Longitudinal Gompertzian analysis of ALS mortality in England and Wales, 1963-1989: estimates of susceptibility in the general population

Incidence, Prevalence, and Geographical Clustering of Motor Neuron Disease in the Netherlands

OBJECTIVE

To assess time trends in motor neuron disease (MND) incidence, prevalence, and mortality and to investigate geographic clustering of MND cases in the Netherlands from 1998 to 2017, we analyzed data from the Netherlands Personal Records database, the Netherlands MND Center, and the Netherlands Patient Association of Neuromuscular Diseases.

METHODS

In this prospective cohort study, Poisson regression was used to assess time trends in MND risk. We calculated age- and sex-standardized, observed, and expected cases for 1,694 areas. Bayesian smoothed risk mapping was used to investigate geographic MND risk.

RESULTS

We identified 7,992 MND cases, reflecting an incidence of 2.64 (95% confidence interval [CI] 2.62-2.67) per 100,000 person-years and a prevalence of 9.5 (95% CI 9.1-10.0) per 100,000 persons. Highest age-standardized prevalence and mortality rates occurred at a later age in men than in women (p < 0.001). Unadjusted mortality rates increased by 53.2% from 2.57 per 100,000 person-years in 1998 to 3.86 per 100,000 person-years in 2017. After adjustment for age and sex, an increase in MND mortality rate of 14.1% (95% CI 5.7%-23.2%, p < 0.001) remained. MND relative risk ranged from 0.78 to 1.43 between geographic areas; multiple urban and rural high-risk areas were identified.

CONCLUSIONS

We found a significant national increase in MND mortality from 1998 through 2017, explained only partly by an aging Dutch population, and a geographic variability in MND risk, suggesting a role for environmental or demographic risk factors.

An epidemiologic investigation of amyotrophic lateral sclerosis in Thrace, Turkey, 2006-2010

OBJECTIVE

The aim of the study was to investigate the incidence and prevalence of amyotrophic lateral sclerosis (ALS) in Thrace, Turkey in a five-year time period (2006-2010).

METHODS

Study population included residents of three provinces (Edirne, Tekirdag, Kırklareli) in the Thrace region. Cases were ascertained from all of the neurologic centers and hospitals of these provinces. Demographic and clinical information was collected for each patient. Newly diagnosed ALS patients who are fulfilling the El Escorial revised diagnostic criteria were enrolled into the study.

RESULTS

We identified a total of 145 patients (93 males, 52 females). The mean age at diagnosis was 57.0 ± 13.6. According to El Escorial criteria, 60.0% of the cases were definite ALS, 24.8% were probable, and 15.2% were possible ALS. Thirty-two cases were bulbar (22.1%), 113 cases (77.9%) were spinal onset. Mean time delay from onset to diagnosis was 12.0 ± 11.2 months. Age-gender standardized incidence rates with reference to Turkey, USA 2008 census were 1.9 (95% confidence interval (CI), 1.8-2.1), 1.9 (95%CI, 1.8-2.2) for overall. There were 112 living ALS patients at the end of the study. Crude point prevalence was calculated as 7.3 per 100,000 population (95%CI, 5.9-8.7).

CONCLUSIONS

This is the first study to provide fundamental data about demographic and clinical characteristics about ALS in Thrace region of Turkey. Incidence and prevalence of ALS in Thrace region of Turkey appear to be comparable with European countries.

Can the age at onset give a clue to the pathogenesis of ALS?

Pathogenesis could play an important role in the mid- to late-life onset of symptoms in amyotrophic lateral sclerosis (ALS). An analysis of the age at onset of ALS among the incident cases occurring in the population in the Health District of Ferrara, Italy, in the period 1064-2009 was carried out. Two subsequent 23-year time intervals (1964-1986 and 1987-2009) were considered. The mean age at onset (MAAO) was estimated in relation to gender, onset type and area of residence (urban or extra-urban) at disease onset among the incident cases which occurred in the two subsequent time intervals. An uneven increase in the MAAO over time was observed as it was significant only among the female cases (from 56.7 95 % CI 51.6-61.7 years to 65.4 95 % CI 61.8-69.0 years), the overall bulbar onset cases (from 58.0 95 % CI 54.0-62.1 years to 69.3 95 % CI 66.2-72.4 years), the overall cases occurring in the extra-urban population (from 54.5 95 % CI 49.0-60.1 years to 65.1 95 % CI 60.4-69.8 years) and the bulbar onset cases occurring in the extra-urban population (from 57.1 95 % CI 53.5-60.7 years to 69.6 95 % CI 66.3-73.7 years). Although the increasing age of the population combined with improvements in ALS diagnosis among the elderly may have played a part, these uneven findings among the incident cases occurring in a well-defined homogeneous population with a stable ALS incidence would seem to suggest the involvement of risk factors associated with the extra-urban environment.

Epidemiological surveillance of amyotrophic lateral sclerosis in Saguenay region

OBJECTIVES

The Neuromuscular Registry of Saguenay-Lac-Saint-Jean (SLSJ), Québec, Canada was established for epidemiological surveillance of neuromuscular disorders including amyotrophic lateral sclerosis (ALS). The objectives of this study are to analyze the ALS clinical characteristics of the SLSJ population and to determine the incidence rate over time by five year periods since 1985.

METHODS

The Registry was validated by a review of the medical records maintained at the CSSS de Chicoutimi, the regional university hospital and, by the estimation of the number of hospitalizations for ALS patients using the Quebec Hospital inpatient database (MED-ECHO).

RESULTS

A total of 109 patients were included. Overall, the clinical features of ALS observed in SLSJ population are similar to those described in the literature. We observed a significant increase in the incidence rate of ALS during the 2005-2009 period compared with the previous periods. This is due to a significant increase in the incidence rate among the ≥65 years old group, from 4.68 per 100,000 persons/year (CI 95% 2.88-6.48) during 1985-2004 period to 12.22 (CI 95% 7.43-17.02) during 2005-2009 period.

CONCLUSION

Given the small size of the SLSJ population, a longer observation period will be needed to confirm a new steady state incidence of ALS in this region.

Birth cohort effects in neurological diseases: amyotrophic lateral sclerosis, Parkinson's disease and multiple sclerosis

BACKGROUND

Generational differences in disease rates are the main subject of age-period-cohort (APC) analysis, which is mostly applied in cancer and suicide research. This study applied APC analysis to selected neurological diseases: amyotrophic lateral sclerosis (ALS), Parkinson's disease (PD) and multiple sclerosis (MS).

METHODS

The analyses were based on Swiss mortality data. Age-stratified data has been available for MS, PD and ALS since 1901, 1921, and 1942, respectively. APC analysis was performed within the framework of logit models. Main effect models were extended by implementing nested effects, i.e. age effects nested in subperiods, in order to account for the fact that age profiles may change for reasons other than generational influences.

RESULTS

In preliminary analyses, APC analysis yielded noteworthy birth cohort effects in all three diseases. After implementing nested effects, the birth cohort effects disappeared in ALS, and smoothed out in PD, where they were greater for the generations born before the 1920s. In MS, the birth cohort effects remained stable, and exhibited a peak in cohorts born in the 1910s and 1920s.

CONCLUSIONS

APC analysis yielded some evidence for birth cohort effects, i.e. predisposing risk factors that may change in historical terms, in MS and PD, but probably not in ALS.

Smoking may be considered an established risk factor for sporadic ALS

OBJECTIVES

A 2003 evidence-based review of exogenous risk factors for sporadic amyotrophic lateral sclerosis (ALS) identified smoking as the only risk factor that attained "probable" (more likely than not) status, based on 2 class II studies. The purpose of the current, evidence-based, update was to see if the conclusion of the previous review needed to be modified, based on studies published since.

METHODS

A Medline literature search was conducted for the period between 2003 and April 2009 using the search terms smoking and (ALS or "amyotrophic lateral sclerosis" or MND or "motor neuron disease"). The references of primary articles and reviews were checked to assure completeness of the search. Primary articles published since the previous review were classified as before.

RESULTS

Twenty-eight titles were identified, but only 7 articles met inclusion criteria. Of these, 1 provided class II evidence, and 1 class III evidence: both showed increased risk of ALS with smoking. The class II study showed a dose-response effect, and risk decreasing with number of years since quitting smoking. Five articles provided class IV or V evidence, which may not be relied upon to draw conclusions.

CONCLUSIONS

Smoking may be considered an established risk factor for sporadic amyotrophic lateral sclerosis (ALS) (level A rating; 3 class II studies, 1 class III study). Evidence-based analysis of epidemiologic data shows concordance among results of better-designed studies linking smoking to ALS, and lets those results drive the conclusions.

Incidence and prevalence of amyotrophic lateral sclerosis in Uruguay: a population-based study

OBJECTIVE

To determine the incidence and prevalence of amyotrophic lateral sclerosis (ALS) in the Republic of Uruguay.

METHODS

The study was performed in Uruguay (3,241,003 inhabitants) during a 2-year period (2002-2003). To ensure complete case ascertainment, multiple sources of information were used, including all the neurologists, other medical specialties, general physicians, neurophysiology laboratories, hospital medical records and death certificates. ALS diagnosis was based on El Escorial criteria. Although all patients with motor neuron disease were enrolled in the follow-up, only probable and definite cases are included in the study.

RESULTS

Between January 1st, 2002, and December 31st, 2003, 89 new patients were diagnosed with probable or definite ALS. The mean annual incidence rate was 1.37 per 100,000 persons. The incidence was higher for men (1.95) than for women (0.84) with a male to female ratio of 2:1. For both, the incidence increased throughout the years showing a peak in the 65-74 age group among men and the 55-64 age group among women. Mean age at onset of ALS disease was 58.7 years. The estimated mean annual incidence for ALS calculated by the capture recapture method was 1.42 (95% CI, 1.13-1.72). On December 31st, 2002, the crude prevalence was 1.9 per 100,000 inhabitants.

CONCLUSIONS

ALS incidence is within a narrow range across countries despite the genetic, environmental and socioeconomic differences when similar prospective design, diagnosis criteria and data analyses are applied.

Sports and trauma in amyotrophic lateral sclerosis revisited

An evidence-based review was undertaken of the literature published between 2002 and 2006 about sports, trauma and ALS in order to see if there were new data to modify the conclusions of a previous review (2003). The new data support the previous conclusions that physical activity and trauma are probably ("more likely than not") not risk factors for ALS (Level II conclusions). This review concludes also that the reports of an apparent excess of ALS in Italian soccer players likely reflect incorrect analysis of the data. The appearance of excess relies on accepting as valid estimation methods resulting in improbably low numbers of expected cases. A different method is proposed: it generates more plausible numbers of expected cases, compared to which there is no excess of total cases (Level C conclusion). A theoretical framework is developed to analyze the possible influence of a "healthy worker effect" on incidence of neurodegenerative diseases in cohorts of employed or formerly employed individuals. In lieu of theoretical speculations, data are needed to measure this effect, while controlling for known lifestyle factors and accounting for the effect of loss of competing causes of mortality.

Genetics of sporadic ALS

The only known gene to be involved in ALS is the CuZn-superoxide dismutase (CuZn-SOD) gene. Since 1993, 89 disease-associated mutations have been found in this gene, 14 of them in cases with apparently sporadic ALS. Most frequent are the D90A (most often with recessive inheritance, but a few with dominant inheritance) and the I113T (dominant inheritance with variable penetrance). Statistical and genealogical evidence suggest that quite a number of diagnosed sporadic cases may in fact be familial cases in pedigrees with very low disease penetrance.

Risk factors in the early diagnosis of ALS: European epidemiological studies

Significant changes in the epidemiology of amyotrophic lateral sclerosis (ALS) have been observed over the last few years. Based on reports of studies from the 1970s and early 1980s, the incidence of ALS in Europe has been considered to be constant, with only slight differences in the incidence of ALS between different countries. However, flaws in the methodologies of these studies, such as case definition, case ascertainment, selection bias, study design and difficulties in the early diagnosis of cases, have been identified. More recent studies reveal a trend towards an increase in the ALS mortality rate over the past two decades, but the significance of this trend remains unclear. Recent ALS incidence studies, particularly those based on the 'register model', have given new insight into ALS epidemiology. ALS seems to be a uniform problem across Europe, with age-specific incidence rates showing a progressive increase up to the 70-79 age group. False-negative cases are frequent, ranging from 26-42% of cases. The rate of false-positive cases is approximately 10%. In approximately half of the false-positive cases, the possible diagnosis of ALS was withdrawn because the initial symptoms did not progress. No consistent epidemiological clues concerning the cause of ALS have been found in epidemiological studies. The only possible associations that perhaps warrant further investigation include farming, mechanical and electrical traumas, heavy labour and toxins or chemicals.

The size of the subpopulation susceptible to malignant neoplasm of the brain

A decline of mortality dependence on age from the exponential relation is observed for some diseases. This decline could be explained by the existence of an inherently susceptible population subset which is depleted faster than the general population. A model is presented which describes this situation using malignant neoplasm of the brain. The model assumes that only those who are members of the subset can die of malignant neoplasm of the brain. This model was used to fit the actual mortality curve of malignant neoplasm of the brain for women and men in the USA in 1979. The size of this subset equalled one of two parameters used to fit the actual data. The decline of mortality dependence upon age can be explained by this model. The size of the subpopulation is 0.390% for men and 0.417% for women. The theoretical curves resulting from that model capture the actual mortality due to malignant neoplasm of the brain.

Intersections of mortality-rate and survival functions: model-independent considerations

In work reported previously (Hirsch, 1995), it was shown that families of straight lines intersect at a single point if and only if the slopes of the lines are linearly related to their intercepts. This slope-intercept relation was applied to several mathematical mortality models including the Gompertz-Makeham and the Weibull. In all cases, survival functions intersected at greater ages than the corresponding mortality-rate functions. It was further demonstrated that a common point of intersection can exist for members of a family of survival functions or for members of the corresponding family of mortality-rate functions but not for both. Here the same results are obtained with respect to intersections of general model-independent survival and mortality-rate functions. The generality of the results strengthens the conclusion reached earlier that these intersections imply only the existence of a valid slope-intercept relation and have little other significance with regard to the biology of aging.

Clinical epidemiology of amyotrophic lateral sclerosis

The introduction of palliative therapies in amyotrophic lateral sclerosis (ALS) will alter the epidemiology of ALS as it is known now. Although incidence rates will remain unchanged in the near future, prevalence rates will likely increase dramatically. Better understanding of the age-specific presentation of motor neuron diseases worldwide will shed light on the vexing questions concerning the variable incidence rates in some countries and apparent incidence gradients in North America and Europe.

Ecological correlates of motor neuron disease mortality: a hypothesis concerning an epidemiological association with radon gas and gamma exposure

This study investigates variations in motor neuron disease (MND) mortality rates between the counties of England and Wales from 1981 to 1989, and their relationship with gamma-ray dose rates, indoor radon gas concentrations and enhanced general life expectancy. A strong correlation was confirmed between age-adjusted rates of MND mortality and life expectancy. Weaker, but statistically significant, associations were observed between indoor radon gas concentrations, terrestrial gamma radiation and marginal variations in MND mortality. Life expectancy and radon gas concentrations were positively associated with MND mortality rates whilst gamma radiation was negatively associated. The negative correlation of gamma radiation with MND mortality may be understood with reference to its negative effects on overall population life expectancy. Radon gas concentrations seemingly account for a small elevation in MND mortality, amounting to at most 4% of total deaths. Further research is required to investigate this association.

Do intersections of mortality-rate and survival functions have significance?

Common points of intersections have frequently been reported among members of families of linearized mortality-rate and survival functions. A general condition for the existence of such intersections is derived. It is shown that a common point of intersection between straight-line functions exists if and only if the intercepts of the functions are linearly related to their slopes. This slope-intercept condition is applied to a didactic model to illustrate its generality and to three models, the Gompertz-Makeham, the Weibull, and the logistic, which are often used in the analysis of mortality data. The slope-intercept condition for the Gompertz-Makeham mortality-rate model proves to be the well-known Strehler-Mildvan correlation. Families of mortality-rate functions or of the corresponding survival functions but not both may display common points of intersection. Differences between the ages at which survival functions intersect and those at which the associated mortality-rate functions intersect are calculated to be of the order of magnitude of 10 to 20 years. Survival function intersections lie close to the limit of human life span but often arise in consequence of unsupported extrapolations of data obtained at younger ages. These and other results lead to the conclusion that, in themselves, the intersections of survival and mortality-rate functions are not of great importance. To the extent that significance can be attributed to the intersections, it lies in the existence of linear relationships between their slopes and intercepts.

Rising mortality from motor neurone disease in Sweden 1961-1990: the relative role of increased population life expectancy and environmental factors

Recent studies of mortality from motor neurone disease (MND) in Sweden have demonstrated rising levels of mortality from the disease, especially amongst older age groups. Case-control investigations have suggested that certain environmental factors are significantly related to variations in mortality from the disease, and are associated with a probable individual susceptibility to MND. This study applies an innovative epidemiological technique to longitudinal and cohort analysis of Swedish mortality from MND during the period 1961 to 1990. Survival modelling shows that a subpopulation susceptible to MND exists in Sweden, as has been demonstrated in other countries. The increased life expectancy of the Swedish population since 1961 has resulted in more of that susceptible population living to the ages at which MND is expressed, explaining the majority of the increase in mortality from the disease. However, environmental factors may play a role in accelerating the course of MND and may affect the timing of death within the susceptible sub-population.

Rising amyotrophic lateral sclerosis mortality in France 1968-1990: increased life expectancy and inter-disease competition as an explanation

Gompertzian analysis is a statistical technique which has been successfully applied to the analysis of amyotrophic lateral sclerosis (ALS) mortality in England and Wales, Japan and the United States. This paper analyses the consistent trend of rising ALS mortality in France over the years 1968-1990, a period during which crude mortality rose from 400 deaths in 1968 to 950 deaths in 1990. The findings indicate that age-specific mortality rates have risen at ages older than 54 years for men and 53 years for women and decreased slightly at younger ages. The evolving ALS mortality pattern is attributable to changing inter-disease competition resulting from the increased life expectancy of the French population, rather than to changing environmental aetiopathogenic factors or to substantial artefact effects.

Motor neuron disease in a defined English population: estimates of incidence and mortality

Linked statistics from hospital records and death certificates were used to study the incidence of and mortality from motor neuron disease in a defined English population. The incidence of motor neuron disease, measured as first-admission rates for the disease, was studied from 1963 to 1985 and death certificates for the patients admitted to hospital were obtained to the end of 1990. The average annual first-admission rate for motor neuron disease was 2.1/100,000 men (95% confidence interval (CI) 1.9 to 2.4) and 1.7/100,000 women (95% CI 1.5 to 1.9). First-admission rates increased with age and peaked in the age range 65-84 years. Motor neuron disease was recorded on the death certificate for 86% of patients who died while they had the disease and there was no appreciable change over time in the recording of motor neuron disease as the underlying cause of death. The admission and mortality data derive from different sources, hospital statistical abstracts and death certificates respectively, but trends over time in the two data sets were similar. There was an increase in mortality during the period covered by the study, as there has been in mortality from motor neuron disease nationally, and the increase in mortality in the Oxford region was accompanied by an increase in first-admission rates. It is concluded that the increase in mortality from motor neuron disease probably occurred as a result of an increase in the diagnosed incidence of the disease rather than changes in death certification practice.

Motor neuron disease: a disease of old age

There is little information dealing specifically with motor neuron disease (MND) in the elderly. Given current epidemiological trends, geriatricians will be increasingly called upon to diagnose and manage this condition. We report four patients who presented within a six month period to a geriatric medical unit, and place this experience in the perspective of 229 patients from a population-based study of adult-onset MND in Scotland in 1989 and 1990. In 1990 Scotland had a crude annual incidence of MND of 2.25/100,000; the figure for those over 65 is four times greater. MND is more common in men, but the sex ratio was nearly equal over the age of 65. The risk of presenting with bulbar palsy was greater in women, and even higher in elderly women. This, together with increasing age, is the most important negative prognostic factor in MND. Problems with the diagnosis and management of MND in the elderly are highlighted.

Reinterpreting mortality statistics: some uses of Gompertzian analysis in epidemiological research

Gompertzian analyses of mortality data have recently been undertaken for a number of individual conditions (Riggs JE. Mech Ageing Dev 1990; 55: 207-220 [1]; Neilson S et al. Mech Ageing Dev 1992; 64: 201-216 [2]; Neilson S et al. Acta Neurol Scand 1993; 87: 184-191 [3]). Such analyses are in principle of particular epidemiological value in circumstances where demographic change is occurring and where the balance between mortality from different conditions is subject to change. However, the extent to which a Gompertzian relationship between age and mortality holds for particular conditions has been subject to debate. In this analysis it is demonstrated that even some conditions which do not superficially hold to a Gompertz relationship do in fact do so, if such conditions are considered to be restricted to small, inherently susceptible subpopulations. By analysing mortality from a range of neurological conditions within the context of general mortality in England and Wales, conditions with different aetiologies such as Huntington's chorea, amyotrophic lateral sclerosis and multiple sclerosis can be shown to have a Gompertzian mortality rate distribution. Such analyses are of substantial value in indicating how demographic change affects the balance of mortality between conditions, as well as directing interest to revised aetiological possibilities.

A new analysis of mortality from motor neurone disease in Japan, 1950-1990: rise and fall in the postwar years

Recent studies have demonstrated a worldwide rise in mortality from motor neurone disease (MND). However, in Japan mortality appears to have fallen significantly since the late 1960s, especially amongst women. Studies of the cause of both the worldwide rise, and the unique decline in MND mortality in Japan, have largely failed to substantiate the role of any single factor, or group of factors in these phenomena. Modelling the relationship between age and mortality using gompertzian analysis has already shown that the rise in MND mortality in England and Wales, and the United States, is mainly the result of increased longevity and decreasing competition from other causes of death amongst a susceptible subpopulation. Employing the same techniques on Japanese mortality data from 1950 to 1990 demonstrates that an unusual and accelerated increase of mortality occurred in the 1950s and 1960s, probably caused by an earlier unknown but extremely potent environmental agent or agents. This premature depletion of the susceptible subpopulation resulted subsequently in a lower than expected mortality rate. Mortality is now rising slowly to expected levels as the size of the susceptible subpopulation recovers to reach the ages at which MND is normally expressed. Further substantial rises in mortality are anticipated in future decades.

Comparison of the Gompertz and Weibull functions as descriptors for human mortality distributions and their intersections

The Gompertz and Weibull functions are compared with respect to goodness-of-fit to human mortality distributions; ability to describe mortality curve intersections; and, parameter interpretation. The Gompertz function is shown to be a better descriptor for 'all-causes' of deaths and combined disease categories while the Weibull function is shown to be a better descriptor of purer, single causes-of-death. A modified form of the Weibull function maps directly to the inherent degrees of freedom of human mortality distributions while the Gompertz function does not. Intersections in the old-age tails of mortality are explored in the context of both functions and, in particular, the relationship between distribution intersections, and the Gompertz ln[R0] versus alpha regression is examined. Evidence is also presented that mortality intersections are fundamental to the survivorship form and not the rate (hazard) form. Finally, comparisons are made to the parameter estimates in recent longitudinal Gompertzian analyses and the probable errors in those analyses are discussed.

Cross-sectional Gompertzian analysis: the development of a Gompertz mortality ratio (GMR) and its applicability

Many conventional epidemiological analyses of the distribution and aetiology of disease employ standardised mortality ratios (SMRs) as a basis upon which to evaluate comparative studies of disease in populations. However SMRs, whilst constructed to control for age and sex, are not capable of incorporating other variables such as life expectancy which has been demonstrated to be of crucial importance in understanding the changing relationships between mortality from different causes. The development of a Gompertz mortality ratio (GMR) and its application to recent mortality from amyotrophic lateral sclerosis (ALS) in the Counties of England and Wales illustrates the value of substituting GMRs for SMRs in the analysis of competitive relationships between conditions, especially those associated with enhanced life expectancy.

Rising mortality from motor neurone disease: an explanation

There is considerable debate about the increasing mortality from motor neurone disease (MND). However, examination of the relationship between increased life expectancy (through decreased general mortality) and increased mortality in both England and Wales and the United States indicates a close association between the two variables. Using a statistical model, defined sub-populations susceptible to MND can be identified in both countries. The size of such a sub-population has been estimated from the 1989 mortality data to be approximately 160,000 people in England and Wales. The proportion of this sub-population dying from MND has increased over the last 30 years, rather than, as previously, dying at an earlier age from other conditions. On this basis, deaths from MND are expected to increase by a further 20% in this sub-population between 1991-2021 because of continuing changes in life expectancy. MND is a condition made increasingly visible in mortality statistics through decreased general mortality, rather than one in which the underlying population at risk has substantially changed. Aetiological extrapolations from the data indicate that susceptibility to the disease is acquired early in life, and that it is unlikely, given the relative stability of the underlying sub-population, that either changed environmental circumstances or artifactual factors can account in themselves for the rise in mortality.

Static and dynamic models of interdisease competition: past and projected mortality from amyotrophic lateral sclerosis and multiple sclerosis

Longitudinal Gompertzian analysis is an effective method for determining both the pure probability of death for a given condition and the size of inherently susceptible subpopulations [1]. Gompertzian analysis has been used in this study to provide the parameters necessary to construct a stationary population lifetable (static model) of mortality for amyotrophic lateral sclerosis (ALS) and for multiple sclerosis (MS). The static model demonstrates the relative effect of changing general mortality upon the mortality from each specific disease in a situation where interdisease competition is continuously changing. In order to represent mortality in a real population more closely (where age structure is not the result of mortality rates alone) a dynamic model was constructed for both conditions using the age distributions of the population of England and Wales. The quality of the model was verified by comparison of estimated mortality with historical data from the last three decades. The dynamic model has then been used to estimate mortality from each condition over the next three decades on the basis of population projections made by the Central Statistical Office [2], assuming no major change in the factors which lead to either condition. This analysis demonstrates both the theoretical applicability and practical capabilities of Gompertz-derived mortality models for analysing changing mortality patterns.