Farid -

This does sound 'doable,' but i think that accuracy will be the question. Finding the sample sizes needed to study the results you want to consider may be a bit involved. I am not an actuary, but I would guess you want to see how believable official statistics are, so if you have the crude death rate (CDR) from the official statistics, might you first compare them directly to your CDR?

For table rates, such as the probability of living to age 50 given that you already lived to age 30, for example, for a given group of interest, say females in a given geographic region, you would estimate from your data, I suppose, by dividing the number of those who lived to 50 by the number of those people who were alive at 30, but this is not my field, so I do not know how your data have been collected and organized. It depends upon the specific nature of the data available to you. But I think obtaining point estimates should be 'doable,' regardless. (At any rate, the point probability estimate just described would be a "conditional probability.")

The question is How accurate will your results be, so that you might know if the official results appear to be reasonable? Obtaining standard errors for your results would seem problematic, depending upon how the data are collected, and how much you can collect. Often a pilot study is needed to obtain preliminary standard error estimates. But if the official statistics were supplied with standard errors, you could see if your results appear reasonably close to the official ones. Standard error is not all there is to consider. There are distributional assumptions (or Chebyshev 's Inequality could be used), bias problems, and nonsampling error problems such as measurement error - and measurement error can cause bias and standard error problems, especially if you strain your resources.

So, not being an expert in these data collections, I do not know how best to study accuracy, to see if your results and official results are 'close,' but I'm rather certain you could obtain point estimates for your own table, and I expect you could find some way to study accuracy to see if your results and official statistics agree reasonably enough, given the data sources.

Perhaps you could involve some simple regression through the origin (almost certainly quite heteroscedastic - at least as much say as the classical ratio estimator, CRE) where you could compare results and consider the estimated variance of the prediction error, where one is used to estimate ("predict") for the other. Note that the square root of the estimated variance of the prediction error in SAS PROC REG, for example, is STDI. Note the attached which I doubt would relate more than very indirectly to your problem, but is an example of using regression prediction to compare results, and might possibly serve to stimulate an idea more appropriate to your application.

I'd also encourage any graphical comparisons, such as scatterplots.

Could be an interesting study. But I suggest that you should first obtain some literature (textbooks and articles, etc) on (1) actuarial science and (2) reliability theory, to see what others may have done for a similar study. There may even be some web sites dedicated to this, I would guess.

Best wishes - Jim  

Technical Report A Note on Estimating Impact of Data Collection Mode Change f...

Farid - I don't know the nature of the survey data you have for your analysis, but in most cases, surveys that provide data on mortality also have information on the population from which these data were collected from so in most cases one does not need separate data on the risk population from an independent source to calculate age-specific death rates (ASDRs) and construct a survey based life table. Assuming that the survey is well designed and sampling error is less of an issue, one should then be able to compare this survey based life table with 'official' estimates for the same population and year. However, if your concern is not getting enough cases to construct a complete life table (i.e. a life table based on single years of age), I think one of the things you can do is first to construct an abridged life table based on ASDRs for broad age groups to get enough cases and then generate a "complete life table by fitting parametric (i.e. such as the Heligman-Pollard 8 parameter mortality schedule) or non-parametric (such as spline) curve to your data. Again assuming that the survey is well designed and sampling error is less of an issue, you can then easily compare the smoothed complete life table from the survey data with your ‘official’ estimates. If need be (i.e. you want to be more precise in your comparison), you can also obtain sampling error around your survey based life table values. The following are some useful references that you may wish to refer for more:

Life Table Techniques and Their Applications  by Krishnan Namboodiri & C. M. Suchindran (1987 ).

Demography: Measuring and Modeling Population Processes by Samuel Preston, Patrick Heuveline and , Michel Guillot   2000.

Good luck

Thank you all for your answears, I want just to be more clear about my question :

The point is that the principal objectif of this survey is not to construct life table, but just to get a death distribution by causes. so the survey was focused on some observed death (in hoousehold). in margin, the distribution of these death by age was published in the final report of the survey, but we dont have any detailed information about the size and age distribution of the population. 

My idea was to supoze a CDR near to the official one, to estimate the age-specifique death rates, to interpolate to obtain detailed age mortality rate. the final result depends on the supposed CRD. so, I have just compared the global form (by dividing qx/q0) of the two life tables (survey and offiacial). this comparaison leads to some differences for some age. is there another method or approach to improve the obtained results

Farid:

It´s very difficult to work on mortality measures if you don´t have enough information about the size of population at least.

Do you have any other information related with the observed deaths? For example, if there is information about some social characteristic of the households (like poverty conditions, house quality, etc) you could correlate available life expectancies at birth of some regions (areas, provinces, States, etc) with their social conditions. And then you could apply this pattern to the age distribution of deaths you have.

Of course it is an indirect way to estimate mortality measures, but sometimes it´s the only way to work with small populations or with incomplete data.

Good luck.

Basically you need age specific mortality rate to make a lie table, so that you need age specific population size in addition to age specific number of death,

To estimate the age specific population size, you will have to accept the following two assumptions.

1) The crude death rate is same as national official statistics.

2) The population structure is same as national population pyramid.

If you accept them, you can get the estimate of mx by the following steps.

1) You already have the age specific number of death, dx.

2) Total number of death D = sum(dx),

3) Using CDR of national official statistics, total population size P = D/CDR.

4) Using age specific population proportion of national statistics Cx = (Age specific population size of the national population pyramid) / (Total population size of the national population), you can get Px = P*Cx.

5) You can get mx = dx / Px.

Once you get mx, it's possible to estimate life table using ordinary methods.  However, it's quite implausible.  Generally speaking, it's unacceptable.  I don't recommend it.

(Death%)/(population%) x (1/CMR) = deaths by age and ..... I have done this and I supposed that CMR in survey as the population survey structrure is same like the Global population. and i got a life table: can I use the obtained result to evaluate the official death statistics: That was my question! Thank you again

Farid if the goal is only to compare the mortality data from the two sources, actually I would approach it differently. Instead of constructing a life bale that is going to be too much dependent on external data and loaded with numerous assumptions, I would simply treat the death distribution from the sample survey as a frequency and then calculate some measures of central tendency (such as median age at death) and compare the resulting statistic with the one from the official life table.  This comparison does not require you to make any assumption or borrow data from an external source. The only requirement for such comparison to be valid is that the sample population is an unbiased representative, and hence its age distribution is fairly identical with that of the total population, which I  assume to be the case here, as both the survey data and the official mortality statistics come from the same population.  However, if there is a reason to suspect that the sample population is not a true representative of the population from which the official life table was obtained, then your may face some challenges.  By the way, if your interest is to evaluate the official death statistics, as you seem to suggest in your last posting,you could try using Brass' "general growth balance method" or the Bennett-Horiuchi extinct generation method to evaluate the death coverage in the data used for constructing the official life table, and then adjust it accordingly, if need be.

Best of luck

Dear Farid,

I am not an expert in this field. But I agree with others that using your own data is worthwhile rather than adopting assumptions. In your situation I would have done my preliminary analysis presenting death rates by using the data I have, then provide standardized mortality rates using world population structure and then compare with rates from other countries. The WHO standard world population is

Available online at: http://www.who.int/healthinfo/paper31.pdf

rubina

the problem for the algerian case, is that there is about 5 years of difference in life expectancy at birth between national statistics and thoses of UN and WTO. i want to get a jugement in this way by using the inforlation in this survey which can provides more ideas about the question. i will try to finalize the paper and to post it in RG soon as possible. thanks

Hi Farid.

A few years ago the U.S. Census Bureau provided online some spreadsheets for the calculation of different demographic measures.

The program was called PASEX (Population Analysis Spreadsheets in EXcel).

In particular, I remember there were some of the spreadsheets which allow to compute a complete life table in the case of data deficiency about the age structure (as in your case), starting from nMx or nqx. Obviously, a few other parameters are needed in order to proceed: for instance, it requires you to indicate the separation factors from a Coale-Demeny region model life table and some other parameters (it depends on the spreadsheet you use and on the procedure which is applied in it).

I don't know if the U.S. Census Bureau still provides this program, but it worth trying to find it because it can be useful in your case.

Best regards.

Manuela

Dear Manuela thank you for all these usefull remarks.

I think that the program you mentionned is still existing and i use also "MORTPACK" for these kinds of calculation,

Thank you again.

Best regards