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Estimate of variance of Sullivan index

It can be shown that the variances of tex2html_wrap_inline998 and tex2html_wrap_inline1304 can be approximated by[7] gif:



where tex2html_wrap_inline1306 and tex2html_wrap_inline1308 be the mean of the fractions of the interval tex2html_wrap_inline1284 lived by persons who die in the intervalgif.

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


is negligible in comparison with the other term (because tex2html_wrap_inline1314 is much smallergif [18]).

Generally tex2html_wrap_inline996 can be approximated by:


where tex2html_wrap_inline1320 is the number of persons of age i participating to the surveygif. 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 tex2html_wrap_inline994 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