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Letters

Indirect Estimation of Chronic Disease Excess Mortality

van Baal, Pieter H. M.; Hoogenveen, Rudolf T.; Engelfriet, Peter M.; Boshuizen, Hendriek C.

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doi: 10.1097/EDE.0b013e3181d7773f

In Brief

To the Editor:

Estimating differences in mortality rates between persons with and without a chronic disease is usually done with observational studies requiring long periods of follow-up. Another way to estimate the mortality associated with a disease is to exploit the interrelatedness of epidemiological parameters such as incidence, prevalence and mortality, which can be expressed mathematically.1–5 We propose a method that allows the calculation of excess mortality rates due to a chronic disease (defined as the difference in mortality rates between persons with and without the disease) using aggregated cross-sectional data consisting of incidence and prevalence counts. In addition, we show how to quantify uncertainty in the estimates of excess mortality rates. In combination with population mortality rates this method can be used to calculate life expectancy with and without chronic disease. Our method produces valid results for diseases without recovery if incidence and prevalence are approximately stable over time.

In the eAppendix (http://links.lww.com/EDE/A384) we show that excess mortality rates can be expressed as a function of incidence and prevalence once we know how these quantities develop over time in a closed cohort. Assuming that age-specific data on incidence and prevalence available from cross-sectional studies actually represent the changes a person experiences over time, it is possible to calculate age-specific excess mortality rates from cross-sectional data using the formula: η(a) =

where η(a),i(a) and p(a) denote, respectively, excess mortality rate, incidence rate, and prevalence proportion at age a. Using regression modeling we can estimate incidence and prevalence as a function of age. Excess mortality rates can then be estimated by calculating the change in the prevalence proportion over age

and applying the formula.

Uncertainty assessment for excess mortality rates is accomplished by Monte Carlo simulation using the estimated coefficients and their covariance matrix from the regression model describing incidence and prevalence. However, in doing so, one must take into account the likely correlation between incidence and prevalence (as high incidence will lead to high prevalence). A positive correlation between incidence and prevalence implies that uncertainty around excess mortality rates decreases. With such correlation, combinations of prevalence and incidence that lead to extreme low or high estimates of excess mortality rates are less likely to occur (eg, a combination of high incidence and low prevalence leads to a high estimate of excess mortality rate). This can be achieved by modeling incidence and prevalence as one outcome variable, using a dummy variable indicating whether the outcome is incidence or prevalence. By modeling incidence and prevalence simultaneously, it is possible to quantify the correlation between parameters that describe incidence and prevalence. A potential drawback is that uncertainty in the incidence estimates is no longer independent from uncertainty surrounding prevalence, which might be unwelcome if it is known that incidence is estimated more accurately.

The Figure displays results of an application of our method using data from several general practitioners registrations in the Netherlands on chronic heart failure in men.6 In this example we estimated a generalized linear mixed model describing incidence and prevalence as a function of orthogonal polynomials of age, with the registration identifier acting as a random intercept. Estimates of life expectancy with heart failure, based on our indirect estimates of excess mortality, match well with those previously published.7,8 The validity of our method strongly rests on the crucial assumption of a steady state population. Major deviations from this assumption, such as may occur with a strong time trend in incidence or mortality rates, can lead to distortions in the estimates.2

FIGURE.
FIGURE.:
Estimates of excess mortality and life expectancy with heart failure for men based on cross-sectional data on incidence and prevalence counts from 4 general practitioners registration networks in the Netherlands from the year 2007. The shaded areas represent 95% confidence intervals.

Pieter H. M. van Baal

National Institute for Public Health and the Environment (RIVM)

Expertise Centre for Methodology and Information Services

Bilthoven, The Netherlands

Erasmus University Rotterdam

Institute of Health Policy and Management

Rotterdam, The Netherlands

[email protected]

[email protected]

Rudolf T. Hoogenveen

National Institute for Public Health and the Environment (RIVM)

Expertise Centre for Methodology and Information Services

Bilthoven, The Netherlands

Peter M. Engelfriet

National Institute for Public Health and the Environment (RIVM)

Centre for Prevention and Health Services Research

Bilthoven, The Netherlands

Hendriek C. Boshuizen

National Institute for Public Health and the Environment (RIVM)

Expertise Centre for Methodology and Information Services

Bilthoven, The Netherlands

REFERENCES

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