In order to estimate HALE we set up an abridged life table using mortality rates for the Netherlands from 1999 [10]. The number of life years obtained from the life table were multiplied by one minus the average disability weights:

*HALE*
_{g,a, }
*health-adjusted life expectancy gender g age a*

*L*
_{g,a}
*number of life years lived between age a and a+5 for gender g*

*L*
_{g,85+ }
*number of life years lived after age 85 for gender g*

*m*
_{g,a}
*average disability weight between age a and a+5 for gender g*

*m*
_{g,85+ }
*average disability weight after age 85+ for gender g*

*l*
_{g,a}
*number of survivors at age a in the life table cohort for gender g*

*z last open-ended age interval in the life table*

Age and sex specific average disability weights are a function of disease specific prevalence rates and disability weights. In our study, data from the Dutch Burden of Disease Study was used to estimate average disability weights. The Dutch Burden of Disease Study estimated disability weights, using a large panel of experts and the person trade off method [11], and disease prevalence of 48 different disease categories [12]. All data used in our calculations (mortality rates, disease prevalences and disability weights) are available in Additional file 1.

To estimate comorbidity prevalence, independence between diseases is assumed so the amount of comorbidity between disease 1 and 2 (the joint prevalence of diseases 1 and 2) is simply the product of their prevalence rates:

*p*(*1*,*2*) *joint prevalence of disease 1 and 2*

*p*(*d*) *joint prevalence of d diseases*

Gender-specific average disability weights were calculated using age classes of five years (0–4, 5–9, 10–14 to 85+). However, for notational simplicity, age and sex indices have been omitted in the notation.

### No adjustment for comorbidity

When no adjustment for comorbidity is made the average disability weight can be calculated by simply adding up the disability caused by all diseases:

*m average disability weight*

*p*
_{
d
}
*prevalence rate of disease d*

*w*
_{
d
}
*disability weight of disease d*

Making no adjustment for comorbidity is equivalent to assuming that effects of comorbidity on disability are additive. Thus, if a person has more than one disease his total disability weight equals the sum of the disability weights for those diseases. However, in this interpretation individual disability weights may add up to more than one. This cannot be interpreted in a plausible way because it would imply that more than one year of health is lost when living for one year with those diseases.

### Multiplicative adjustment method

Using this method, it is assumed that the increase in disability due to comorbidity disability is proportional. Total disability for an individual having more diseases can be written as:

*w*(*1*,*2*) *disability weight of an individual with disease 1 and 2*

*w*(*d*) *disability weight of an individual with d diseases*

This implies that the disability due to comorbidity increases with more comorbid diseases but is less than the sum of individual disability weights for all comorbid diseases. If there are only 2 diseases the average disability weight assuming independence equals:

*m* = 1 - (1 - *p*_{1}) (1 - *p*_{2}) + (1 - *p*_{2}) *p*_{1} (1 - *w*_{1}) + (1 - *p*_{1}) *p*_{2} (1 - *w*_{2}) + *p*_{1}*p*_{2} (1 - *w*_{1}) (1 - *w*_{2}) = 1 - (1 - *p*_{1}*w*_{1}) (1 - *p*_{2}*w*_{2}) (5)

This can be generalized to *d* diseases:

### Maximum adjustment method

Compared to having one disease, having two diseases only leads to more disability if the second disease causes more disability than the first one. Assuming that the diseases are ordered in terms of disability weights, e.g. *w*
_{1}≥*w*
_{2}≥*w*
_{3}............*w*
_{
n
}someone who has disease 1 and 2 has a disability weight that equals that of *w*
_{1} since disease 1 is worse than disease 2:

In order to estimate average disability weights using this method the prevalence rate for which disease *d* has the highest disability weight must be estimated (denoted *H*
_{
d
}). We can recursively define the prevalence rate *H*
_{
d
}(see Appendix for a derivation):

*H*
_{
d
}
*prevalence rate for which disease d has the highest disability weight*

The average disability weight can then be written as:

### Comparing different methods to adjust for comorbidity

Compared to no adjustment, the multiplicative adjustment method results in a lower average disability weight but compared to the maximum adjustment method in a higher average disability weight:

For *d* diseases: