Results
Mortality Rate
Between 1970 and 2009, there were 4,265 deaths attributed to ALS among people 45 years of age or older, for an overall mortality rate of 5.35 ALS deaths per 100,000 person-years. Age-specific male and female mortality rates for the entire study period are shown in Figure 1. Mortality rates peaked between ages 71 and 81 years for both men and women, and in both we observed a drop-off of rates in later years.
(Enlarge Image)
Figure 1.
Age-specific amyotrophic lateral sclerosis mortality rate in Denmark, 1970–2009.
Over the course of the study, mortality rate increased an average of 3.0% per year (age-adjusted linear period model; P < 0.001). Restricted to the post-1982 period, the linear trend was a 2.1% increase (P < 0.001).
Mortality rates tabulated by age and year of death (period) are shown in Figure 2A. We stratified crudely for display purposes; in all APC analyses, the 3 factors are treated continuously with splines. Mortality rates increased across all age groups 51 years of age or older and most dramatically in those older than 71 years. Figure 2B shows mortality rates within age groups by birth cohort; in older age cohorts, a greater increase in mortality rates was seen with progressing birth year. Under the null hypothesis of neither a period nor a cohort effect, we would expect both plots to exhibit parallel lines (on the log scale). That both plots show deviations from parallel indicates that neither the age-period model nor the age-cohort model is sufficient to explain the increase.
(Enlarge Image)
Figure 2.
A) Amyotrophic lateral sclerosis mortality rate in Denmark, 1970–2009, stratified by age at time of death. B) Amyotrophic lateral sclerosis mortality rate by birth cohort, stratified by age at time of death. Lines correspond to each age group (solid: 45–50 years; short dash: 51–60 years; dotted: 61–70 years; dash-dot: 71–80 years; and long dash: >80 years).
Table 1 shows the results from the fit of the APC model for mortality rate, with age, period, and cohort year modeled continuously with splines. Compared with either the age-cohort model or the age-period model, the full APC model provides a significantly better fit to the data. Figure 3 shows the period and cohort effects estimated from the full APC model. The period effect shown here is constrained to be 0 on average with 0 slope for identifiability, but there is a clear deviation from linearity in mortality rate during 1975–1980, when an increase occurred. The cohort effect shows a steadily increasing rate, with a possibly slightly faster increase for those born from 1930 to 1935. Results were unchanged when stratified by sex. When we constrained the cohort effect, rather than the period effect, to be 0 on average with 0 slope, the overall increase over the birth cohorts was (as expected) transferred to the period effect, but the increases in 1975–1980 (period) and before 1910, as well as 1930–1935 (birth cohort), remained (Web Figure 1, available at http://aje.oxfordjournals.org/).
(Enlarge Image)
Figure 3.
Age-period-cohort model of all deaths from amyotrophic lateral sclerosis in Denmark, 1970–2009, with average period effect constrained to be zero. A) Estimated period effects relative to 1990. B) Estimated birth cohort effects relative to 1920.
When we limited mortality data to the post-1982 period (for comparability to the incidence data), the age-cohort model formally provided the best fit to the data, although the full APC model was only marginally nonsignificant (P = 0.10, comparing the age-cohort model with the full model). Plots of the effects from this full APC model (Web Figures 2 and 3) are similar to those from the complete mortality data (Figure 3 and Web Figure 1) for the years they share. Because Denmark switched from ICD-8 to ICD-10 in 1994, we also restricted mortality data to the post-1994 period, and again the age-cohort model was a better fit than the full APC model (P = 0.78, comparing the age-cohort model with the full model). In all of the treatments of the mortality data, the increase in ALS with later cohorts before at least birth year 1910 is consistent.
We stratified results by age to address the possibility that improved diagnosis in the elderly over time manifests as a cohort effect (an age-period interaction). When persons 81 years of age or older were excluded, results were largely unchanged. The full APC model was still strongly preferred (P < 0.001). When persons over 65 years of age were excluded, the period effect failed to reach significance when added to the age-cohort model (P = 0.18).
Incidence Rate
Between 1982 and 2009, a total of 3,228 newly diagnosed ALS cases were recorded among people 45 years of age or older, for an overall incidence rate of 5.55 cases per 100,000 person-years. Figure 4 displays age-period and age-cohort plots for incidence rates. Unlike for mortality rate, age-specific incidence rates were approximately linear over the period 1982–2009, with some evidence of a slight increase across all ages. Age-specific incidence rates by birth cohort also exhibited the pattern we would expect from an age-cohort model, with the possible exception of persons who were at least 80 years old. The age-adjusted linear increase in incidence rates over the study period was 1.6% per year (P < 0.001).
(Enlarge Image)
Figure 4.
A) Amyotrophic lateral sclerosis incidence rate in Denmark, 1982–2009, stratified by age at time of diagnosis (discharge). B) Amyotrophic lateral sclerosis incidence rate by birth cohort, stratified by age at time of diagnosis (discharge). Lines correspond to each age group (solid: 45–50 years; short dash: 51–60 years; dotted: 61–70 years; dash-dot: 71–80 years; and long dash: >80 years).
The APC modeling results (with age, period, and cohort year modeled continuously with splines) formally indicated that the age-period model provided the best fit to the data, although the full APC model was only marginally nonsignificant (P = 0.08; Table 2). Plots from full APC models for incidence showed a slight period increase between 1992 and 1996 and a cohort effect of increasing incidence over birth cohorts before 1920 (Figure 5), which mirrored the mortality data, particularly the post-1982 mortality data. As in the mortality data, reparameterizing the model to constrain the cohort effect, rather than the period effect, to be 0 on average with 0 slope did not materially change these results (Web Figure 4), with some of the overall increase being transferred to the period effect. Of note, though, is that even in this reparameterization, the increase with increasing birth cohorts before birth year 1910 was still seen. Results were similar when stratified by sex, although there was evidence of a stronger birth cohort effect among women, particularly among later birth cohorts (after 1940). Because the cohort effect was borderline significant, we also considered the alternative age-period-interaction model (Web Table 1).
(Enlarge Image)
Figure 5.
Age-period-cohort model of amyotrophic lateral sclerosis incidence in Denmark, 1982–2009, with average period effect constrained to be zero. A) Estimated period effects relative to 1990. B) Estimated birth cohort effects relative to 1920.
Sex Ratio
For both incidence rate and mortality rate, male and female rates converged over time up to 1995–2000 and began to diverge thereafter. The relative mortality rate ratio in women relative to men rose from 0.42 to 0.88 between 1970–1975 and 1995–2000 and decreased to 0.71 by 2005–2010. The relative incidence rate ratio for women relative to men rose from 0.59 to 0.91 between 1982–1985 and 1995–2000 and decreased to 0.80 by 2005–2010 (Figure 6).
(Enlarge Image)
Figure 6.
Relative amyotrophic lateral sclerosis mortality and incidence rates in women versus men in Denmark, 1970–2009.