permanent and total disability. In a later article in the same publication on "The Rate of Mortality among Totally and Permanently Disabled Lives Analyzed according to Duration since Time of Disability," 14 Mr. Mead made an investigation of the duration of time between disability and death and included data from the Knights of the Modern Maccabees embracing 245 invalids and 162 deaths, and from the Royal League embracing 1,972 invalids and 1,126 deaths, as well as the data of the Maccabees of the World, already referred to; a total experience of 5,144 invalids and 2,361 deaths.

McAdam's and Hunter's Rates

All the studies of disability made thus far have been based on the experience noted above. Mr. Arthur Hunter and Mr. Lucius McAdam* have both calculated tables. Mr. McAdam has used Mr. Mead's rates of disability and of mortality among disabled persons except for a slight correction from ages 69 to 80, and from them has computed premium rates both for the waiver of premium benefit and for the benefit of maturing the policy and paying it in installments, using for his purpose a different and simpler actuarial method than had previously been used. Into this actuarial problem it is not desired to enter here. Mr. Hunter's tables are generally credited among actuaries as being the best suited for measuring the risk involved. In fact they have already been made the basis for the valuation of policies with the disability clause in the state of New York. Mr. Hunter used for his purpose the data of the Foresters and the Maccabees which had previously been utilized by Messrs. Mead, Pipe and Landis. The difference in his treatment consists in the introduction of two "factors of safety." In the first place, he explains that net premiums should be calculated on an "ultimate" table of disability, that is, one from which the early policy years have been excluded. He presents the following table1 of experience of the first five policy years in support of his position:

14 Vol. 12, p. 75.

*Now deceased.

15 Transactions Actuarial Society of America, 12:47.

DISABILITY EXPERIENCE OF FIRST FIVE POLICY YEARS MEASURED BY THE

This table shows that the rate of disability among newly selected risks is much smaller than after a policyholder has been a member of the society for several years, the ratio of the actual to the expected rate of disability being only 10 per cent the first year after the policy has been written and not equalling the expected rate until after the fourth year of the life of the policy has been passed. The table therefore clearly demonstrates that from the standpoint of safety it is advisable to eliminate the experience of these first four policy years. The tables by Messrs. Mead and Pipe were "aggregate" tables, that is, they included in their data the experience of these early years.

The second "factor of safety" introduced by Mr. Hunter refers to the question whether, in dealing with the death rate among disabled persons, a "select," an "ultimate" or an "aggregate” table of morality should be used. A "select" table would show the rate of mortality in its relation to the time elapsed since disablement has taken place. For instance, it would distinguish the death rate at age 40, among persons disabled at age 35, from the death rate at age 40 among persons disabled at age 39. In other words, it would show the effect upon the rate of mortality produced by the time which has elapsed since disability occurred, and it is composed of "select" rates of mortality for the several years immediately following disability. An "ultimate" death rate, like the "ultimate" disability rate first mentioned, eliminates these first years; in this case, the years immediately following the occurrence of disability and not, as in the case of "ultimate" disability, the years following the writing of the policy. The "aggregate" death rate represents the rate of death among disabled persons at each age regardless of

whether the experience includes mostly persons just disabled or those disabled for many years; and in computing it the complete data at hand for deaths at each age is included and no notice is taken of the duration of disability prior to death. Messrs. Mead and Pipe had used such an aggregate death rate. This is theoretically incorrect, because the death rate which will be experienced under the operation of the disability clause and which will determine how many premiums are to be paid by the insurance company is the death rate which results immediately after the occurrence of disability. An aggregate death rate, which, in the data for a particular year, does not note whether the data are of the first year after disability or of some other year; or an ultimate rate, which eliminates the first years after disability, are clearly incorrect. Mr. Hunter analyzed the data at his disposal to determine the "select" rate of death among disabled lives. The following table showing his results for each fifth year demonstrates that the rate of mortality is very high immediately after disability and decreases rapidly: 16 RATES OF MORTALITY AMONG EACH 1,000 DISABLED LIVES

Mr. Hunter concluded, however, after having thus analyzed his data, that premiums based upon "select" death rates involved so much calculation as to be impractical and that an "aggregate" rate could be obtained which would be just as safe, by eliminating from the aggregate experience the deaths of the first policy year following

16 Op. cit., p. 51.