SISA Research Paper

About the Lifetable Spreadsheet

The life table spreadsheet is fully based on a paper by Chiang. The life table spreadsheet contains the same data as Chiang's paper, the 1960 U.S. data. We consider that you consult Chiang's paper to learn about the meaning of each column in the life table spreadsheet. However, a short introduction seems appropriate. The life table describes the process of mortality in a population. The life table can be considered to be an old and distinguished predecessor of methods such as Kaplan-Meyer or Cox-Regression. A life table is a hypothetical construct with age specific death rates as input (the 'M' column) and remaining years of life left, or life expectancy, at various ages as an important output (the 'e' column). The probability to die in a certain age band can be calculated by taking the ratio of numbers from column 'd' and 'i'. What the life table represents is what a cohort of a 100.000 babies would experience in terms of mortality and age structure had they have the age specific death rates, which are based on the current mortality experience of a population, as given in the 'M' column.

In the 'M' column are mostly the age specific death rates experienced by a population during a certain period. That is why we speak of the "current" life table. In case of a true cohort we would speak of generation life tables. Lastly, life table analysis does not have to be limited to demography or epidemiology. It can equally be used in estimating the life expectancy after medical operations or the life expectancy of televisions or other industrial products. Similarly, death does not necessarily have to be the outcome studied, however, few examples exist were something else is used. A paper comparing the life expectancy with the Standardized Mortality Ratio (SMR) can be found here.

A second spreadsheet allows for considering the effect of a particular cause of death 'k' on the mortality in a population. The number of death from cause 'k' is included in the appropriate column. In the a.k column you give the mean point in each age group in which the deaths occurs, a.k is thus the fraction in the age period concerned which was on average lived by the death from cause k. The spreadsheet calculates the Potential Gains in Life Expectancy (PGLE) after removing cause k, considering competing causes of death and following the notation by Chiang (1991). Furthermore, the spreadsheet calculates the (Premature) Years of Potential Life Lost (YPLL), this is the number of person years added to the total number of person years lived in a population if cause of death k would be removed. Often the YPLL is only calculated for the productive population, basically the age groups 15-64. The LYPLL gives the lifetime loss of life years for a particular disease in a population. This is calculated on the basis of the life expectancy. The YPLL is also often presented as the number of (premature) life years lost (up to a certain age) per 10,000 persons in a particular age group. The user has to sum the life years lost for a selection of age groups him-, or herself.

The (P)YPLL is more often used in research than the PGLE. The fact that you can restrict the YPLL to particular age groups makes it easier to consider a disease in terms of economic costs. Also, the YPLL can be easily adapted to consider other factors than death, for example, the economic costs due to the number of years of productivity lost because of people suffering from a particular disease who are unable to work. The disadvantage is that the (P)YPLL will mostly not consider competing causes of death, which is a particular problem in populations, were the pressure of mortality or inability is high. The YPLL will overestimate the economic consequences of disease in such populations. For this situation the SISA spreadsheet introduces the mortality adjusted YPLL, were it is considered that survivors from a removed cause of death k have a certain probability of dying from competing causes in future years. Another problem is that the YPLL is highly sensitive to population age structure and findings regarding the costs of a disease are difficult to generalize from one population to another. The PGLE is actuarially less problematic, it allows for easy comparison between populations, and it does consider competing causes of death. However, gains in life expectancy are difficult to apply in a wider macro economic analysis. For a discussion about discounting and mortality adjusting the YPLL please consult this paper

The spreadsheet also considers discounted YPLL. Discounting is used to weigh years in the near future as more important compared with years in the far away future. It is usual to discount financial/money data at or slightly above the rate of inflation as time progresses. So if you use the data to do a cost benefit analysis discounting seems appropriate (at about 5%). Discounting of life is considered much more problematic and there is a philosophy that it is incorrect to consider future life-years of less value than current life-years. This is certainly not the case with individuals; the immediate gratification of smoking a cigarette mostly weighs more heavily compared with the possibility of a future early death. However, at the level of society discounting might not be right and it is considered that therefore no discounting or only a low level of discounting is appropriate (at about 1.5%). SISA is of the opinion that discounting, at a higher level than 1.5%, should be recommended. The reason is that the (P)YPLL is a strange concept. If we would eradicate a disease now we say (using the YPLL) that we will obtain a certain benefit. However, this benefit will not occur now immediately but be accrued in the (far away) future. In-build in the YPLL is therefore a measure of uncertainty considering the continuation of the outcome and the possibility of alternative and more efficient and effective courses of action developing. This uncertainty increases with the passing of time. It seems therefore appropriate to consider benefits in the far away future as less important compared with benefits in the near future.

To make the spreadsheet complete a Standardized Mortality Ratio (SMR) calculation is presented. SMR basically compares the mortality observed in the sub-population with the mortality that could be expected, if the sub-population had an age specific mortality pattern, which is comparable with the mortality in the standard population.

Breslow NE, Day NE. Statistical methods in cancer research. Vol 2: The design and analysis of cohort studies. Lyon: International Agency for Research on Cancer 1980.

Chiang CL. The life table and its construction. In: Chiang CL. Introduction to stochastic processes in Biostatistics. New York [etc.]: John Wiley 1968.

Chiang CL. Competing risks in mortality analysis. Annual Revue of Public Health 1991;12:281-307. ->Medline

Gardner JW, Sanborn JS. Years of Potential Life Lost-What does it measure? Epidemiology 1990;1:322-329. ->Medline

Lai D, Hardy RJ. Potential gains in life expectancy or years of potential life lost: impact of competing risks of death. International Journal of Epidemiology 1999;28:894-898. ->Oupjournals

Torgerson RJ, Raftery J.. Economic Notes: Discounting British Medical Journal 1999;319:914-915. ->BMJ

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SISA Research Paper