CHAPTER V RATES OF WITHDRAWAL AND SICKNESS ALL the investigations that we have described up to the present have been made with the object of finding the rates of mortality that have been experienced, but it is sometimes necessary to find rates of withdrawal or sickness. Rates of withdrawal are generally required in connection with industral insurance, friendly society business, or pension funds, and the methods are in principle the same as those already discussed, except that as we are working out withdrawal rates we must interchange " withdrawal" and " death " through- out the description of our work. In other words, the duration of the deaths will be given as an approxima- tion to the exact duration—e.g. nearest duration— while withdrawals will now be shown according to the number of complete years in force (curtate duration). In practice, when rates of withdrawal are calcu- lated it is usually desired to get out the rates of mortality from the same experience, and if one of these methods is used, without modification, it follows that all the cases of withdrawal and death must be tabulated both according to nearest duration and 40 RATES OF WITHDRAWAL AND SICKNESS 41 curtate duration, and thus require to be dealt with twice over. As, however, rates of withdrawal are not often required very accurately, it is generally sufficient to obtain approximately the exposed to risk of with- drawal from the exposed to risk of death. The method will naturally depend on that adopted to obtain the rates of mortality, and may be illustrated by reference to the approximation given on pp. 30, 31. We saw that as a first approximation we can assume that the average duration in the final year of each withdrawal is 6 months. The same assumption can be made with at least equal accuracy for deaths, and the exposed to risk of withdrawal at duration 5, for instance, is therefore the exposed to risk of death at duration 5 decreased by half the deaths and increased by half the withdrawals at duration 5. The adjustment in other cases may become rather more complicated if it is desired to investigate the experience according to duration, and it is often more convenient to use the same approximation in calculat- ing both rates of death and withdrawal. For instance, adopting the assumption that deaths and withdrawals occur evenly over each year of duration and tabulating both according to " curtate " duration, we can calculate a special mean exposed to risk by including in the exposed to risk in any year one-half of both the deaths and withdrawals in that year. The addition to this figure of one-half the deaths will give us the exposed to risk of death, and the addition to the same figure of one-half the withdrawals will give us the exposed to risk of withdrawal. There is no distinction in principle between finding 42 MORTALITY AND SICKNESS TABLES rates of mortality and rates of withdrawal, but when we come to deal with rates of sickness we have to remember some points in which such investigations differ from mortality and similar investigations. In the first place the "rate of sickness" is not strictly analogous to the rates of mortality and withdrawal. It is not the ratio of the number of persons falling sick within one year from the attain- ment of a specified age to the number who were under observation for one year from the attainment of that age. This ratio, which we may call the " rate of incapacitation," is often very useful, but it is not what is commonly known as the " rate of sickness." The latter function depends on the number of weeks sickness, and has sometimes been taken as the ratio of the number of weeks of sickness to the number alive at the beginning of the year. The exposed to risk by this method is the same as the exposed to risk of death. The accepted definition at the present time of the rate of sickness at any age is the average number of weeks sickness experienced by those under observation during one whole year following the attainment of that age, and is found by dividing the total number of weeks sickness at any age by the average number alive during the year. This last number may be calculated in the same manner as the special mean exposed to risk of p. 41, or by tabulat- ing all the deaths and withdrawals according to their nearest duration, as an approximation to the exact duration, the effect of either method being to observe cases of death and withdrawal up to the date of death or withdrawal, and not up to the end of the year. RATES OF WITHDRAWAL AND SICKNESS 43 The rate of sickness is very important in friendly society work, as the allowance in sickness is a payment, usually weekly, during incapacity, and not merely a sum down for each illness. It is for this reason that we require to work on the basis of the amount of sickness, and not on the number of people falling sick. We must also remember that a person may receive sickness benefit several times, and does not necessarily pass out of observation after once receiving benefit, as he does of course in the case of a mortality experience. In consequence of these differences, investigations have to be made on slightly modified lines, and it is necessary to record how many weeks' payments have been made in each case. A further complication arises in practice, because friendly societies pay a scale of benefits varying with the duration of the illness. These scales vary considerably. Under the National Insurance Act, 1911, for instance, there is no benefit for the first three days of sickness; then sickness benefit is allowed for 26 weeks, and subsequently a " disablement benefit" of a reduced amount is paid —" disablement" benefit being another name for reduced sickness pay. Some friendly societies grant benefits which decrease at the end of 3 months, again at the end of 6 months, and perhaps again at the end of 12 months, but it will suffice if we deal with the rates of sickness in two groups only, namely, "first 26 weeks' sickness " and " subsequent sickness "—the principle being the same if there are more sub- divisions. 44 MORTALITY AND SICKNESS TABLES As a consequence of the practice of reducing the sickness benefit in this way it is necessary to calculate the rate of sickness for each period of attack, and in our final table we shall have a series of columns showing for each age the rate of first period sickness, i.e. the average number of weeks per person during which the full sickness benefit was paid; second period sickness—i.e. the average number of weeks during which the first reduced benefit was paid ; and so on. In making investigations into sickness rates a different form of card is used from that adopted for mortality investigations, and the specimen opposite will be found to give the information required. If we are dealing with the experience of a single society granting the same benefits to all its members, the columns for the dates on which sickness began and ended may be dispensed with, and the figures in the columns for first 6 months and subsequent sickness will be the number of weeks' full and reduced pay respectively, shown against the members' names in the society's claim register. For a larger or more varied experience, however, the former columns are necessary, and the sickness in each period will be calculated from an inspection of the dates there recorded. In this connection it is necessary to notice a very usual rule among friendly societies, that any illnesses not separated by a fixed minimum period (for Approved Societies under the National Insurance Act it is one year) are treated as though they were continuous for the purpose of deciding what benefit is to be paid. In the case of any illness, therefore, the sickness benefit RATES OF WITHDRAWAL AND SICKNESS 45
Name Occupation
Member's Number
Date of Birth „ Entry „ Freedom „ Exit
Age at Entry „ Exit Mode of Exit
Tear.
*^e- Began. Ended. Flrat 8ix Montht.
Illness Illness
Sickness.
Weeks. Days. Weeks. Days.
Thereafter.
NOTE.—In nearly all friendly societies no sickness benefit is allowed until after the expiration of a certain period, and the date of freedom means the date when such allowance may begin, 46 MORTALITY AND SICKNESS TABLES
paid may have been that for either the first or second period or for both, and the number of weeks' sickness in respect of that illness may run over several ages. As an example, let us suppose a man born 8th August 1884 to have had the following sickness experience:— Fall 111. Recovered. 12th January 1909. 13th April 1909. 10th November 1909. 10th March 1910. 6th February 1911. 6th March 1911.
4th April 1912.
Recovered. 13th April 1909. 10th March 1910. 6th March 1911. 13th January 1913.
If the rules of his society provide for 6 months' full benefit and reduced benefits thereafter, with an "off" period, as it is called, of 52 weeks, the actual benefit paid by the society would be as follows:— TABLE XIV
1 Benefit is commonly paid in respect of working days only. This should be remembered in reading the following Table XV.
RATES OF WITHDRAWAL AND SICKNESS 47 The manner in which this is entered on the ex- perience card will depend on the method adopted in investigating the experience and calculating the exposed to risk. Let us assume that the experience of the five years 1909-1913 is under investigation and that nearest ages are dealt with—the member coming into the experience on 1st January 1909 at his then nearest age. Bearing in mind that this is an ap- proximation to the exact age, so that we must assume age 25 to be attained on 31st December 1909, age 26 on 31st December 1910, and so on, we see that the following entries (Table XV) must be made on the card:— TABLE XV
48 MORTALITY AND SICKNESS TABLES These entries can be very easily understood. The assumption of the nearest age at 1st January 1909 leads to the further assumption that calendar years and years of age are concurrent, so that we simply require to calculate the amount of sickness of each period occurring in each calendar year and enter the result on the card against the appropriate year of age. Thus we have assumed that the man in question was 24 last birthday throughout 1909, 25 last birth- day throughout 1910, and so on. In 1909 he had one illness of 13 weeks, and a second illness, which lasted during the last 7 weeks and 2 days of that year and continued for 9 weeks and 5 days in 1910. The amount of " first period sickness " at age 24 was thus 13 weeks plus 7 weeks 2 days, or 20 weeks 2 days, and, as less than one year separated these attacks, 5 weeks and 4 days only (the balance of the 26 weeks sickness payment allowed) of the continued illness at age 25 in 1910 would be paid for at the full rate, the balance of 4 weeks and 1 day being paid for at the reduced rate. The third illness occurred in 1911, within 12 months of the second, and reduced pay only was received, therefore, through- out its duration of 4 weeks, which must be entered against age 26 on the card. The last illness com- menced more than 12 months after the expiration of the previous sickness and full benefit was again due for 26 weeks; it continued for 38 weeks and 4 days in 1912 and for 1 week 5 days at the beginning of 1913. We must therefore record 26 weeks at full pay and 12 weeks 4 days at reduced pay against RATES OF WITHDRAWAL AND SICKNESS 49 age 27, and 1 week 5 days of reduced pay against age 28. r / & One special point requires mention in connection with the apportionment of the sickness among the different periods of attack. As the experience of five calendar years only is being investigated, we shall find that the payments made during the first illness re- corded on some of the cards will be affected by previous illnesses, and a special note must be made of such cases. This can generally best be effected by placing a mark against the date of commencement of such illness, when the card is written, with a note at the bottom of the card pointing out the exact circum- stances. Attention would be drawn to such cases when the cards are written by the fact that reduced sickness benefit would have been paid either from the commencement of such illness or before it had con- tinued for 26 weeks. When dealing with mortality investigations we explained that the number of deaths, withdrawals, etc., at each age or duration could be found by sorting the cards and counting them, but when judging the total amount of sickness at each age to be compared with the exposed to risk, a little more trouble has to be taken, because one card may give sickness for various ages. If the experience extends only over a few years the difficulty can be met by filling up all other particulars and then separating the cards on which any sickness is shown. These can then be sorted according to the first age at which sickness appears, and the total amount of sickness found by addition either by sight or, if the numbers are large, 4 50 MORTALITY AND SICKNESS TABLES by an adding machine and then carrying forward each card to the next higher age where sickness is shown. In many cases where the experience is large, auxiliary sheets will have to be used for tabulating the sickness. As an illustration of the calculation of the rate of sickness we may take the last example in Chapter IV, the further particulars required being shown in Table XVI. Columns 2, 3, 4 and 6 of Table XIII are omitted to save space, but it will be noticed that we could calculate rates of mortality and sickness in the same table. TABLE XVI
As already explained, the " deaths " are given their exact duration in calculating the exposed to risk of sickness, and this will include on the average half a year's exposure in the year of death. Each such case
RATES OF WITHDRAWAL AND SICKNESS 51 is counted for a full year in the exposed to risk of death, and we must therefore deduct one-half of the figure in column (3) from the figure in column (2) at each age. The result is given in column (4). The figures in columns (5) and (6) are obtained, as shown above, by adding up the total sickness at each age recorded on the cards, and the rate of sickness for the different periods is found by dividing these figures by the figures in column (4). The practice of the different friendly societies varies considerably, and a number of conditions modifying the payment of a sickness benefit are met, each of which necessitates some modification of the methods outlined in this chapter. For instance, sickness benefit is frequently not allowed for the first six months of membership, but a death benefit may be payable although the member die within the six months. In this case each new entrant would enter into the exposed to risk of death and withdrawal at entry, but would not enter into the exposed to risk of sickness until six months later, and the method of working has to be modified. Other rules of a more troublesome nature may also occur, but if the funda- mental principles of calculating the exposed to risk are borne in mind, no difficulty should arise in any individual case.