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## Estimate of variance of Sullivan index

It can be shown that the variances of and can be approximated by[7] :

where and be the mean of the fractions of the interval lived by persons who die in the interval.

In case of life table use, the first term of equation 17:

is negligible in comparison with the other term (because is much smaller [18]).

Generally can be approximated by:

where is the number of persons of age i participating to the survey. So, equation 17 can be approximated by:

And for the same reasons, equation 18 can also be approximated by:

Remark: In some cases, it could be more appropriate to take an other variance of than equation 20, related to the special characteristics of the sample used for the survey. In that case, reader needs to refer to the details of the survey itself (for example, in case of a stratified sample).

Eric Hauet
Fri Apr 25 22:40:35 DFT 1997