Trends in Amyotrophic Lateral Sclerosis in Denmark
Trends in Amyotrophic Lateral Sclerosis in Denmark
We obtained death records from the Danish Cause of Death Registry, which has been kept electronically since 1970. Deaths in Denmark were coded according to the International Classification of Diseases, Eighth Revision (ICD-8) before 1994, after which the International Classification of Diseases, Tenth Revision (ICD-10) was used. Cases of ALS were defined as persons with underlying or contributing causes of death with ICD-8 code 348.0 or ICD-10 code G12.2. The inclusion of contributing causes is generally considered the best practice, particularly for capturing ALS diagnoses in the elderly.
We obtained data on hospitalizations from the Danish National Hospital Registry, which has collected nationwide data on all somatic hospital admissions since January 1, 1977. Incident cases were defined as first inpatient discharge diagnoses with the aforementioned ICD-8 or ICD-10 codes. To avoid prevalent cases, we included patients only from 1982 and later. Date of first inpatient discharge was considered the case date. Date of birth was obtained from the Central Person Register, which is linked to hospital and death registries through a personal identification number. We excluded all deaths from ALS (n = 123) and diagnoses of ALS in men and women less than 45 years of age (n = 204). Age- and sex-specific population denominators in 1-year, 1-age bins were obtained from Statistics Denmark.
We used the APC method described by Carstensen. Briefly, to solve the identifiability problem inherent in attempting to simultaneously model age, period, and cohort, which are linearly dependent (age = period – cohort), we fixed 2 levels and 1 slope among the 3 effects. We placed no constraints on age, constrained the cohort effect to be relative to 1920, and constrained the period effect to be relative to 1990 and to be 0 on average with 0 slope. In this parameterization, age effects are interpretable as longitudinal rates within the reference cohort (1920) over time. Cohort effects are interpretable as the relative rate from the 1920 reference cohort, in the reference period (1990). Period effects are deviations from the rate predicted by the age-cohort combination; this allows us to test for deviations from linear period effects over time. The estimated effects in this parameterization are dependent on the constraints used to identify them and thus must be interpreted with caution. However, testing between models for goodness-of-fit is not constraint dependent, because although the linear dependence of age, period, and cohort results in nonunique effect estimates (i.e., the estimated model coefficients), the predicted values from each model are unique, and thus tests for goodness-of-fit can be performed without additional assumptions. All models were also assessed visually to check for differences in estimated effects between models.
We tabulated 1-year rates for each year of the study. In all modeling we used natural cubic splines, with 6–10 knots for each effect spaced equally at quantiles. All analyses were performed in R (R Foundation for Statistical Computing, Vienna, Austria). APC analyses were implemented with the EPI package for epidemiological analysis in R.
Materials and Methods
Data Source
We obtained death records from the Danish Cause of Death Registry, which has been kept electronically since 1970. Deaths in Denmark were coded according to the International Classification of Diseases, Eighth Revision (ICD-8) before 1994, after which the International Classification of Diseases, Tenth Revision (ICD-10) was used. Cases of ALS were defined as persons with underlying or contributing causes of death with ICD-8 code 348.0 or ICD-10 code G12.2. The inclusion of contributing causes is generally considered the best practice, particularly for capturing ALS diagnoses in the elderly.
We obtained data on hospitalizations from the Danish National Hospital Registry, which has collected nationwide data on all somatic hospital admissions since January 1, 1977. Incident cases were defined as first inpatient discharge diagnoses with the aforementioned ICD-8 or ICD-10 codes. To avoid prevalent cases, we included patients only from 1982 and later. Date of first inpatient discharge was considered the case date. Date of birth was obtained from the Central Person Register, which is linked to hospital and death registries through a personal identification number. We excluded all deaths from ALS (n = 123) and diagnoses of ALS in men and women less than 45 years of age (n = 204). Age- and sex-specific population denominators in 1-year, 1-age bins were obtained from Statistics Denmark.
Statistical Analysis
We used the APC method described by Carstensen. Briefly, to solve the identifiability problem inherent in attempting to simultaneously model age, period, and cohort, which are linearly dependent (age = period – cohort), we fixed 2 levels and 1 slope among the 3 effects. We placed no constraints on age, constrained the cohort effect to be relative to 1920, and constrained the period effect to be relative to 1990 and to be 0 on average with 0 slope. In this parameterization, age effects are interpretable as longitudinal rates within the reference cohort (1920) over time. Cohort effects are interpretable as the relative rate from the 1920 reference cohort, in the reference period (1990). Period effects are deviations from the rate predicted by the age-cohort combination; this allows us to test for deviations from linear period effects over time. The estimated effects in this parameterization are dependent on the constraints used to identify them and thus must be interpreted with caution. However, testing between models for goodness-of-fit is not constraint dependent, because although the linear dependence of age, period, and cohort results in nonunique effect estimates (i.e., the estimated model coefficients), the predicted values from each model are unique, and thus tests for goodness-of-fit can be performed without additional assumptions. All models were also assessed visually to check for differences in estimated effects between models.
We tabulated 1-year rates for each year of the study. In all modeling we used natural cubic splines, with 6–10 knots for each effect spaced equally at quantiles. All analyses were performed in R (R Foundation for Statistical Computing, Vienna, Austria). APC analyses were implemented with the EPI package for epidemiological analysis in R.