The meaning and use of the cumulative rate of potential life lost

O International Epidemiological Association 1998

Printed in Great Britain

International Journal of Epidemiology 1998;27:1053-1056

The meaning and use of the cumulative rate of potential life lost Wen-Chung Lee

Conclusions The CRPLL has several desirable properties, rendering it a promising alternative for quantifying health status. Keywords Age standardization, cumulative rate, epidemiological methods, health-status indicator, life expectancy, vital statistics, years of potential life lost Accepted 20 April 1998

The 'years of potential life lost' (YPLL) is a public health measure in widespread use.1 The statistic measures the total number of life yean lost due to premature deaths in a population. The definition of premature includes death at the age of less than 65, 70, 75 or the average life expectancy, etc.1 The measure YPLL was introduced mainly because simple mortality rates, including the age-specific and the age-adjusted ones, do not fully address the issue of premature mortality, the impact of disease/death and its cost to society. Although, YPLL does provide a means of comparing the relative importance of different causes of death for a specific population at a specific point in time, the index does not apply when one moves a step further in making comparisons between different populations or across different time periods.2 This is because the YPLL lacks a 'denominator' to adjust for the differences in the population sizes and age structures of the groups being compared.2 Such modified indices as "YPLL per death' or 'RPLL (rate of potential life lost) do have a denominator with them.3 However, these indices should be viewed as a kind of 'crude' rate at best. To facilitate valid comparisons between groups, some suggest using age standardization.23 However, this leads to further 'arbitrariness' in choosing a suitable 'standard Graduate Institute of Epidemiology, College of Public Health, National Taiwan University and National Defense Medical Center, ROC. Reprint requests: Dr Wen-Chung Lee, Graduate Institute of Epidemiology, National Taiwan University, No. 1, Jen-Ai Rd, 1st Sec Taipei, Taiwan, ROC.

population'. Also, the resulting age-standardized indices of potential life lost are not easily interpretable by themselves. Another problem with the YPLL index is that it quantifies the cross-sectional (current) but not the prospective (future) impacts on society. It should be noted that the deaths in a crosssectional table have already taken place and are no longer preventable.4 Therefore, when setting health goals for preventing and controlling diseases, it seems more pertinent to consider the future impact rather than the current burden.4 In this paper, we propose a new years-lost index, namely the 'cumulative rate of potential life lost' (CRPLL). It is in fact a very simple index—a simple marriage of the 'cumulative rate' (CR)5 and the YPLL. Yet, it serves the purpose of between-group comparison. It can also be considered a projection of future impact under the assumption that the age-specific mortality rates in the current year prevail. The author uses vital statistics in Taiwan for demonstration and compares the new index with existing health-status measures.

The Cumulative Rate of Potential Life Lost (CRPLL) We use mortality data of pneumonia and suidde in Taiwan (including the Kinma area), 1995, for the demonstration of the new index. Table 1 presents the death counts, population numbers, and mortalities in 5-year age groups. We assume the

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Background The 'years of potential life lost' (YPLL) is a public health measure in widespread use. However, the index does not apply to the comparisons between different populations or across different time periods. It also has the limit of being crosssectional in nature, quantifying current burden but not future impact on society. Methods A new years-lost index is proposed—the 'cumulative rate of potential life lost' (CRPLL). It is a simple combination of the 'cumulative rate' (CR) and the YPLL. Vital statistics in Taiwan are used for demonstration and comparison of the new index with existing health-status measures. Results The CRPLL serves the purpose of between-group comparison. It can also be considered a projection of future impact, under the assumption that the age-specific mortality rates in the current year prevail. For a rare cause of death, it can be interpreted as the expected years (days) of potential life lost during a subject's lifetime.

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Table 1 Population size and mortality due to pneumonia and suidde in Taiwan, 1995 Age 0-4 5-9

10-14 15-19 20-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59 60-64 65-69 70-74 75-79 80-84

Suicide

Death

Death

1 596 058 1 608 446 1 918 327 1 988 479 1 790 146 1 886 651 1 959 013 1 846 480 1 632 355 1 060 675 866 026 799 674 718 617 655 406 457 317 263 482 149 406 71 094

59 14 11 11 6 18 31 27 36 29 65 90 167 266 431 583 638 588

Mortality" 3.70 0.87 0.57 0.55 0.34 0.95 1.58 1.46 2.21 2.73 7.51 11.25 23.24 40.59 94.25 221.27 427.02 827.07

0 0 12 44 105 163 165 145 154 92 102 114 114 125 131 66 59 27

Mortality3 0.00 0.00 0.63 2.21 5.87 8.64 8.42 7.85 9.43 8.67 11.78 14.26 15.86 19.07 28.65 25.05 39.49 37.98

95% C.I. of CRPLL =X[('|-n,)-mi]±l-96-

where the pi is the population number of the age group ;. For the example of pneumonia death, the 95% CI of the CRPLL are calculated as 32.8, 37.5 (days). And for suidde, the 95% CI are 52.0, 57.9 (days).

Comparison with Other Health-status Measures In this section, we compare the newly proposed CRPLL with some existing health-status measures, namely, the crude rate, the 'ASR' (age-standardized rate), 5 the CR,5 the 'life table risk', 6 the YPLL,1"3 the YPLL per death, 3 the RPLL,3 the 'SRPLL' (standardized rate of potential life lost),3 and the T.YPLL' (lifetime years of potential life lost). 4 The formulae for these indices are shown in Table 2. It can be seen that all these indices are similar in form —they either take average or sum the age-spedfic mortalities

" Per 100 000 population.

Table 2 Comparison of various health-status measures In quantifying the impacts of pneumonia death and suidde in Taiwan, 1995

deaths, on average, occur at the mid-points of the intervals. And for the last interval (age *85), we assume an exponential decay. This is of course a very rough approximation, especially in the younger and the older age groups. For refinement one should turn to a more refined age grouping. We stop short of doing so in this paper since the principle remains the same. We also assume the upper age limit of the potential life lost to be 75, though the methodology can easily be modified for other cutoffs. The proposed CRPLL is simply a cumulative rate with the 'weight' taken, in addition to the usual interval length, as the average years lost of a death occurring in each age group. Given the assumptions presented above, the average lost years in each age group i (denoted as /,) can be calculated as /,- = 75 - (5i - 2.5), for / «£15. And for i >15, /, = 0. The CRPLL is defined through the following equation:

CRPLL =£[(/,-

Pneumonia death 14.44C

Suicide

14.55C

7.06c

0.0834

0.0122

0.0353

0.0080

20 207.5

43 500

6.58

26.89

RPLL

95.02 c

2O4.5c

SRPLL

107.08c

181.2C

LYPLL

30.4 d

51.0 d

CRPLL

35. l d

55.0 d

Measures* Crude rate

ASR

where the nf is the interval length of each age group and the mi is the age-spedfic mortality of the cause under concern. For the above example of death from pneumonia, the CRPLL is calculated as 0.0961. And for suidde, it is 0.1505. Note that they take the unit of 'year1. However, for ease of presentation and interpretation, we change their units into 'day' (CRPLL = 35.1 days for pneumonia death and 55.0 days for suidde). It is of interest to note that the above-defined CRPLL has an intuitive appeal when applied to a rare cause of death. The appendix shows that it can be interpreted as the expected years (days) of potential life lost due to the cause under concern (e.g. pneumonia and/or suidde) during a subject's lifetime, if he/she does not succumb to other competing causes of death.

AtA IK"1-]

CR life-table risk

7.61 C

[loo.ooo YPLL YPLL per death

ni)m\

i

Formula1"

1

b

c d

ASR: age-standardized rate, CR. cumulative rate, YPLL years of potential Ufe lost, RPLL rate of potential life lost, SRPLL: standardized rate of potential hfe lost, LYPLL: lifetime years of potential life lost, CRPLL cumulative rate of potential life lost. /,: average lost years in age group i, />,: population number In age group i. m(. mortality rate in age group i. n(: population structure of the standard population (1976 world standard population in our examples), yf. personyear in age group i of a life-table population, n,: interval length of age group i. Per 100 000 population. In days.


85+

Pneumonia Population

The formula for the confidence intervals (CI) of the CRPLL can be derived easily which takes a very simple form:

CUMULATIVE RATE OF POTENTIAL LIFE LOST (the w,-'s) of the population under study. The differences lie in the 'weights' being used. And this greatly determines the properties of the various indices. First, we see that the weights in calculating the crude rate, the YPLL, the YPLL per death, and the RPLL indices involve the age structure of the population under study (p,'s). Thus they are, as is already well known, crude measures unsuitable for between-group comparisons. The SRPLL is a standardized index like the ASR. They circumvent the problem of disparate population structures by introducing the 'Kj (standard population structure) as the basis of comparison. As has been pointed out however, the choice of such a standard may sometimes present a problem. By contrast, we see that the newly proposed CRPLL does not have this kind of problem. Its weight (/,• • ttj) does not involve the population under study or any other standard populations at all. Therefore, the CRPLL can legitimately be used to compare the impact of disease on different countries.

Fourth, it is also of interest to compare the CRPLL with the LYPLL.4 The LYPLL is a projected risk as well. However, the index is developed using the life table methodology (it involves the 'y(, the person-year in age group i of a life-table population). A life table explicitly assumes the presence of competing

deaths. Thereby the loss measured by the LYPLL is the interplay of the cause of death under study and the competing deaths. By contrast, the CRPLL in this paper quantifies specifically the pure effect from the cause of death under concern. Just as the CR can be called a 'conditional risk' and a life-table risk, an 'unconditional risk', we may refer to the CRPLL as the 'conditional' years-lost index and the LYPLL, a YPLL of 'unconditional' type. Finally, we note that the CRPLL, though it is a population summary index, is best understood at the individual level—a property also shared by the CR, the life-table risk, or the LYPLL. These indices reflect, from different perspectives, the lifetime history of an average subject in the population. This is in sharp contrast to the traditional YPLL index which, though it quantifies succinctly the burden of disease for the entire population, doesn't by any means possess an individual-level interpretation by itself. The properties of these various health-status measures are summarized in Table 3.

Discussion In this paper, we see that the proposed CRPLL has several desirable properties, rendering it a promising alternative for quantifying health status. It nicely condenses the whole table of age-specific mortality into a single but meaningful value—the expected year of potential life lost during a subject's lifetime. This valuable information is not readily discernible from a simple inspection of the mortality table per se. However, one should note that any index derived from condensation or summarization can mask important features of the data. For an aetiologic investigation, we believe that comparisons should still be based primarily on the table of age-specific rates rather than on a summary of it. Secondly, it should be pointed out that the CRPLL is based on 'cross-sectional' but not 'longitudinal' data. The situation is just like the case of cumulative risk or life expectancy. All of them rely on the same assumption, i.e. each subject in the population will be subject throughout his or her life to the same agespecific mortality rates prevailing in the current year. Clearly, this is a bold assumption. In previous papers, the age-periodcohort (APC) modelling technique has been adopted to obtain the cohort-specific lifetime risk7 and the cohort-specific life expectancy8 from cross-sectional data. The same technique can

Table 3 The properties of the various health-status measures Need for an external standard

Value judgment on death

No Yes

No No

No

No

Yes No

No No

Yes

RPLL

No No

No No

No Yes Yes Yes

SRPLL

Yes

Yes

-

LYPLL

Yes Yes

No No

Yes Yes

No No Yes

No

Yes

Yes

Yes

Measures*

Between-group comparison

Crude rate

No

ASR

Yes Yes

CR Life-table risk YPLL YPLL per death

CRPLL ' See the footnotes in Table 2.

Lifetime projected risk

Conditional risk

Individual-level interpretation

No

-

No

No Yes

-

Yes

No Yes

No -

Yes No

-

No No

No No

No Yes Yes


Second, we see that the weights of the various years-lost indices all involve the /,-, while the crude rate, the ASR, the CR, and the life table risk don't. The /,-, the average years lost of a death occurring in each age group, can be viewed as a value judgment imposed on each death. It reflects, in some sense, consequent social, family and economic burdens. Without it, the impact of a death will be the same irrespective of the age. Third, we note that the interpretation of the CRPLL as the expected years of potential life lost during a subject's lifetime is similar to the well-known link between the CR and the lifetime disease probability.5 They both reflect the projected risk an individual will have as he/she progresses through each age. However, the CR weighs the risk according to the amount of time spent in each age category (the nt), whereas the CRPLL weighs the cumulative risk additionally with value judgment. Consequently, these two indices have different implications. From Table 2, we see that the lifetime risk of pneumonia death in Taiwan is 0.0834 (CR = 0.0834), and it causes, on average, 35.1 (CRPLL = 35.1) days of potential life lost. As for suicide, we see that its lifetime risk (CR = 0.0122) is lower. Yet, it causes more potential life lost (CRPLL = 55.0 days) during a subject's lifetime.

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also be applied to the present context. However, such modelling is technically involved and is beyond the scope of this paper. At present, it is advised that we interpret CRPLL with due caution as with lifetime risk and life expectancy. Finally, the CRPLL, being an index of the lost years due to death, is a measure of disease burden on society. However, a disease or an illness can exert its impact before death, by causing disability or jeopardizing quality of life, etc. Recently, there have been considerable efforts directed toward combining the two dimension of morbidity and mortality into a single index for disease burden (for example, the QALY and the DALY).9 It is possible that the concept of cumulative rates may shed new light on the problem of constructing composite burden-of-disease indicators as well.

5

Breslow NE, Day NE. Statistical Methods in Cancer Research, Vol II, The Design and Analysis of Cohort Studies IARC Scientific Publication, No. 82, Lyon, France, 1987.

6

Schouten LJ, Straatman H, Kiemeney LALM, Verbeek ALM. Cancer incidence: life table risk versus cumulative risk. J Epidemiol Community Health 1994:48:596-600.

7

Campbell MK, Feuer EJ, Wun LM. Cohort-specific risks of developing breast cancer to age 85 in Connecticut. Epidemiology 1994:5:290-96.

8

Lee WC, Hsieh RL. Estimating life expectancy using an age-cohort model in Taiwan. J Epidemiol Community Health 1996;50:214-17.

9

Morrow RH, Bryant JH. Health policy approaches to measuring and valuing human life: conceptual and ethical issues. Am J Public Health 1995:85:1356-60.

Appendix Acknowledgements This paper is partly supported by the National Science Council, ROC.

References 1

2

Marlow AK. Potential years of life lost: what is the denominator? J Epidemiol Community Health 1995;49:320-23.

3

Esteve J, Benhamou E, Raymond L. Statistical Methods in Cancer Research, Vol TV, Descriptive Epidemiology IARC Scientific Publication, No. 128, Lyon, France, 1994.

4

Lee WC. Quantifying the future impact of disease on society: life tablebased measures of potential life lost. Am J Public Health 1997;87: 1456-60.

CR, =^d[nj-mj]

(see5)

This probability is approximately equal to CR,, provided that it is small. Therefore, the probability of dying in the ith interval is CR, - CR,_j = rij mt Such a death incurs, on average, /,- years of life lost (see text). We see that the expected years of potential life lost due to the cause under concern during a subject's lifetime is

X[/,-i,

m

;] = CRPLL

if he/she does not succumb to other competing causes of death.


Gardner JW, Sanbom JS. Years of potential life lost (YPLL)—what does it measure? Epidemiology 1990,1:322-29.

Let the age groups be indexed by ;', and the interval length and the cause-specific mortality of each age group be represented by n, and m, respectively. In the absence of compering deaths, the lifetime disease risk (probability of death) from birth to the end of the ith age interval is l-exp(-CR,), where