This SISA spreadsheet allows you to do a life table analysis

Simple Interactive Statistical Analysis

Life table/YPLL/SMR/CMF

Input.

The spreadsheet available does a full abridged current life table analysis to obtain the life expectancy of a population. 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. You will have to provide your own data by overwriting the second (total number of deaths in an age category during a particular period) and third column (mean population size in an age category). It might be necessary to shorten the life table for your purposes, be particularly careful about deleting the 0-1, 1-5 and 95+ entries, as these work differently from the other entries. Furthermore, speadsheets have now been added to calculate the YPLL, the SMR and the CMF. Please read the discussion below.

There is now an inexpensive mortality analysis for windows program available. This program contains the same functions as the spreadsheet but in addition has better mathematical procedures and is more flexible to use compared with the spreadsheet. It has particularly been developed to make standardization easy. Please download the free demonstration program.

Explanation.

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.

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. The Comparative Mortality Figure (CMF) compares the mortality expected in the standard population -if it would have had a mortality pattern similar to the mortality in the sub-population- with the mortality observed in the standard population. This spreadsheet with real data immediately shows the weakness of these techniques. The SMR basically says that Caribbeans living in Amsterdam would have a 20% lower mortality (compare with 1=no different) if they had a mortality pattern like the people in the Netherlands generally. This is contradicted by the CMF, which shows that Netherlanders would have had a 5% lower mortality if they had a mortality pattern like Caribbeans living in Amsterdam. The very different age structure of the two groups interacting with the different mortality patterns in the groups, results in two true, but apparently contradictory, conclusions. The consistency test also tells you that the analysis is probably unreliable. SISA would much prefer comparing the life expectancies for the two groups in this particular case. However, for comparing groups regarding particular diseases the SMR and CMF are still important techniques, but the problems with these techniques should always be considered in interpreting the results. The data and the use of the SMR is further discussed here. Other techniques to calculate confidence intervals for the SMR and discussions are available on the SMR page. Calculations for the CMF come from the book by Breslow and Day, which also has a nice discussion of some topics related to SMR, CMF and standardization.

Considering the spreadsheet itself, it proved very difficult to put discounting in a flexible way in the spreadsheet. You might want to change the discounting percentage, however. See the discounted YPLL columns as a demonstration and be very careful if you tinker with it. SISA is happy to help you in doing it all correctly or to check your calculations for the usual consultancy fee $.

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