Key points

Introduction

Life expectancy is defined as the expected number of years left to be lived for a given person or group of people. Determining life expectancy (ie, estimating the remaining lifespan of an individual) is sometimes necessary to properly adjudicate a legal dispute. The question of life expectancy often arises when there is a need to quantify periodic payments for damages over the rest of the life of an injured or aggrieved party or when the valuation of a pension or lifelong annuity is in question (in a case of divorce, for instance). When such a case arises, the life expectancy expert will be required to perform the calculations. The expert will need to synthetize pertinent medical information and reach an opinion grounded in scientific principles and a fair application to the facts at hand. These calculations should then be presented in a clear and relevant format so they can be used by other experts such as life care planners, economists, and actuaries. This article discusses some of the important aspects of determining life expectancy and the principles employed to formulate expert opinion on life expectancy.

Introduction

Life expectancy is defined as the expected number of years left to be lived for a given person or group of people. Determining life expectancy (ie, estimating the remaining lifespan of an individual) is sometimes necessary to properly adjudicate a legal dispute. The question of life expectancy often arises when there is a need to quantify periodic payments for damages over the rest of the life of an injured or aggrieved party or when the valuation of a pension or lifelong annuity is in question (in a case of divorce, for instance). When such a case arises, the life expectancy expert will be required to perform the calculations. The expert will need to synthetize pertinent medical information and reach an opinion grounded in scientific principles and a fair application to the facts at hand. These calculations should then be presented in a clear and relevant format so they can be used by other experts such as life care planners, economists, and actuaries. This article discusses some of the important aspects of determining life expectancy and the principles employed to formulate expert opinion on life expectancy.

Definition

Life expectancy is a mathematical concept applied to survival; it is defined as the average remaining years of survival for a group or an individual. It is sometimes confused with, but is distinct from, the median survival time (ie, the expected age at which half of the individuals in a population will have died). Life expectancy may generally approach the same value as median survival time, but it remains a fundamentally different concept. It should also be underscored that life expectancy refers to the remaining years to be lived, not the expected age at death. Confusion abounds on this, because the only widely disseminated information on life expectancy is what is properly called, but almost never is, “life expectancy at birth.” Thus, the life expectancy of a 50-year-old man will never be 80, for example, but it could very well be, say, 30 years.

Given that life expectancy is by definition a projection, inherent in its calculation is some hypothesis about the future of mortality. Most often, the hypothesis is that the current state of mortality—the mortality observable at the time of the projection—will remain constant forever. The soundness of this hypothesis is of course debatable, but in the context of calculations for litigation, it is by far the most popular assumption, as it does not involve complicated projection models about the evolution of mortality patterns. (Some jurisdictions may dictate the hypotheses to be employed. For instance, British courts will mandate that a schedule of projected (evolving) mortality rates be used ). Using a collection of age-specific mortality rates, it is possible to apply straightforward calculations to generate a complete life table comprising the future probabilities of survival at each age, the person-years lived in each age range, and the life expectancy at each age, among other quantities.

Basic notions

Some have claimed that estimating life expectancy for an individual is impossible, as the very concept applies only to a group. This is not a sound argument, given that the principle of statistical inference is valid. Moreover, often this spurious claim is immediately followed by the proposal that the general population life table be used instead of the expert’s calculation, thus defeating the very argument. The theoretical notion of group is, however, important to the concept of life expectancy. To reach a reasonable opinion, the expert needs to identify and discern a group of people that fits the profile of the individual. In theory, the expert would want the match to be perfect on all significant parameters. This usually starts with age, sex, nationality, and sometimes race; the expert would then add the specific medical information pertinent to the individual. In practice, the data available in the real world are limited. The expert will therefore try to match the available data to the individual in question as best as practically and reasonably possible to ensure that the mortality rates employed in calculations truly reflect the expected mortality profile of the individual (For example, an individual with coronary artery disease might be matched on the number of affected vessels, the ejection fraction, and perhaps even the concentration of N-terminal probrain natriuretic peptide (NT-proBNP), a biomarker used to estimate cardiovascular disease risk). Once a group is identified, it is possible to calculate, estimate, and extrapolate life expectancy based on the data pertaining to the known group.

Survival of individuals in the group will of course vary; some people will live longer, and some will live shorter. But in the absence of information, variables, or parameters that allow the expert to make a statistically grounded distinction among the individuals in the group, imputing the group average to all individuals is the best policy. The average is in such cases an unbiased estimator.

About expertise

An opinion on life expectancy prepared for the court will need to comport with well-established evidentiary standards. In the United States, these are the rules either of Daubert or Frye, depending on the jurisdiction (federal courts and most states have adopted the standards put forth by the Supreme Court of the United States in Daubert v Merrell Dow Pharmaceuticals . Some states retain the standards of Frye v United States ). Among the factors the court will consider when assessing admissibility are whether the method has been subject to peer review and publication, the existence of standards and controls for the method, and the degree to which the method has been accepted by the relevant scientific community. The method outlined in this article meets those requirements and has been accepted by numerous courts in the United States, Canada, United Kingdom, and Australia. In contrast, several purported methods fail on all prongs of the Daubert test. Among the methods to be avoided is the deduction of a fixed number of years for any given medical condition (Because the mathematics of life tables is nonlinear, this direct but simplistic attempt necessarily fails, despite the claims of some ). Defaulting to the general population life expectancy (usually on the grounds that the general population contains everyone and is therefore an appropriate estimate for anyone) also should be avoided (The general population life expectancy is appropriate when differentiating factors are not known. However, if some factors are known and present in the individual, the general population is no longer an appropriate estimate. As an illustration, the mean annual income in the United States is a general average. If one wants to estimate the expected annual income of a Fortune 500 chief executive officer (CEO), the general US mean is inappropriate even if all CEOs are included in the larger average. The fact that they are CEOs makes them a distinct subgroup with its own average). Additionally, declaratory statements based on nothing more than nonsystematic data, such as from personal clinical experience should be avoided. Similarly, statements to the effect that an individual could live to a normal life expectancy or that the average of a subgroup does not apply to the individual because of alleged but not demonstrably distinguishing characteristics should not be credited, as they merely betray a misunderstanding of the very concept of life expectancy.

Experts in general must be qualified by education, training, or experience. In the case of life expectancy, the expert must be knowledgeable about and adept at statistics. Typically, although perhaps not exclusively, this will mean graduate-level education in statistics, biostatistics, epidemiology, demography, or actuarial science. Although statistical knowledge is the only requirement per se, an individual wishing to qualify as an expert for life expectancy would be well advised to possess some knowledge of medicine, or, failing that, retain the services of qualified assistants.

Sources of data

The most often-used data are the national life tables. These tables would be appropriate if the only information known about a patient was age, sex, and nationality. Here, the match of the individual to the group would be perfect (same age, sex, and nationality). If any medical condition is involved, however, the expert needs to take into account any excess mortality that may apply. Data on the excess mortality of various conditions can be found in treatises, specialized journals, medical journals, and medical textbooks. But even then, it will probably be necessary to make some use of base mortality rates, usually from national tables. These are most often produced by national statistical agencies and are easily obtainable. In the United States, the tables published by the Centers for Disease Control and Prevention (CDC) are certainly adequate. Sometimes, other organizations may hold collections of life tables derived from official data ; a cursory look at their methodological specifications should suffice to ascertain the value of such tables. Some even estimate data at the subnational level. However, employing these tables rather than national tables would probably be advisable only after verifying the jurisdictional requirements.

Mathematics of life expectancy

Life expectancy cannot, for practical reasons, be measured directly. This would entail waiting for everyone in the whole group of interest to die (Note that, when preoccupied with historical matters, such tables are compiled upon extinction. These life tables are called cohort life tables, in contrast with the much more common period life tables). The way to measure life expectancy is to calculate age-specific mortality rates. It should be noted that although rates and probabilities are related concepts, they are not the same quantity, and although it is possible to calculate life expectancy based on age-specific probabilities of death, mortality rates are preferable for technical reasons that will be explained. Life expectancy is calculated by amalgamating a series of age-specific mortality rates to replicate the mortality experience of a whole life span. Applying this series of rates to a theoretical population yields a set of survival probabilities at each age. For example, one can calculate the 1-year mortality rate of people age 20 by relating the number of deaths occurring in a given year to people between 20 and 21 to the number of 20-year-olds alive during that year (for national tables, this is done using census data and death records). For a given year, this is done for all ages. Thus, as an example, the life table for Canadian females in 2007 ( Table 1 ) will be constructed using a collection of age-specific mortality rates from ages 0 to over 100, each of which was calculated on the basis of the number of observed deaths between ages x and x + 1 and the estimated population of people aged x, for x in values of 0 to the maximum age of the life table.

Table 1

Abridged life table, Canada, females, 2007

Age	lx	dx	mx	qx	ax	Lx	Tx	ex
0	100,000	477	0.00478	0.00477	0.07	99,557	8,295,368	82.95
1	99,523	29	0.00029	0.00029	0.5	99,509	8,195,811	82.35
2	99,494	19	0.00019	0.00019	0.5	99,485	8,096,303	81.37
3	99,475	10	0.00010	0.00010	0.5	99,470	7,996,818	80.39
4	99,465	10	0.00010	0.00010	0.5	99,460	7,897,347	79.40
5	99,455	14	0.00014	0.00014	0.5	99,449	7,797,887	78.41
6	99,442	13	0.00013	0.00013	0.5	99,435	7,698,438	77.42
7	99,429	14	0.00014	0.00014	0.5	99,422	7,599,003	76.43
8	99,415	10	0.00010	0.00010	0.5	99,410	7,499,582	75.44
9	99,405	10	0.00010	0.00010	0.5	99,400	7,400,172	74.44
10	99,395	7	0.00007	0.00007	0.5	99,391	7,300,772	73.45
11	99,388	8	0.00008	0.00008	0.5	99,384	7,201,381	72.46
12	99,380	11	0.00011	0.00011	0.5	99,374	7,101,997	71.46
13	99,369	11	0.00011	0.00011	0.5	99,364	7,002,622	70.47
14	99,358	18	0.00018	0.00018	0.5	99,349	6,903,259	69.48
15	99,340	21	0.00021	0.00021	0.5	99,330	6,803,910	68.49
16	99,319	20	0.00020	0.00020	0.5	99,309	6,704,580	67.51
17	99,299	26	0.00026	0.00026	0.5	99,287	6,605,270	66.52
18	99,274	34	0.00034	0.00034	0.5	99,257	6,505,984	65.54
19	99,240	31	0.00031	0.00031	0.5	99,225	6,406,727	64.56
20	99,209	30	0.00030	0.00030	0.5	99,194	6,307,503	63.58
30	98,902	36	0.00036	0.00036	0.5	98,884	5,316,914	53.76
40	98,401	78	0.00079	0.00079	0.5	98,362	4,330,091	44.00
50	97,050	217	0.00224	0.00224	0.5	96,942	3,351,702	34.54
60	93,842	514	0.00549	0.00547	0.5	93,585	2,395,083	25.52
70	86,337	1190	0.01388	0.01378	0.5	85,742	1,488,783	17.24
80	69,102	2583	0.03810	0.03738	0.5	67,811	700,495	10.14
90	33,896	4045	0.12707	0.11933	0.5	31,873	170,019	5.02
100+	3615	3615	0.41254	1.00000	0.5	8763	8763	2.42

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