On 30 April 1984 a discussion took place on the Continuous Mortality Investigation Report, number 7, which investigated the “Sickness Experience in 1975–78 under Individual PHI Policies”.

ABSTRACT OF THE DISCUSSION

Mr R. H. Plumb: It is my task to introduce on behalf of my colleagues the discussion on the Continuous Mortality Investigation Report, number 7, dealing with the Sickness Experience on Individual PHI policies for the years 1975–78. It has been a matter of deliberate policy to continue this report along the lines of that published in number 4. The sub-committee realized that it was necessary to anchor the research on firmer ground and that is why we have repeated the use of the 1975 data in our report. It is an important move in that we have used a sub-set of the data available to graduate and produce our main results. The experience exhibited by what we have termed standard data was markedly different from the entire data.

This report has been constructed with the aim of providing an overall view of the experience and its subsequent analysis. We have therefore included some theoretical explanations of our views, especially in Section 4 and Appendices F & G. The graduations and results we have obtained should be of some use in formulating PHI premium rates and reserves.

I would have liked to be able to announce the introduction of a new standard table to replace Manchester Unity, but this is not the case and as such is a disappointment to all of us. The sub-committee discussed this point at length on many occasions and we agreed unanimously that the publication of such a table would be premature. When it is eventually produced, I would point out to the offices and the authorities that there is a very wide variation in sickness experience between offices, and I do not mean just ± 10% (see § 1.5).

Section 3 deals wih the subject of female experience. The sub-committee does and can only report on the sickness experience of female policyholders. Everybody is asked to read and judge the results for themselves.

Alongside the main thrust of the investigation into the underlying shape and construction of working models of sickness experience we have also been considering specific sub-sets of the data. The results are tabulated in Section 7. We have been able to draw few firm conclusions, but the results emanating from business in the Republic of Ireland are significant in that possible over-insurance could be a factor in this area.

These results and views have considerable validity in today’s environment. We are at long last getting to grips with the concepts of Manchester Unity and almost certainly will need to change our minds towards the use of inception rates and disability annuity values. It is heartening to see that the graduation of inception rates has been so much easier than other things.

I must utter one note of caution about the report, The bland and slavish application of these results in other elements of the PHI and waiver of premium industry will lead to unprofitable business. There is thought to have been a worsening of sickness experience since 1978, and we shall return to the effect of the economic recession in future publications.

Our next task is to examine claims by cause of disability, to assemble disability annuity values and to report on group business.

Mr T. A. Sibbett (opening the discussion): In the introduction to the paper the sub-committee refer to earlier doubts about the reliability of the 1972–75 data, and have now decided to disregard the first 3 years of that period. The report before us covers the 4 years 1975–78, and introduces the distinction between the aggregate experience and the standard experience.

The sub-commmittee’s target was to produce a standard experience table for practical use, but this has not yet been achieved. A careful analysis of data and methods led the sub-committee to doubt whether the Manchester Unity type framework would ever enable them to produce a standard table for general use. The North American practice of using claim inception rates and disabled life

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annuities is now favoured. It would be helpful to know how long it is likely to be before a table for practical use can be produced by the American, or any other, method.

In Table 1.1 the number of policies exposed-to-risk for the medical evidence unknown group fell from approximately 110,00–85,000 over 4 years; that is at a rate of 6½% per annum. If this is typical of withdrawal rates as a whole for individual PHI business, then in the long term there may be quite significant implications for the sickness experience.

Table 1.2, which deals with claims, has an item ‘Benefit rate changed’ under the heading of ‘Mode of commencement’ of claims, and a further item ‘Benefit altered’ under the heading ‘Mode of cessation’ of claims. Presumably these are merely descriptive items and any change or alteration of benefit does not cause a claim to be regarded as terminated, or a new claim to be regarded as commenced, in any of the tabulations of data referring to policies.

The earlier report, C.M.I.R. 4, voiced the suspicion that policies effected for longer deferred periods have lighter sickness rates than policies for shorter deferred periods when the same periods of sickness are investigated. This is confirmed for the standard male experience in the current report. When this feature becomes incorporated in PHI premium rates, the change in the relative prices of policies may alter some prospective policyholders’ choice of deferred period, and hence the future experience may alter. Further, it will not be satisfactory where, for example, a person holds two policies with different deferred periods, if the risk for similar periods of sickness in each policy is charged at different rates.

In view of present interest in the comparative levels of male and female sickness, I shall consider the historical background.

In 1662 John Graunt in his work on bills of mortality observed “. . . I have heard physicians say, that they have two women patients to one man, which assertion seems very likely.” Nearly 200 years later, in 1854, Mr A. G. Finlaison, the Actuary of the National Debt Office, in a report to the House of Commons, wrote: “In respect of the sickness incidental to female members of Friendly Societies, there is much reason to believe that it is heavier in amount than that undergone by the males.” In 1911, the committee of actuaries recommended the Government to use the same sickness rates for men and women. In 1918, as a result of adverse experience, the portion of the National Insurance contributions for women paid to Friendly Societies’ benefit funds in respect of sickness was increased, and the Women’s Equalization Fund, which lasted 4 years, was set up. In 1921, 1924 and 1927, unmarried women’s sickness rates for the insured population at durations over 6 months were 172, 160 and 177% of the corresponding figures for men. For married women the ratios were greater. In the 1950s and 1960s the annual Digests of Statistics Analysing Certificates of Incapacity produced by the then Ministries of Health and Social Security show by age and duration much higher proportions sick in respect of married and other women than for men.

The comparison of female sickness rates with those of men has frequently been controversial. There are almost always reasons why any particular experience being examined may not be typical of all women or all insured women, as a small part of the data often looks anomalous and there can be quite wide fluctuations. Nevertheless, in the United Kingdom the picture as a whole points persistently, if sometimes erratically, in the same direction.

The standard female experience falls into the same pattern. The number of policies at risk is small, ranging from about 7,800 at the beginning of the period to about 12,400 at the end. The actual weeks of sickness observed were 16,465 compared with 8,335 expected on the basis of the standard ungraduated male experience. The data have been extensively analysed in order to ascertain if there is any distortion of the results caused by different weightings of average age and distribution of exposed-to-risk in comparison with men. There appears to be no such distortion,

The lower percentages at each end of the range in Table 3.3 suggest that the shape of female sickness rates may be different from that of men, although this feature was not so marked in the previous report. In the longer term, separate tables of sickness rates for women are desirable. In order to produce these tables, a period of observation longer than 4 years should be acceptable, provided this did not span a time of comparatively rapid changes in the rates of claim and in the duration of sickness. In the shorter term it may be desirable for the market to consider whether the current ad hoc adjustments made to PHI premium rates to reflect female morbidity are consistent with the results of this and other investigations.

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In Section 4, which deals with technical aspects of the Manchester Unity method, the importance of durational effects is stressed. The sub-committee comment that separating the 104/all claims into 3rd, 4th and 5th year, etc., claims would cause the resulting data to be subdivided to an extent which would make analysis and graduation difficult. This problem is not confined to a Manchester Unity method modified to produce extensive age and duration specific sickness rates. Under the alternative American method a separate disability annuity value is required for each year of age and each period of sickness in order to be able to value policy liabilities in respect of claims. It is impractical to wait 20 years or more to calculate the sickness rate or to estimate claim termination rates by recovery for each separate year of sickness. Quite apart from the problems of paucity of data mentioned in the paper, the passage of time and new medical methods of treating sick persons would render the resulting sickness tables inappropriate for use in calculating premium rates. There are currently many advances in all forms of medicine which are likely to continue in future and may significantly alter sickness rates, although whether the net effect of these medical advances will be to increase sickness rates as a result of persons who would otherwise have died being kept alive but unwell for long periods, or whether sickness rates in total will reduce, is not clear. It may be necessary, for practical purposes, to adopt either implicitly or explicitly age and duration specific sickness rates which include a degree of subjectivity at these financially important longer durations.

It is apparent, after consideration of the sub-committee’s analysis, that the z function as currently calculated is not independent of withdrawals in past years for the period of sickness 52/52 and longer periods. This lack of independence results in zx being numerically larger than it would otherwise have been. It may be that this feature compensates in a haphazard way for the missing durational effect and could explain why the Manchester Unity method seems to have worked in practice for most of this century.

The sub-committee’s analysis, demonstrating that the features concealed by an unmodified Manchester Unity method can cause problems of misinterpretation, is persuasive. It is, however, not absolutely clear that using the American approach will enable the problems to be solved in a completely satisfactory manner.

The sub-committee members did a large amount of work in the area of the graduation process, and they explain the problems and conclusions in considerable detail.

Technically, the final graduations of zx were not entirely satisfactory. In particular, the combined 104/all data did not graduate satisfactorily as a single curve, and two curves joining at age 48 were used. The graduated sickness rates for differing deferred periods were compared with the rates for the deferred period of 1 week in Table 6.3. Some of the ratios seem, intuitively, to be different from what might be expected. However, the individual tables of graduated data, when considered alone, seem to be sufficiently smooth and satisfactory.

A feature of the specimen net premium reserves is the sensitivity of the reserves to the shape of the sickness curve. The reserves at some durations for particular policies can exceeed 100% of the corresponding reserves calculated on Manchester Unity, A.H.J., even though the net premiums are less than 70% of the Manchester Unity A.H.J. net premiums. When the CMI sickness experience becomes more mature and the durational effect is fully included, the shape of the reserves is likely to change.

In 1982, the Economic and Social Research Institute in Dublin reported Irish sickness absences to be double those of the U.K. The investigation of Irish policies in the sub-committee’s paper shows, as did C.M.I.R. 4, higher sickness rates than for the corresponding U.K. contracts. The differences are much less marked than those in the corresponding national data and this no doubt arises from careful underwriting practices in the Republic.

U.K. policies with an occupational loading show sickness rates nearly twice as large as those of the standard male experience.

The occupationally loaded category of U.K. policyholder and the standard Irish policyholders are currently sold policies at premium rates which seem to be low in comparison with those of the U.K. Class 1 category when the differences in the sickness rate ratios ar taken into account.

It would be reassuring if the experienced sickness rates in the U.K. do not vary significantly according to the policy termination age, and I should like to know if the sub-committee can give any information on this feature.

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Mr R. H. Daw: For many years I have been concerned with the effect of duplicate policies in mortality data and the lack of much real knowledge of their extent. I was therefore pleased to find in Appendix F a discussion of the effect of duplicates in relation to sickness data and to see some figures. However, my pleasure was reduced by the text which said that some indications were obtained of the numbers of duplicates and that these took the form of estimates of the number of first, second, third and subsequent policies. Thus it is clear that the breakdown set out in Appendix F has not been arrived at by a complete analysis of the total inceptions. Until something is known about the accuracy of the figures it is a waste of time to consider whether a geometric progression gives a good enough fit to use in estimating the likely effect of duplicates on the variance of inception rates.

Appendix F deals only with the effect of duplicates on the variance of inceptions; there remains the more important question of their effect on sickness. On the basis of the paper by Beard and Perks (J.I.A. 75, 75) on the relation between the distribution of sickness and the effect of duplicates on the distribution of deaths, it is likely that the increase factors given for inceptions will apply, perhaps only approximately, to sickness which includes duplicates.

Over the last 2 or 3 years I have made many calculations on the 1972–75 sickness data given in C.M.I.R. 4. I wish to try and find how far the statistical tests usually applied to mortality tables can legitimately be used on sickness data. I began by applying to the 1972–75 sickness data the test put forward by Redington and Michaelson. This test is described briefly in relation to mortality data in the appendix to my paper (J.I.A. 101, 415) and involves the calculation of a standard deviation, called σ r, which should not differ greatly from unity, if certain conditions hold. For example, the presence of duplicates would be expected to increase the value of σ r, while correlation between the sickness rates at consecutive ages, or approximations made in calculating the exposed-to-risk, might affect σ r in some way.

If Appendix F, which relates to the 1975–78 data, can be assumed to give an indication of the proportion of duplicates in the 1972–75 data, on which I am working, we can say that the data for deferred period 1 week contains about 40% duplicates and the other three deferred periods about 10%. Duplicates on this scale may perhaps be expected to increase σ r by factors which are something like the square roots of those given in Appendix F, say 1·5 for deferred period 1 week and 1·1 for deferred periods 4, 13 and 26 weeks,

I have calculated values of σ r for each sickness period up to 52/52 weeks, within each deferred period except 52 weeks. The standard deviation of each of my values of σ r is about ·2, so that a 5% confidence interval, assuming the normal distribution, perhaps a rather dubious assumption, is from about ·6 to 1·4. Of the 14 values of σ r which I have obtained for sickness rates, only two, the largest and the smallest, lie outside these limits. The largest, 1·74, for deferred period 1 week, sickness period 1/3 weeks, is well in excess of the upper limit due to the presence of duplicates which, as just indicated, leads us to expect a value of about 1·5, but the other values of σ r for deferred period 1 week and sickness periods 4/9, 13/13, 26/26 and 52/52 weeks are ·91, ·58, ·93 and ·85 respectively, that of ·58 being the lowest of all the 14 values. Thus, for deferred period 1 week only one of the five values of σ r gives any indication of the presence of duplicates, which is rather puzzling. The remaining nine values of σ r relating to deferred periods 4, 13 and 26 weeks, range from ·75 to 1·11 and average ·94. Taking account of duplicates we would expect an average of about 1·1. Possibly some form of correlation or something similar has tended to reduce the values of σ r. I have to consider this further.

I have made a further set of calculations for each deferred period and period of sickness for which I calculated ο r. For each individual age, I calculated the difference between the actual weeks of sickness and those expected by the graduated rates and then divided each difference by the corresponding standard deviation of sickness. The method of Coward (J.I.A. 75, 12) was used to calculate the standard deviation of sickness.

A notable feature of these values, which might be expected to be something like normally distributed if duplicates were not present, is that out of 475 values there are six which exceed + 3·0. The expected frequency of a value of + 3·0 or greater is, by the normal curve, less than one out of 475. However, the negative deviations, that is expected greater than actual, show no values numerically over 3·0. Of the six values which are greater than + 3·0, four relate to deferred period 1 week which has the large proportion of duplicates. These high values often occur as isolated, very high actual weeks of sickness. Can it be that sickness duplicates tend to show up strongly as positive deviations

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when the multiple policies have sickness claims irrespective of the overall proportion of duplicates, and that the effect when the multiple policies do not have sickness claims is less noticeable as large negative deviations?

Duplicates in sickness data may behave in a rather different way from those in mortality data and produce isolated high values of sickness which tend to be spread over several ages by the process of calculating third differences, which is a part of determining σ r. Also. perhaps correlation between successive ages or the assumptions made in calculating the exposed-to-risk tend to reduce the value of σ r.

Some of these remarks are rather tentative and there are a number of problems to investigate. However, I am hopeful that I may be able to provide some sort of justification for applying to sickness data the usual statistical tests, perhaps adjusted in some way.

Dr H. R. Waters: It seems that there are two important issues to be discussed in relation to individual PHI. The first concerns the form of the end product of a sickness investigation required by the offices issuing such business. The second sentence of §4.2 states that: “Modern Individual PHI business requires the calculation of guaranteed level annual premium rates and the valuation of existing portfolios of business.” What I mean by the end products of a sickness investigation are the functions which will eventually be tabulated in order to carry out these two tasks of premium calculation and valuation. For historical reasons the intended end products of this investigation were tables of sickness rates in the style of the Manchester Unity tables. Section 4 explains why the Manchester Unity method is unsatisfactory for the calculation of premiums. The fact that it is also unsatisfactory for the valuation of a portfolio is mentioned only briefly in §6.11, although this point will be of increasing importance as existing portfolios mature. Thus, it is not surprising that the sub-committee are considering an alternative end product for future investigations. In the penultimate paragraph of the introduction and also in § 4.6 they indicate that they are considering switching to an inception rates and disabled life annuities method. which is common in most countries of Europe and North America and is logical and technically sound. From my knowledge of such methods, I am sure that they would be an improvement on the Manchester Unity method, but it is difficult to be more enthusiastic about this proposed change as the sub-committee do not indicate precisely what they have in mind. It would be helpful if they could give some references on this subject so that a fuller discussion could take place within the profession on what could be a very important change in relation to individual PHI.

The second issue is the way in which the data are analysed. This and the form of the end product of the investigation are clearly related to each other, but they are also separate issues. For example, it would be possible to have as an end product of a sickness investigation tables of sickness rates and the derived commutation functions more or less in the style of the Manchester Unity tables, if this was what the offices required and they were prepared to accept the limitations of this approach, even though the data were analysed in a very different way from that presented in this report.

In order to analyse the relevant data, an investigation of this type should, like a mortality investigation, be built on the foundation of a well-defined probabilistic model, A key quantity, or quantities, in that model should then be chosen, for example qx, the probability of death within 1 year, or µx the force of mortality. in a mortality investigation, and data should be collected such that an estimate of this quantity can be calculated. However, one of the most important considerations is that the quantity chosen and the form of the estimate should be such that the statistical properties of the estimate are known. It would then be possible, for example, to test statistically whether the experience of one group of offices is significantly different from another one, or to test a graduation of the chosen quantity for goodness of fit, just as in a mortality investigation.

The probabilistic model underlying the analysis in this report is not made explicit and is very difficult to determine. The quantity chosen to be estimated was the sickness rate at successive ages and for various durations of sickness. This is a very natural choice, but not the only possibility, if the end product of the investigation is seen as tables of sickness rates, especially since they can be estimated very simply, as described in § 4.4.

Unfortunately, whatever the underlying model may be, sickness rates are rather complicated functions in probabilistic terms and so the statistical properties of the estimate of a sickness rate are not easily determined. This causes difficulties at several points in the report. For example, the third

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paragraph of the introduction says: “One of the features of the experience reported in C.M.I.R. 4 was a possible overall trend of worsening morbidity over the period of investigation although the evidence for such a trend was not consistent for the separate tables by deferred period and no firm conclusion was drawn.” A statistical test of the data was required to determine whether the apparent worsening morbidity could have been caused by random fluctuations in the experience or was more likely to have been the result of a genuine trend.

Another example can be found in §6.5 where, in order to test graduations of sickness rates, a particular test statistic is assumed to have, approximately, a χ 2 distribution purely on the basis that it is a sum of individual terms each of which, on empirical evidence, has a mean value of 1. The fact that the individual terms in the summation are likely to be highly dependent on each other seems to have been ignored. I appreciate the sub-committee’s difficulty in this respect and they acknowledge this in both the opening sentence and the final sentence of § 6.5, but the remainder of this paragraph appears, in terms of statistical theory, to be bordering on the reckless.

If the analysis of the data, based on observed sickness rates, as presented in this report is unsatisfactory, is there a more satisfactory alternative? In my opinion there is and, broadly speaking, it would be based on observing inception rates and recovery rates with the latter depending not only on attained age but, possibly. also on the duration of the current sickness. The sub-committee may have an analysis of this type in mind when it discusses switching to an inception rates and disabled life annuities method, but I would stress the importance of having a well-defined model as the foundation for the analysis.

Mr H. A. R. Barnett: The Chairman of the sub-committee has described the observation of an experience as it passed through time as ‘only a snapshot.’ This is a useful concept, but strictly the correct analogy is to a time exposure. A snapshot would be the observation of a function such as a µ, but as this is not feasible in practice it has to be observed over a period. If the period of exposure is too short the outline is not clear; if too long the image is blurred; and this applies not only to sickness but also to mortality and other similar investigations. For some time the CMI committee have considered a 4-year period about right to even out year-to-year fluctuations without blurring secular changes, and the PHI sub-committee have seen no reason to change the length of the cycle.

I disagree with the suggestion in the penultimate paragraph of the Introduction that, because it is based on ‘only a snapshot’, the observed experience is not a suitable basis for a standard table. In 12 years’ time there will be three more quadrennial experiences which may indicate a regular trend enabling a projection to be made into the future, or which may indicate fluctuations from period to period suggesting that there would be no need to change from a current standard table. Also, by then there will be a series of observed claim inception rates and durations of claim. Until that time the tables now produced are the best we have, and the profession and the PHI offices should make the best use of them with whatever margins may be considered prudent.

There is a need for a standard table, and the only alternative to publishing and using a new one is to

fall back on a table nearly 90 years out of date, in the construction of which there is a fallacy, as stated in Section 4. I have been unable to find any reference in the introduction to the Manchester Unity tables to the approximation in calculating the exposed-to-risk, which resulted from the fact that in the early years of cover there could be no exposure to the later periods of sickness. It does not seem to have been stated that this approximation was financially unimportant for the Friendly Societies for which the tables were constructed. It could only have been unimportant if the proportions of members in the earlier years of cover were to remain unchanged. I will concede that the inaccuracy might have been recognized at the time, but it was not mentioned in the publication and might not have been appreciated by all who used the tables. I question whether Manchester Unity should be retained as the latest available standard table just because the present work is based on ‘only a snapshot’. Was not 1893–97 also only a snapshot? Surely this new work must become a standard table, even if additional functions have to wait until the sub-committee have completed further work on the 1975–78 experience, and even if the new table is to be superseded in 12 years’ time by one based on a projection. Furthermore, was not the production of a standard table one of the reasons for setting up the PHI investigation in the first place?

Considering female sickness rates, I undertook a preliminary statistical investigation for the

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sub-committee, and the figures indicated a very appreciable, and statistically significant. difference between the sickness rates of the two sexes The argument that if the premiums for females had been lower the sickness rates would also have been lower is incorrect. A woman effects a PHI policy if she feels she needs the cover, if she can afford the premium, and if the cost looks reasonable. She does not make a detailed actuarial calculation on assumed bases, and she is most unlikely to know in advance what rates of sickness she is likely to suffer in the future. That female data are too scanty for the direct construction of a separate graduated table does not preclude the use of a technique similar to graduation by reference to a standard table. I suggest modifying the figures given in Section 3 to produce a set of graduated multipliers, which may be used to convert male sickness and inception rates to female ones; then from the graduations in the paper and the graduated multipliers. female graduations may be produced. A similar techique might be found suitable for graduating the data under group PHI policies when the experience of this class for a quadrennium has been compiled.

Mr P. E. B. Ford: I wish to suggest an extension to the approach of the sub-committee to the graduation of the full range of sickness rates by a single three-dimensional mathematical surface. This would be used to provide a consistent basis for PHI actuarial investigations, and one that is easy to incorporate in computer calculations.

In §4.6, reference is made to an analysis of claim termination rates; from these, analysed by duration, it will be possible to derive disability annuity values. This sort of approach was mentioned by Mr Bond in the discussion on the 1972–75 experience in C.M.I.R. 4 (J.I.A. 106, 289) and would provide a very flexible system of basic rates from which a wide variety of disability benefits could be costed.

In the short term, however. pending the derivation of these detailed results, there is a need for a reasonably well-ordered. although possibly subjective. model of sickness rates. Those shown in the paper have been fitted separately for each original deferred period and each period of sickness, using a cubic polynomial in attained age X to derive the natural logarithm of the relevant zx sickness rate. A valuable extension to this approach would be to fit a two-dimensional polynomial surface to the zx sickness rates. by attained age x and duration of sickness t.

I have used a model described by Hymans and Lane (J.I.A. 76, 87) to achieve sickness rates graduated by sickness duration. They treat the sickness rate zxt/all as the weighted sum of two functions x1 and β 1, where the weights depend only on age X, and the constants α and β are independent of age. Although empirical. this formula is based on the broad supposition that the α term represents short-duration sickness and the β term long-duration disability. Different values can be used for each class of deferred period. if desired.

The value of having the rates fitted by a formula dependent on the sickness duration t is that, by differentiating that formula with respect to t, you get the probability of suffering illness of exact duration I in the life year x to X–1 and. by taking the logarithm of that result and again differentiating with respect to t, you get the force of recovery from sickness of duration t during the same life year.

With these basic components all sorts of results can be achieved, such as the construction of exposed-to-risk formulae allowing for duration selection, or premium rates for lump sum disability benefits or for escalating benefit policies, where the assumption for the rates of recovery from sickness can be varied. depending on the rate of benefit escalation. However, this method is empirical and it only gives a formula in one dimension. namely the sickness duration. Looking at the results in Appendix H. together with the comment in §2.3 concerning the reasonably well-ordered pattern of the original deferred pod tables in relation to one another, I wonder whether it might be possible to extend the current graduation approach to a more general surface whereby the kzxt/all sickness rates for the parameters age x. sickness duration t and original deferred sickness period k are fitted by a three-dimension polynomial in x. t and k (or possibly transforms of those parameters).

One of the two main end products of the sickness tables will be the production of actuarial premium rates. against which actual office premium rates will be measured, and I know of one set of current published PHI premium rates which have been graduated in a similar sort of way, for the parameters entry age. original term and deferred sickness period. A surface-fitting technique using the usual least-squares approach might possibly be applied to the three dimensions of the kzxt/all sickness rates,

510 Sickness Experience 1975–78 for Individual PHI Policies

with sickness duration t replacing original term n. The problem with using this method for fitting office premium rates is that there are monotonic constraints on the run of the rates in each dimension, if the results are not to appear odd to the public (with possible lapse and re-entry occurring as a result). However, that problem, although manageable, does not apply directly to the construction of the underlying surface of sickness rates. There is an analogy with the hump at the younger ages in the A67/70 mortality curve, which does not normally feed through to term assurance premium rates.

I note that in Appendix H, the rates for the youngest ages for sickness period 104 all show this reverse monotonic effect for each of the original deferred periods. I suspect that this is more than just a mathematical aberration arising from the particular graduation method adopted, and in fact reflects the reality of the situation. The wards of hospitals contain many patients from motor-bike and car accidents that have led to these long-term disabilities. where the younger age groups are most vulnerable to the risk. Paragraph 2.4 draws attention to this feature in the actual experience. Since it is not necessary to smooth out this feature in the graduation. I wonder if a three-dimensional polynomial surface in X. t. and k might be found to fit the z rates or, possible, following the approach of the sub-committee, the logarithm of the rates. The office premiums mentioned earlier used a 48-term polynomial of third degree in entry age and original term. and second degree in deferred period. If a satisfactory surface of this form could be produced, it would provide a very useful orderly base from which disability annuities. claim inception rates or z sickness rates could be produced in a consistent way.

As indicated in Section 4. there will be problems in breaking down the actual CMI sickness data in sufficient detail to provide a wide enough spread of z values to enable the suggested surface to be fitted, but the same data problems must be inherent in the formation of disability termination rates. It seems that we have the choice of starting from a surface formula fitted to the z rates and differentiating it to obtain sickness duration or sickness termination probabilities. or alternatively, starting from a termination rates surface and integrating or summing that formula to produce z factors. Either way a unified model results.

Dr S. Haberman: I welcome the comments that the sub-committee are moving towards a system of data collection, analysis and presentation that reflects the true nature of the processes underlying measures of sickness, The sickness rates zx, originally introduced in the seminal work of Sir Alfred Watson on the Manchester Unity experience, are not rates at all but are rather complex functions of the underlying stochastic processes of becoming sick, recovering, dying and so on. These processes have been hinted at by Dr Waters and have been described in a recent paper on multiple state life tables. A switch to claim inception rates and persistence rates will assist greatly in our understanding of PHI experience and, as the authors indicate, will take us further in the development of standard tables. As mentioned in §4.6, this alternative approach will not suffer from the problems in a Manchester Unity type study where policy duration is ignored. The analysis would be more difficult and probably require more sophisticated techniques than are normally used by actuaries in this field. but I do not think that this difficulty should deter us.

I have reservations concerning the graduations performed in this report. In the Conclusion. the authors confess to having spent “a considerable amount of effort. on deriving graduation formulae for practical use.” I have a simple question for them and the U.K. profession as a whole: why are we obsessed with parametric graduation methods or, as our textbooks call them, graduation by mathematical formulae? In his magnificent piece of work Sir Alfred Watson was not tempted by the words Gompertz, Makeham or Cubic or any prior view about the progression of the rates. He was satisfied with a 15-term summation formula for graduating his sickness rates. The trouble is that parametric methods and mathematical formulae have found an aura of modern scientific respectability.

To some extent, in the mortality area, the recent arrival of splines (in E.L.T. 13) has represented a shift away from the formal parametric methods used hitherto and by the sub-committee in this report. What I have in mind is perhaps more fundamental than just graduation by splines; it is the suggestion that we approach graduation occasionally from a non-parametric viewpoint. In a recent paper, J.I.A., 110, 135, I described a non-parametric approach, namely graduation by kernel methods. These do not involve any a priori view of the form of the true rates, and are akin to

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summation formulae and the adjusted average methods widely favoured in the U.S.A. and Canada, but kernel methods are simpler to use. They require just one input, a smoothing constant, which can be regulated in a continuous way to produce desired changes in, and balance the conflicting characteristics of, smoothness and adherence to the crude data. This continuous modification is a major advantage and rather an unusual feature.

By contrast, the smoothness of parametric methods can only be regulated in discrete steps, for example, by increasing the degree of a polynomial, as in the report, increasing the number of knots in a cubic spline or changing from one family of curves to another. The mathematical properties of such curves can also change abruptly. The kernel method involves a single formula without any statistical fitting of parameters.

None of the conventional methods of graduation is capable of continuous improvement in the way that the kernel methods are, and I am confident that these methods would have given better results more quickly than the approach described in Section 5.

Mr N. Massey: The main area of debate seems to lie in whether the Manchester Unity or disability annuity method is more appropriate. Different considerations apply to the calculations of premium rates and valuation reserves. For premium rates I believe disability annuity is better, as it allows for more accurate costing of, for example, different options or current cost premiums. However, the argument is not nearly so clear cut for valuation work. and I wish to identify three particular areas of concern.

The first is the purely practical problem in valuing the claimants. Offices will be required to have both the facility to transfer claims data to the valuation file and also to hold and then operate on all the various double decrements associated with each combination of sickness duration and age at falling sick. I cannot see how my office would adapt its systems to cope with those demands, and I suspect other offices would be in a similar position. This is not simply a matter of administrative convenience. The disability annuity method is undoubtedly more complicated, and the more complex the valuation system the more likely it is that mistakes will arise.

My second concern relates to the stability of disability annuity valuations. Under the Manchester Unity method, the same future claims experience is assumed irrespective of the experience in the valuation year. This is not true for disability annuity as an unfavourable year’s experience will probably be reflected in more claims outstanding at the valuation date, and so a higher reserve for claimants will result. The office will, therefore, suffer the double strain of payment of heavy claims and the setting up of additional reserves. The reverse, of course, applies in favourable years. This leads me to expect rather more volatile surpluses and deficits from the disability annuity method, with a tendency for it to exaggerate the random fluctuations which are bound to occur in any office’s year-to-year experience.

The final concern is more relevant at the shorter sickness durations. Both inception and recovery rates are significantly affected by seasonal factors. so that claims paid in the summer months are rather less than those in the winter months. Would not a disability annuity valuation therefore produce different results according to the time of year it was carried out?

The dangers in incorrectly valuing claimants are more relevant at the longer durations, and durational selection only applies in the 104/all period. Would it be more sensible in valuation work to use Manchester Unity methods for the first 2 years of sickness and a disability annuity method thereafter? This begs the further question: “can recovery rates be ignored once sickness has lasted 2 years?’ At least such an assumption errs on the conservative side, and would considerably simplify the algebra.

The period of review 1975–78 was one of very high inflation. At the time most policies provided a level benefit and so, for all but the earliest claims, benefit levels fell rapidly below corresponding earnings levels. To what extent may the overall claim levels in the period have been influenced by the fact that there was a large financial incentive to return to work? The position in 1975–78 contrasts sharply with the present, when inflation is relatively low, and an increasing proportion of policies provide escalating benefits.

Considering durational selection. the two formulae in §4.5 show the true and approximate net premiums. As I understand it, the approximate formula overstates zx+t at short durations t, and

512 Sickness Experience 1975–78 for Individual PHI Policies

understates at the longer durations, so that for individual policies the shape of the morbidity curve is always steeper than that of the underlying morbidity table. This seems to have very serious implications regarding undervaluation in the 104/all period. Offices are now required to produce valuations at least as strong as a net premium valuation, and I wonder whether the committee could give some indication of the extent of undervaluation, on a net premium basis, using their tables.

We now seem extremely badly placed to deal with the durational selection factor. The disability annuity method will take account of it, but the tables are not yet available, whereas the tables produced in the report do not directly allow for it. The problem may be more amenable to disability annuity treatment, but might it be possible to deal with it within the Manchester Unity framework? Two possible approaches are either deriving formulae for the true values of zx+t in terms of x and t, or, just for the 104/all period, publishing tables with a very long select period—probably 10 years would suffice.

Considering medical selection, Table 7.1 gives a breakdown between select and ultimate morbidity according to policy deferred period. I would expect the initial underwriting process to be more effective in removing risks of long duration than of short duration, and therefore feel that more informative results might have been obtained from a breakdown by sickness duration. If medical selection operates in the 104/all period then, of course. it will tend to reinforce the effects of durational selection.

The report seems to have favoured the disability annuity system, and it would appear to be the wishes of the committee to move uniquely to this method. I believe such a move would be premature. Manchester Unity methods have been used successfully in this country over a very long period. They have stood the test of time. Disability annuity may look good in theory, but are all the practical complications always worth while? I do not think they are.

Mr R. E. Hayward: The sub-committee has a problem with long-term sickness and I have seen how valiantly they have wrestled with it. One problem is that the proportion of policies on healthy lives at long durations is small, Another is that inflation has created an increase in the numbers of second and subsequent policies and this effectively reduces the average duration since underwriting, which relates to the last issued policy, not to the first. There could be a case for eliminating all previous policies from the experience. Perhaps this feature explains some of Mr Daw’s results. A third problem is that relatively few of the claims cases die as compared with recoveries and the mortality of the sick cannot be estimated from the sub-committee’s data.

Whilst looking at the problem of estimating sickness benefits in another way, I have consulted the Transactions of the Society of Actuaries and have found, in the 1981 ‘Reports of Mortality and Morbidity Experience’, a table showing the probabilities of ceasing to be sick at various durations after falling sick. Using the table for males with a 26-week deferred period, I estimated the number of weeks of sickness for the given ages of falling sick. Duration was recorded only up to 8 years and there was still a large proportion sick at that duration; between 24% of those who fell sick at age 25 and 52% of those who fell sick at age 55 were still sick after 8 years.

Not having any mortality rates applicable to the sick, I assumed that those who were sick at duration 8 would remain sick until they died and would follow the A1967–70 Ultimate table; a table that was usable, not one chosen because of any knowledge that I had. I then had the ingredients required to estimate the average length of sickness up to age 65 using the American claim cessation rates up to duration 8 and mortality only after that until age 65. Combining these with the claim inception rates of the Standard 1975–78 PHI experience and A1967–70 Ultimate Mortality for the period before falling sick, and assuming no lapses, I deduced the cost, for a healthy life, of sick pay up to age 65. For age 25 the average length of sickness per healthy life joining was 52·5 weeks. The sickness rates in C.M.I.R. 7 over the same period gave a total of 18·0 weeks. For age 55 the corresponding figures were 21·2 from my model and 14·3 from the C.M.I.R. 7 data.

My model was partly guesswork and there is some scope for error, but the sickness periods which I have calculated are so far in excess of those which I have helped to produce as a servant of the PHI sub-committee that I am bound to suspect that the C.M.I.R. 7 experience lacks so much long-term sickness that the sub-committee was right not to publish a standard table for use in PHI valuations and right to say that there is still much more research to be done.

Sickness Experience 1975–78 for Individual PHI Policies 513

Professor A. D. Wilkie: As Chairman of the CMI committee, I want to thank the members of the PHI sub-committee for all the work that has gone into producing this paper, and I shall encourage the sub-committee to continue their analysis of inception rates and recovery rates, even though this will require much further work.

Mr R. D. Corley: (closing the discussion): Permanent health insurance is well established in the British market, and it is therefore surprising to find that only 13 offices contributed to the 1975–78 experience for individual policies. It is perhaps even more surprising to discover that at the end of this period these offices were reporting on a combined total of less than a quarter of a million individual PHI policies, a total which included many duplicates. C.M.I.R. 5 reported on another 58,000 lives covered by group PHI, which is probably only a small part of all those insured by their employers, but adding all these figures together does nothing to show that the British people have been convinced of the need to protect their standard of living against the risk of prolonged disability.

The experience we have been discussing relates to the years 1975–78. One of the traditional fears of the PHI underwriter has been a sharp increase in unemployment. How many serious psychosomatic disorders that prevent work continuing have been caused by a fear that work may not continue? The 1975–78 experience will give us a reference point from which to judge the experience of, say, 198l–84. On the next count there may well be other factors operating alongside the effect of maturing portfolios.

Anyone who is unfamiliar with PHI business. could hardly have a better starting point than by considering Table D13. This table shows the pattern of falling sick enough to make a claim, and from it, two things stand out: (i) 1 week deferred business produces claims at such a high multiple of the other deferred periods that different considerations affect the organization of the claims administra- tion, and (ii) females make more claims than males.

The lighter morbidity for longer deferred periods has been a consistent feature of this and earlier investigations, and the opener suggested that as this flows through to premium rates, policyholder preference of deferred period may change. In general, smoothing of premium rates will probably prevent such anomalies overriding the policyholder’s natural preferences, which will probably be strongly influenced by his financial circumstances. However, we need more analysis of the underlying causes of disability to get closer to understanding the mechanism behind this phenomenon. We can at present only speculate on whether there is selection at outset or at the time of becoming sick. Could it be that some illnesses last longer once the benefit has commenced?

All the evidence in the report points to female sickness rates being higher than male, and the opener introduced evidence from several sources to show that this has been the trend for a long time. Our critics would argue that we are basing our conclusions on slim evidence, and that the present report is based on only 14,000 policies on females against 230,000 on males. Some females may be selecting against the offices, that is, some of those who take out policies have reason to fear long-term sickness, although both Mr Barnett and I would doubt whether this is happening. One or two small life offices and friendly societies have charged unisex premium rates, although some would claim that these are closer to the normal females rates than to the lower male ones, but we have not yet heard from one which can justify its actions by its experience.

The background to the higher female sickness rates is interesting, and perversely, seems to arise from the fact that the ladies are, in the long run, the stronger sex. Sickness inception rates for females are higher, but recovery from sickness within the first year or so is also higher than for men. However, in the longer term, sick females seem to outlive sick males just as healthy females outlive healthy males. In the discussion on C.M.I.R. 4 (J.I.A. 106,289) Mr J. H. Miller drew on American experience to give us this explanation, and there is nothing in C.M.I.R. 7 to challenge his views.

Again, it would be interesting to have more analysis of the cause of disability to obtain the fundamental differences between male and female sickness rates.

Mandatory unisex PHI premiums are likely to give actuaries nearly as many problems as mandatory unisex pensions. If the demand is made, the proper reaction is probably to change the product by disallowing claims based on one or two particular causes of disability and by limiting the benefit period.

The Manchester Unity method of deriving sickness rates and hence premiums has three virtues:

514 Sickness Experience 1975–78 for Individual PHI Policies

that it is well understood by British actuaries; that it avoids the problem of collecting termination rates; and that it was originally based on a 4-year exposed-to-risk of nearly 3 million, a data base of a size unavailable to the CMI Bureau, but its weaknesses have been well catalogued in the report, and Dr Waters emphasized the list of defects. In particular. the report observes that it is unsuitable for offices with immature portfolios, On the other hand, Mr Massey raised practical problems that he foresees if the Manchester Unity methods are abandoned. Perhaps some knowledge of how these problems are overcome in other countries will be helpful.

I am convinced that the way forward, as shown by the report, is to use claim inception rates and disability annuity values. The problem is the length of time needed to build up information on termination rates, and although the sub-committee states that it is well advanced in the necessary development work, the opener rightly worries about the time it will take to have this essential tool. Here the suggestion made by Mr Ford may prove invaluable in filling the time gap. He has pointed to one method which, by using surfaces, may allow pseudo-disability-annuity values to be derived from inception rates and Manchester Unity type sickness rates.

Manchester Unity will not pass into oblivion entirely without regret, and it is comforting to see that the sub-committee checked their graduations against this table after using the completely different approach of Lloyd, but it will be a relief to all when it no longer appears that we are basing our opinions on a method relating to the nineteenth century.

The values of 104/all sickness benefits have given trouble, because they vary with the maturity of the experience, and it is interesting that no one has speculated on the cause of this effect. I would hesitate to trespass into medical fields, but the maturity effect causes me to think of diseases like diabetes, which are diagnosed at comparatively young ages, but are then controlled and give no cause for sickness for perhaps 20 or more years. Clearly. an underwriter would turn down, rate up or reassure a diagnosed diabetic, but would be likely to accept some policyholders in which diabetes would subsequently develop. It would then be at least 20 years from the commencement of business before sickness from this source could arise on unrated lives. When we obtain the analysis by cause of disability the variations by the maturity of the portfolio will make a fascinating study.

The problems caused by duplicate policies detract from the confidence with which the tables can be used, and Mr Daw drew attention to the unsatisfactory state of the art at present. It must be considered whether today’s record-keeping methods would allow this problem to be eliminated at source, at least as far as it occurs within an office.

It is difficult to gauge whether individual PHI will become more popular in the market place, but we can expect that the efforts to publicize its benefits made by the issuing offices and by the Equal Opportunities Commission are likely to have a cumulative effect.

Individual permanent health insurance provides an inexpensive method for a man or woman to protect future earnings against disability. C.M.I.R. 7 and its successors will give us a firmer base on which to offer the appropriate cover.

The President (Mr C. S. S. Lyon): For all the reservations the sub-committee has expressed about the use of the results of the investigation in a practical context, of one thing I am in no doubt: namely, that at working ages women experience heavier sickness than men. In terms of rates of sickness, Table 3.3 puts the excess at more than 100%, often much more, for every age group between 29 and 54 in most sickness periods. This evidence reflects the much higher invalidity rates experienced by women than by men in the National Insurance Fund as reported by the Government Actuary 2 years ago, and it is steeped in history, as the opener has reminded us. There may still be some outside the profession who would attribute these differences not to any underlying propensity of women of working age to experience heavier sickness, but rather to differences in the composition of the labour force. It is therefore worth drawing attention to an official publication some years ago (1970–71 Socio-Economic Analyses-Office of Population Censuses and Surveys, H.M.S.O.) on the subject of morbidity statistics from general medical practice in 1971–72. This included a detailed analysis of consultations with general practitioners by age, sex and medical diagnosis. Even after eliminating consultations for specifically female conditions, the incidence of medical consultations is substantially higher for women than for men. Although there is obviously not a direct relationship, this does appear to provide independent evidence of a greater propensity to sickness amongst women than men. I would

Sickness Experience 1975–78 for Individual PHI Policies 515

find it more credible if, instead of denying that such propensity exists, those who believe in unisex rates for permanent health insurance would admit the actuarial case for discrimination in premium rating and concentrate on the social arguments against it.

We must not judge this report by the reliability or otherwise of its female data. The purpose of the Continuous Mortality Investigation is to provide tables useful to offices, and indeed it succeeds well in this function.

Not long ago at a board meeting of a company with which I have some acquaintance, one of the non-executive directors asked me why in my actuarial valuation I had used the A49/52 mortality table; could I not be more up to date than that? If he had turned a page or two further on in the report he would have discovered that another class of business was being valued by the Manchester Unity experience 1893–97, and I wonder what his comments would have been then.

Has the Manchester Unity approach in fact had its day? It is very unsuited to group business costed by recurring single premiums. The discussion has thrown up a number of views and ideas for the sub-committee to consider, some favourable to Manchester Unity, some favourable to the American approach, and indeed some new ideas altogether. We must look forward with anticipation to the sub-committee’s next report on this subject.

The notice of the meeting did not list the authors of the report, and perhaps in moving a vote of thanks I could do so now. The PHI sub-committee comprises the following members: Messrs R. H Plumb (Chairman), P. H. Bayliss. R. Garden. E. A. Hertzman, F. W. G. Martin, A. R. Marshall, G. C. Orros and R. J. Sansom, and other people who have given help to the committee. Perhaps we should not forget because of the time-span of this investigation the names of people who are no longer with us who are also mentioned in the introduction to the report: Mr J. Hamilton-Jones, who was Chairman of the PHI sub-committee from 1970–79. and Mr J. A. Cairns, who was Chairman of the sub-committee from then until his death in February 1982, and also Mr F. W. Eschrich.

Mr P. H. Bayliss (replying): The sub-committee will study the criticisms, comments and suggestions which have come from the discussion with a great deal of attention and will take them into account in its further work.

There seems to have been fairly widespread support for the sub-committee’s opinion that it should be moving towards studies of inception rates allied with claims persistency or claims recovery rates, although there were one or two who threw in some valuable comments in defence of Manchester Unity. It was suggested that Manchester Unity had stood the test of time because it was the only table which actuaries have been able to use, and had not come to grief. It is not known to what extent this is due to a not-too-difficult market in which actuaries have been able to build in contingency margins in their assumptions in premium rates and in reserving, and whether this state of affairs would continue if the business were more competitive.

The sub-committee would not like to have to produce another Manchester Unity type investigation report, except as a parallel to what we hope will be a very interesting investigation on the disability annuity basis. The reasons for that approach were very succinctly set out by Dr Waters, that is the necessity, if serious work of this kind is to be undertaken, to be able to define the variables in a way which makes them amenable to statistical analysis. This has been a problem throughout the work of the sub-committee, especially with graduation work. I expect the criticism about the χ 2 test is valid and we will certainly look at that.

Considering Mr Barnett’s remarks, the sub-committee has been in two minds about just how far it could place reliability on the graduated tables it was producing. In the end we felt that the opinion we expressed in the paper was the correct one.

Dr Haberman made a most distinctive contribution in which he challenged the formula graduation approach, and I agree that it is tempting to use that method. It removes some of the problems for the person effecting the graduation if he begins with that approach. One particular feature of the PHI experience gives a problem which is perhaps distinctive from mortality data. Mortality data extend from the youngest to extreme old age. It may be scanty at the extremes, but at least there is something to look at. One problem with PHI data is that it breaks off at age 64, where it is just becoming interesting. Much of the experience is in the upper fifties and early sixties age range, and the shapes of the curves and the level at that upper end of the range are basic to the graduations and financially

516 Sickness Experience 1975–78 for Individual PHI Policies

important. This was one of the reasons why a summation type approach was originally felt by the sub-committee not to have much promise; we thought we would not be able to cope with the abrupt end of the available data at age 64. I will look to see whether one of the methods suggested by Dr Haberman could be applied. I made a trial of splines which was not very successful. suffering partly from my own experience with the method and partly from the well-known problems with splines. that they have a sort of whip-lash effect going through all sorts of peculiar curves if enough care is not taken.

Mr Daw raised some interesting questions regarding Appendix F. on the question of duplicates. I did not quite understand his criticism of the numbers, but I believe the data given in Appendix F is intended to be based on comprehensive data rather than a sample of the data.

Mr Corley mentioned that only 13 offices have contributed to the data which is under investigation. There are other offices which are writing business and I hope that anyone who is in a position to persuade offices to contribute data will do so.

WRITTEN CONTRIBUTION

Dr S. Haberman: In his reply to the Discussion on behalf of the sub-committee, Mr Bayliss referred to my suggestion that alternative methods be considered. He remarked that the problem of graduating the rates at the extremities of the age range makes these methods impracticable. For example, the use of a symmetrical moving weighted average of 2m + 1 terms to smooth equally spaced observations of a function of one variable (e.g. Spencer’s 15- or 21 -term averages) does not yield graduated values of the first m and the last m observations unless additional data beyond the range of the observations are made available. Such objections are somewhat out-dated as solutions have been proposed and successfully used.

The Whittaker-Henderson graduation methods used in the U.S.A. and Canada do not suffer from difficulties at the extreme ages, Further, the historic problems associated with summation methods (or Moving Weighted Average methods) have now been solved independently by T. N. E. Greville and P. U. K. Linnemann. In two papers in the Scandinavian Actuarial Journal (1981, parts 1 and 2) Professor Greville has described a natural method for extending the smoothing process to the extremities of the data for symmetrical moving weighted average formulae. The result is a unique graduation. A more general approach has been separately proposed by Dr Linnemann (University of Copenhagen Laboratory of Actuarial Mathematics Working Paper, No. 28, 1979) which is not limited to symmetric averages.

The sub-committee subsequently wrote: In opening the discussion, Mr Sibbett stressed that withdrawal rates may appreciably affect sickness experience. We think this could work in two ways: firstly by affecting the mean duration of business in force; and secondly by reducing through selection the proportion of healthy lives in the remaining experience. He also wondered whether policy expiry age may be an experience factor. We have not obtained evidence of this, but surmise that any such effect would be more likely for group than for individual business, We have not hitherto investigated the effects of withdrawal rates or of expiry age but will consider whether any relevant data could be extracted without too much difficulty. We confirm Mr Sibbett’s assumption that a change in level of benefit payable under a claim, though recorded, is not treated as a discontinuity of the claim. He remarked also on the length of time which would be needed to gather enough data on long-term claims for a disability annuity analysis. We do envisage having to make some broad assumptions about long-term claim termination rates to overcome the paucity of data and avoid protracted delay in producing tables. As alluded to in §4.6 of the report, we believe this can be done with a sounder understanding of the nature of those assumptions than would be the case under the Manchester Unity method.

Mr Daw sought clarification of the source of the data on duplicates used in Appendix F, which described the figures as ‘estimates’: a term which, it seems, was misleading. The information was obtained by sorting the claims file for the 1975–78 Aggregate experience so as to group together

Sickness Experience 1975–78 for Individual PHI Policies 517

records for any policies carrying identical information in certain fields. The fields scrutinized were those for: investigation year. sex. age definition code. deferred period. date of birth and date of falling sick. Policies having the same data in all these fields were assumed to be all on the same life. Although the procedure is thought to be reliable. it cannot be perfect and there may be a few errors of omission or wrong attribution. As we were unable to vouch for their complete accuracy, we described the resulting figures as estimates.

It is impracticable in this short note to do full justice to the many valuable points and suggestions concerning the graduations made in particular by Dr Waters. Mr Ford and Dr Haberman, but these will receive full consideration and certainly suggest new avenues for us to explore. We would mention that the paper by Professor Copas and Dr Haberman on kernel methods (J.I.A. 110, 135) appeared too recently to influence the work reported in C.M.I.R. 7. We will ensure, as Dr Waters requests, that adequate explanations of the disability annuity form of investigation accompany our first publication of results. The approach described by Mr Ford is interesting, in that he claims to have applied it himself with practical results, though, given our reservations about the Manchester Unity method, we question whether curves or surfaces fitted to predominantly short-duration sickness rates can be reliably extrapolated to give projected rates at long durations.

Mr Massey foresaw a practical problem in valuing Claims on the disability method. We can only comment that this method is used in North America and numerous other territories without these problems being considered insurmountable. For most valuation purposes we think his desire for stability, year by year, in the results is inappropriate. If experience has been heavy, it is surely all the more important to ensure that the valuation reserves are adequate, and not to seek to soften the impact. With regard to his request for an indication of the possible extent of under-reserving which may result from a net premium valuation on the Manchester Unity basis, we draw attention to Table 6.5 and the comments in §§ 6.10 and 6.11, but do not feel able to add anything further at the present time.

Attention is drawn to the following errata in Appendix H, on page 104 of the Report: For sickness period 52/52. the coefficient E for deferment period 1 week should be 1·35 (and not

1·13 as printed); For sickness period 104/all, a term has been omitted in the second line of the formula for zx, which

should read:

[A related paper by Mr R. H. Daw entitled “The effect of Duplicate Policies upon the variance of Sickness Data” appears on p. 565 et seq.]