Actuaries

The number of pharmacists leaving practice (the separation rate) is harder to estimate. These rates typically rely on actuarial data for deaths and retirements but cannot account for those leaving the profession or the percentage of an age- or sex-based cohort who will leave the workforce in a given time period. 

The value placed on efficiency and predictability, and the institutional pressures for cost-containment, accountability and measurability are enhancing the appeal of reductionist theories. They fit with the tendency to locate social problems in individual pathology. They suit the actuarial mentality that places faith in statistical information as a means to predict and minimize future risk.7 Genetic and evolutionary explanations have become a way to address the issues that trouble society - the perceived decline of the family, the problems of crime and persistent poverty, changes in the ethnic structure of the population, and the pressures on public schools. 

For a discussion of the actuarial mentality and its institutional implications, see Nelkin and Tancredi (1994). 

We start by considering the (free) health insurance market. An actuarially fair insurance premium is one that equals the expected value of its yield in health... 

Voluntary insurance would be the market solution to uncertainty for risk-averse individuals. In this context, the user chooses the optimum co-insurance rate. Theory offers some analytical results on optimal health insurance contract designs.1 The consumer decides the extent of the coverage and the optimum co-insurance rate, and ultimately the price to be paid for the premium. In competitive markets, with actuarially fair premiums, the optimum co-insurance rate varies between individuals and depends on the risk of falling sick and the price elasticity of demand. 

Recently, Nyman7 took a fresh look at the traditional approach presented in Figures 7.1 and 7.2, which dates back to Pauly.8 Nyman argues that Pauly overestimated the welfare loss attributable to insurance, because he unduly included the income effect on consumption, whereas it should have been subtracted to leave the price effect. The income effect to be subtracted is due to the income transfer from the healthy to the sick. The pure price effect of insurance is the change in consumption of medical care that would occur if a consumer who is already ill were to purchase a contract from an insurer to reduce the price of medical care in return for an actuarially fair premium . In order to calculate the extent of the welfare loss of the insurance - which Nyman understands as the transaction cost of the insurance itself - it would be necessary to apply the classical Slutsky equation, but in practice it has yet to be quantified. 

The stochastic tools used here differ considerably from those used in other fields of application, e.g., the investigation of measurements of physical data. For example, in this article normal distributions do not appear. On the other hand random sums, invented in actuary theory, are important. In the first theoretical part we start with random demand and end with conditional random service which is the basic quantity that should be used to decide how much of a product one should produce in a given period of time. 

Compound densities, also called random sums, are typically applied in modeling random demands or random claim sums in actuarial theory. The reason for this is simple. Assume that customers randomly order different quantities of a product. Then the total quantity ordered is the random sum of a random number of orders. The conversion to the actuarial variant is obvious The total claim is made from the individual claims of a random number of damage events. Zero quantities usually are neither ordered nor claimed. This leads to the following definition. 

Health Care Financing Administration, Office of the Actuary (2001). 

The Log-Rank Test as presented by Peto et al. (1977) uses the product-limit life-table calculations rather than the actuarial estimators shown above. The distinction is unlikely to be of practical importance unless the grouping intervals are very coarse. 

Ideally the report would cover remanent life prediction, that is the intermittent inspection of a component and the re-assessment of its probable lifetime based on past service history and its physical or chemical condition the materials analogy of a pensions actuary making his estimate of the likely dates of death of his human charges. Probabilistic remanent life prediction... 

Information on death rates from automobile or other types of accidents or activities is generally much more solid than that pertaining to most chemical risks. Statistical data, compiled by actuaries, are used to derive such risk information. There is uncertainty associated with these actuarial figures, but most are fairly reliable. Most of the risk information about various cancers, presented in Chapter 5, is of this type. 

Note that some of the risk information is actuarial (based on statistical data, typically collected and organized by insurance companies), and some of it has been derived from the type of risk assessment discussed in this book (chloroform in chlorinated drinking water, afla-toxin in peanut products). While the uncertainties associated with the figures in Table 11.2 are much greater for some risks than for others (not a trivial problem in presentation of risk data), such a presentation, it would seem, is helpful to people who are trying to acquire some understanding of extremely low probability events, of the order of one-in-one million. 

Note Risks from activities are actuarial and much more certain than those associated with chemical exposures, which are estimated using regulatory models. Risks of cancer are assumed to equate to risks of death. Lifetime risk will be about 70 times higher if risks do not change substantially from year to year. 

These risks are, for the most part, large ones, and can be measured directly, by epidemiological studies and also by the activities of actuaries, who find ways to collect statistical data on rates of accidents and other safety risks, and on how they are distributed in populations. All-in-all, the relatively few risks that are large - the major causes of... 

Equally ironic, atropine and scopolamine were the only belladonnoids associated with a higher than expected death rate - these medications, used for centuries, evidently were grandfathered into the list of FDA approved pharmaceuticals. There were 8 deaths among 147 volunteers who received only atropine or scopolamine, noticeably more than the actuarially expected 3.7. 

An actuarial study by Milliman Robertson estimated the costs of 12 of the most common insurance mandates and found that they could increase the cost of insurance by from 15% to 30%. However, for 7 of the 12 mandates, the individual mandate increased the cost of coverage by less than 1% (www.ncpa.org/ ba/gif/estimate.gif, accessed Nov. 10,2004). lensen and Morrisey (1999) provide a critical review of actuarial studies of mandates. However, the conclusion that mandates tend to increase the cost of coverage seems to be uncontroversial. 

Modem cancer chemotherapy originated in the 1940s with the demonstration that nitrogen mustard possessed antitumor activity against human lymphomas and leukemias. Approximately 10 types of human cancer have 40 to 80% cure rates using chemotherapy alone or chemotherapy plus surgery or radiation (Table 55.1). For this purpose cure is defined as the disappearance of any evidence of tumor for several years and a high actuarial probability of a normal life span. 

In 1986, the Neutron Therapy Collaborative Working Group (NTCWG) compared neutrons (alone) and conventional photons. A significant difference (P < 0.01) was observed in clinical loco-regional failure, with actuarial 5-year failure rates of 11% vs. 32% after neutrons and photons, respectively (Fig. 12) [34]. Inclusion of routine posttreatment biopsies resulted in 5-year histological local-regional failure rates of 13% and 32%, respectively (P = 0.01). 

Figure 12 Actuarial clinical loco-regional failure in patients with locally advanced prostate cancer. Results of NTCWG trial on prostate. (From Ref 34.)...

Many companies make substantial profits by gathering and distributing information about products and companies (Klein 1997). They bear the fixed costs of learning about the relevant basic research and then sell that knowledge to others at a lower marginal cost. The A.M. Best Company rates life insurance companies actuarial and investment practices. Moody s rates the repayment risk of debt. 

The cascade theory is probably the oldest branching theory. It was developed by the English chaplain, the Reverend Watson16,181 and the biometrician Galton17,181 in 1873 who were evidently stimulated by Darwin s famous book on The Origin of Species . Nowadays cascade theory is widely used in evolution theory19,201, in actuarial mathematics (birth and death processes), in the physics of cosmic ray showers and in the chemistry of combustion due to branched chain reactions21-241. 

This strategy is designed to take you as far as you can go—but not much further. The actuarial strategy involves spending capital at a regular clip so that little or nothing is left over for children, friends, or charitable institutions. 

For example, as a widow of 65, you can, according to the actuarial tables, anticipate 19.5 more years. (This figure will probably increase in the future.) Your income from Social Security or company pension will remain relatively constant no matter how long you live. It is possible for you to plan on spending your capital (and the income it produces) over a specified time period—so much per month or year. 

You must take into account the fact that, as you dip into your capital, the income it produces will diminish. This strategy can be a high risk. If you have a partner, the calculations are more complex, and you may want to talk to a financial expert before embarking on the actuarial strategy. 

I Actuarial tables are for large groups. As an individual, you may outlive the tables by many years. If this happens, you will have lost your security blanket. 

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