Here, we are going to give an example of calculation of the variance of Sullivan index. We use equation 21 on French data (life tables of 1991, males, prevalence ratios derived from health survey).
However, in order to show the use of some previous equations,
we have complicated the example by assuming that the survey didn't
take into account institutionalized persons. If we use the prevalence
ratios directly derived from the survey in the formula 1,
we make the implicit assumption that the prevalence ratios in
institutionalized population are the same as in the non
institutionalized population. Because, we do not want to do such an
assumption in the calculation of 
, we are going to estimate
the variance of the disability free and non institutionalized life
expectancy. To that extent, it is assumed that formula 8
has been used to calculate in section 1.3.