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We consider forecasting from age-period-cohort models, as well as from the extended chain-ladder model. The parameters of these models are known only to be identified up to linear trends. Forecasts from such models may therefore d...
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We consider forecasting from age-period-cohort models, as well as from the extended chain-ladder model. The parameters of these models are known only to be identified up to linear trends. Forecasts from such models may therefore depend on arbitrary linear trends. A condition for invariant forecasts is proposed. A number of standard forecast models are analysed.
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We consider the identification problem that arises in the age-period-cohort models as well as in the extended chain-ladder model. We propose a canonical parameterization based on the accelerations of the trends in the three factor...
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We consider the identification problem that arises in the age-period-cohort models as well as in the extended chain-ladder model. We propose a canonical parameterization based on the accelerations of the trends in the three factors. This parameterization is exactly identified and eases interpretation, estimation and forecasting. The canonical parameterization is applied to a class of index sets which have trapezoidal shapes, including various Lexis diagrams and the insurance-reserving triangles.
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Sociologists and demographers often use Lexis diagrams to visualize temporal data. However, the traditional Lexis plot arranges the data in a matrix of right triangles, with age on the vertical axis and period on the horizontal ax...
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Sociologists and demographers often use Lexis diagrams to visualize temporal data. However, the traditional Lexis plot arranges the data in a matrix of right triangles, with age on the vertical axis and period on the horizontal axis. This representation of the data subordinates cohort to an off-diagonal of unequal length. Not only does this violate the proportionality principle of effective statistical graphics, but it implicitly treats cohort as a residual or epiphenomenal dimension and makes it difficult to compare variation within and across cohorts. As an alternative, the author introduces the Ryder plot, a novel graphical tool that displays cohort, age, and period data as a grid of equilateral triangles, thereby providing an unbiased representation of all three dimensions and facilitating the analysis of intra- and intercohort variability. The author uses Ryder plots to chart the rise and fall of verbal ability in the United States, revealing two epochs of social change across three centuries of cohorts.
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Sociologists and demographers often use Lexis diagrams to visualize temporal data. However, the traditional Lexis plot arranges the data in a matrix of right triangles, with age on the vertical axis and period on the horizontal ax...
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Sociologists and demographers often use Lexis diagrams to visualize temporal data. However, the traditional Lexis plot arranges the data in a matrix of right triangles, with age on the vertical axis and period on the horizontal axis. This representation of the data subordinates cohort to an off-diagonal of unequal length. Not only does this violate the proportionality principle of effective statistical graphics, but it implicitly treats cohort as a residual or epiphenomenal dimension and makes it difficult to compare variation within and across cohorts. As an alternative, the author introduces the Ryder plot, a novel graphical tool that displays cohort, age, and period data as a grid of equilateral triangles, thereby providing an unbiased representation of all three dimensions and facilitating the analysis of intra- and intercohort variability. The author uses Ryder plots to chart the rise and fall of verbal ability in the United States, revealing two epochs of social change across three centuries of cohorts.
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Mortality data of disabled individuals are studied and parametric modeling approaches for the force of mortality are discussed. Empirical observations show that the duration since disablement has a strong effect on mortality rates...
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Mortality data of disabled individuals are studied and parametric modeling approaches for the force of mortality are discussed. Empirical observations show that the duration since disablement has a strong effect on mortality rates. In order to incorporate duration effects, different generalizations of the Lee-Carter model are proposed. For each proposed model, uniqueness properties and fitting techniques are developed, and parameters are calibrated to mortality observations of the German Pension Insurance. Difficulties with coarse tabulation of the empirical data are solved by an age-period-duration Lexis diagram. Forecasting is demonstrated for an exemplary model, leading to the conclusion that duration dependence should not be neglected. While the data shows a clear longevity trend with respect to age, significant fluctuations but no systematic trend is observed for the duration effects. (C) 2014 Elsevier B.V. All rights reserved.
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The 'Lexis Diagram' has traditionally been used in Demography and Epidemiology for graphical representation of event histories. Timeliness is often cited as the Achilles' heel of Swedish health care. This paper explores the use of...
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The 'Lexis Diagram' has traditionally been used in Demography and Epidemiology for graphical representation of event histories. Timeliness is often cited as the Achilles' heel of Swedish health care. This paper explores the use of the Lexis diagram for monitoring lead times and thus contributing to improved timeliness of healthcare processes. The study was exploratory in nature and followed a qualitative approach. For illustrative purposes, data on an outpatient referral process consisting of four milestones were used to produce a Lexis diagram. The Lexis diagram may complement the reporting of waiting times imposed by maximum waiting-time guarantees. It is expected to contribute to a more holistic view of processes and to a more precise measurement of lead times, enhance the ability of practitioners to react on time while the object is still active in the system and motivate improvements in staff scheduling by increasing the knowledge about the number of objects currently active in the system. However, it may contribute to an excessive emphasis being placed on time, which may distort clinical priorities. To the best of our knowledge, using the Lexis diagram for monitoring lead times represents a novel application of the diagram.
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The mortality impact in cancer screening trials and population programs is usually expressed as a single hazard ratio or percentage reduction. This measure ignores the number/spacing of rounds of screening, and the location in fol...
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The mortality impact in cancer screening trials and population programs is usually expressed as a single hazard ratio or percentage reduction. This measure ignores the number/spacing of rounds of screening, and the location in follow-up time of the averted deaths vis-a-vis the first and last screens. If screening works as intended, hazard ratios are a strong function of the two Lexis time-dimensions. We show how the number and timing of the rounds of screening can be included in a model that specifies what each round of screening accomplishes. We show how this model can be used to disaggregate the observed reductions (i.e., make them time-and screening-history specific), and to project the impact of other regimens. We use data on breast cancer screening to illustrate this model, which we had already described in technical terms in a statistical journal. Using the numbers of invitations different cohorts received, we fitted the model to the age-and followup-year-specific numbers of breast cancer deaths in Funen, Denmark. From November 1993 onwards, women aged 50-69 in Funen were invited to mammography screening every two years, while those in comparison regions were not. Under the proportional hazards model, the overall fitted hazard ratio was 0.82 (average reduction 18%). Using a (non-proportionalhazards) model that included the timing information, the fitted reductions ranged from 0 to 30%, being largest in those Lexis cells that had received the greatest number of invitations and where sufficient time had elapsed for the impacts to manifest. The reductions produced by cancer screening have been underestimated by inattention to their timing. By including the determinants of the hazard ratios in a regression-type model, the proposed approach provides a way to disaggregate the mortality reductions and project the reductions produced by other regimes/durations.
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Objective: To provide data on type 1 diabetes (T1D) epidemiology in childhood over a period of 20 years and to predict prevalence and cohort-age-specific incidence rates (IRs) for the next two decades in Germany. Methods: The Bade...
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Objective: To provide data on type 1 diabetes (T1D) epidemiology in childhood over a period of 20 years and to predict prevalence and cohort-age-specific incidence rates (IRs) for the next two decades in Germany. Methods: The Baden-Wuerttemberg Diabetes Incidence Registry (DIARY) includes children and adolescents below 15 years of age with new onset of T1D (period 1987-2006, n = 5108 cases). Results: The mean age- and sex-standardized IR was 15.3/100 000/year (95% CI 14.8-15.7) and the average increase in the IR was 4.4% per year (95% CI 3.9-4.9). Within the next 20 years (2007-2026), the risk for developing diabetes will increase like the square of a linear function with calendar year for all age ranges. There is a strong correlation between the predicted IRs of the cohorts and the observed IRs (n = 300; root mean square error = 0.56; r 2 = 0.71) and a negative correlation between mean age at onset and T1D IR (p = 0.02). On 31 December 2006, the prevalence of T1D was 0.126% (95% CI 0.121-0.132). The predicted prevalence (end of 2026) is estimated to be 0.265% (95% CI 0.25-0.28; predicted cases: n = 2950; 95% CI 2900-3000). Conclusions: In comparison to observations made in the past, the risk of disease rises even faster than expected: The younger the child, the quicker the increase of the cohort-age-specific IR and the higher the risk for T1D during lifetime.
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Two approaches are described for estimating the prevalence of a disease that may have developed in a previous restricted age interval among persons of a given age at a particular calender time. The prevalence for all those who eve...
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Two approaches are described for estimating the prevalence of a disease that may have developed in a previous restricted age interval among persons of a given age at a particular calender time. The prevalence for all those who ever developed disease is treated as a special case. The counting method (CM) obtains estimates of prevalence by dividing the estimated number of diseased persons by the total population size, taking loss to follow-up into account. The transition rate method (TRM) uses estimates of transition rates ad competing risk calculations to estimate prevalence. Variance calculations are described for CM and TRM as well as for a variant of CM, called counting method times 10 (CM10), that is designed to yield more precise estimates than CM. We compared these three estimators in terms of precision and in terms of the underlying assumptions required to justify the methods. CM makes fewer assumptions but is typically less precise than TRM or CM10. For common diseases such as breast cancer, CM may be preferred because its precision is excellent even though not as high as for TRM or CM10. For less common diseases, such as brain cancer, however, TRM or CM10 and other methods that make stabilizing assumptions may be preferred to CM.
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What population does the sample represent? The answer to this question is of crucial importance when estimating a survivor function in duration studies. As is well-known, in a stationary population, survival data obtained from a c...
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What population does the sample represent? The answer to this question is of crucial importance when estimating a survivor function in duration studies. As is well-known, in a stationary population, survival data obtained from a cross-sectional sample taken from the population at time t_0 represents not the target density f(t) but its length-biased version proportional to tf(t). for t ＞0. The problem of estimating survivor function from such length-biased samples becomes more complex, and interesting, in presence of competing risks and censoring. This paper lays out a sampling scheme related to a mixed Poisson process and develops nonparametric estimators of the survivor function of the target population assuming that the two independent competing risks have proportional hazards. Two cases are considered: with and without independent censoring before length biased sampling. In each case, the weak convergence of the process generated by the proposed estimator is proved. A well-known study of the duration in power for political leaders is used to illustrate our results. Finally, a simulation study is carried out in order to assess the finite sample behaviour of our estimators.
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