Lexis Diagram Research Articles

Hepatitis B and C mortality from 1990 to 2019 in China: a Bayesian age-period-cohort analysis.

Significant decreases in hepatitis B virus (HBV) and hepatitis C virus (HCV) infections have been observed in China, but both remain leading public health challenges. Estimating the components and trends in HBV and HCV mortality is vital for disease control planning. The current analysis investigated time trends in hepatitis B and C mortality and the relationships with age, period, and birth cohort from 1990 to 2019. We also made projections for 2030-2034 in China. Mortality data related to hepatitis B and C were obtained from the Global Burden of Disease (GBD) study, which was stratified by complications, age, sex, and specific geographical locations. An age-period-cohort (APC) analytical framework was adopted to measure age, period, and cohort effects, which fits a log-linear Poisson model over a Lexis diagram of observed rates and quantifies the additive effects of age, period, and birth cohorts. We estimated longitudinal age curves (expected longitudinal age-specific rates), net drift (overall annual percentage change), local drift (annual percentage change in each age group), period, and cohort relative risks. A Bayesian APC analysis was used to project future age-specific hepatitis B and C deaths. In China, the age-standardized mortality rate (ASMR) of hepatitis B and C decreased by 67% and 58% from 1990 to 2019, respectively. The overall annual percentage changes in hepatitis B and C were -4.97% and -6.49% for males and -3.85% and -6.09% for females, respectively. After adjusting for period and cohort effects, we observed an exponential increase in hepatitis C mortality with age, with the Bell-like curves peaking at approximately 50 years old for hepatitis B. The Bayesian APC analysis projected that hepatitis B and C deaths would decrease dramatically by 42% and 22% for the periods 2016-2019 and 2030-2034, respectively. The declines in ASMRs related to hepatitis B and C were associated with the improvements in the Chinese Socio-Demographic Index. Although the burden of hepatitis B and C mortality is likely to continue declining in China, the hepatitis B and C mortality was still high. Therefore, the national efforts should still be strengthened to achieve the global hepatitis elimination targets.

Nonparametric Multiple Imputation of Left Censored Event Times in Analysis of Follow-up Data

In this paper, we consider analysis of follow-up data where each event time is either right censored, observed, left censored or left truncated. In the case of left censoring, the covariates measured at baseline are considered as missing. The work is motivated by data from the MORGAM Project, which explores the association between cardiovascular diseases and their classic and genetic risk factors. We propose a nonparametric multiple imputation (NPMI) approach where the left censored event times and the missing covariates are imputed in hot deck manner. The left truncation due to deaths prior to baseline is compensated by Lexis diagram imputation introduced in the paper. After imputation, the standard estimation methods for right censored survival data can be directly applied. The performance of the proposed imputation approach is studied with simulated and real world data. The results suggest that the NPMI is a flexible and reliable approach to the analysis of left and right censored data.

한국 가계의 지출구조 변화(1990-2018): 렉시스 다이어그램 분석 (Expenditure Patterns of Korean Households between 1990 and 2018: A Lexis Diagram Analysis)

Korean Abstract: 본 연구는 1990년, 1998년, 2008년, 2018년의 가계동향조사 지출부문 자료를 활용하여 각 연령대별, 연도별로 가계지출항목 구성비를 비교하고, 코호트의 지출구조 변화추이를 분석하였다. 분석은 연령-시기-코호트 모델(age-period-cohort model)을 설명하는 렉시 스 다이어그램(Lexis Diagram)을 활용하였다(Griffith, 2003; Rau et al., 2018). 렉시스 다이어그램의 세로축은 동일 연도에서 각 연령대의 가계지출구조를 비교하고, 가로축은 동일 연령대의 가계지출구조를 각 시기별로 비교한다. 또한 대각선은 특정 코호트의 가 계지출구조가 어떻게 변화하는지를 보여준다. 연구의 결과 지난 30년간 가계지출구조는 인구통계적, 정책적, 금융환경, 라이프스타일 의 변동상황을 반영하여 변화하고 있는 것으로 나타났다. 인구구조의 변화에 따라서 자 녀의 수가 줄어들어 이에 따른 교육비 비중이 줄어들고, 통신기술이 발달함에 따라 개인 통신장치 및 데이터 서비스를 사용하는 비용이 증가하고, 주 5일제가 시행되면서 여가를 중시하게 되어 교통비와 음식문화 등에 사용하는 비중이 증가하는 것 등은 가계를 둘러 싼 환경이 가계의 소비행태에 어떠한 영향을 미치는가를 보여주었다. 또한 현대의 라이 프사이클은 전통적인 가족의 생애주기의 모습과 함께 그 당시의 트렌드, 환경의 변화 등 을 포함한 라이프스타일을 반영하고 있는 것으로 나타났다. English Abstract: This study analyzes household expenditure patterns using the 1990, 1998, 2008, and 2018 Household Income and Expenditure Survey conducted by the Korea Statistics Bureau. Using a Lexis diagram of an age–period–cohort model, household expenditures were compared based on the head of the household’s age, the survey year, and life cycle stages. Household expenditures were grouped into 13 categories, and the proportion of each category to total household expenditures was compared based on (1) age group in each survey year (age effect), (2) same–age groups in different periods (period effect), and (3) cohort expenditure pattern changes between 1990 and 2018 (life cycle effect). The results show that during the past 30 years, household expenditure patterns have changed in relation to the macro-environmental changes that encompass Korean households, such as population aging, low birth rates, increases in household income and wealth, changes in technology, changes in values, and other regulatory and policy changes. For example, household expenditures on education are decreasing in proportion to the low birth rates; household expenditures on telecommunications have been increasing due to the changes in IT technology and lifestyles; and expenditures on food away from home and lodging and transportation have increased due to changes in working hours and work-versus-leisure values. The expenditure pattern changes resulting from the Lexis diagrams exhibit how the modern Korean life cycle is gradually changing from incorporating traditional life stages and modern values.

한국 가계의 지출구조 변화(1990-2018): 렉시스 다이어그램 분석

한국 가계의 지출구조 변화(1990-2018): 렉시스 다이어그램 분석

Mortality forecasting using a Lexis-based state-space model

AbstractA new method of forecasting mortality is introduced. The method is based on the continuous-time dynamics of the Lexis diagram, which given weak assumptions implies that the death count data are Poisson distributed. The underlying mortality rates are modelled with a hidden Markov model (HMM) which enables a fully likelihood-based inference. Likelihood inference is done by particle filter methods, which avoids approximating assumptions and also suggests natural model validation measures. The proposed model class contains as special cases many previous models with the important difference that the HMM methods make it possible to estimate the model efficiently. Another difference is that the population and latent variable variability can be explicitly modelled and estimated. Numerical examples show that the model performs well and that inefficient estimation methods can severely affect forecasts.

Prevalent cohort studies and unobserved heterogeneity.

Consider lifetimes originating at a series of calendar times [Formula: see text]. At a certain time [Formula: see text] a cross-sectional sample is taken, generating a sample of current durations (backward recurrence times) of survivors until [Formula: see text] and a prevalent cohort study consisting of survival times left-truncated at the current durations. A Lexis diagram is helpful in visualizing this situation. Survival analysis based on current durations and prevalent cohort studies is now well-established as long as all covariates are observed. The general problems with unobserved covariates have been well understood for ordinary prospective follow-up studies, with the good help of hazard rate models incorporating frailties: as for ordinary regression models, the added noise generates attenuation in the regression parameter estimates. For prevalent cohort studies this attenuation remains, but in addition one needs to take account of the differential selection of the survivors from initiation [Formula: see text] to cross-sectional sampling at [Formula: see text]. This paper intends to survey the recent development of these matters and the consequences for routine use of hazard rate models or accelerated failure time models in the many cases where unobserved heterogeneity may be an issue. The study was inspired by concrete problems in the study of time-to-pregnancy, and we present various simulation results inspired by this particular application.

A unified framework of demographic time

Demographic thought and practice is largely conditioned by the Lexis diagram, a two-dimensional graphical representation of the identity between age, period, and birth cohort. This relationship does not account for remaining years of life, total length of life, or time of death, whose use in demographic research is both underrepresented and incompletely situated. We describe an identity between these six demographic time measures and describe the sub-identities and diagrams that pertain to this identity. We provide an application of this framework to the measurement of late-life morbidity prevalence. We generalize these relationships to higher order identities derived from an arbitrary number of events in calendar time. Our examples are based on classic human demography, but the concepts we present can reveal patterns and relationships in any event history data, and contribute to the study of human or non-human population dynamics measured on any scale of calendar time.

Comparison of annual percentage change in breast cancer incidence rate between Taiwan and the United States-A smoothed Lexis diagram approach.

Recent studies compared the age effects and birth cohort effects on female invasive breast cancer (FIBC) incidence in Asian populations with those in the US white population. They were based on age–period–cohort model extrapolation and estimated annual percentage change (EAPC) in the age‐standardized incidence rates (ASR). It is of interest to examine these results based on cohort‐specific annual percentage change in rate (APCR) by age and without age–period–cohort model extrapolation. FIBC data (1991–2010) were obtained from the Taiwan Cancer Registry and the U.S. SEER 9 registries. APCR based on smoothed Lexis diagrams were constructed to study the age, period, and cohort effects on FIBC incidence. The patterns of age‐specific rates by birth cohort are similar between Taiwan and the US. Given any age‐at‐diagnosis group, cohort‐specific rates increased overtime in Taiwan but not in the US; cohort‐specific APCR by age decreased with birth year in both Taiwan and the US but was always positive and large in Taiwan. Given a diagnosis year, APCR decreased as birth year increased in Taiwan but not in the US. In Taiwan, the proportion of APCR attributable to cohort effect was substantial and that due to case ascertainment was becoming smaller. Although our study shows that incidence rates of FIBC have increased rapidly in Taiwan, thereby confirming previous results, the rate of increase over time is slowing. Continued monitoring of APCR and further investigation of the cause of the APCR decrease in Taiwan are warranted.

Constrained Estimators and Consistency of a Regression Model on a Lexis Diagram

This article considers a regression model on a Lexis diagram of an a × p table with a single response in each cell following a distribution in the exponential family. A regression model on the fixed effects of a rows, p columns, and a + p − 1 diagonals induces a singular design matrix and yields multiple estimators, leading to parameter identifiability problem in age–period–cohort analysis in social sciences, demography, and epidemiology, where assessment of secular trend in age, period, and birth cohort of social events (e.g., violence) and diseases (e.g., cancer) is of interest. Similar problems also exist in other settings, such as in supersaturated designs. In this article, we study the finite sample properties of the multiple estimators, propose a penalized profile likelihood method to study the consistency and asymptotic bias, and demonstrate the results through simulations and data analysis. As a by-product, the identifiability problem is addressed with consistent estimation for model parameters and secular trend. We conclude that consistent estimation can be identified through estimable function and asymptotics studies in regressions with a singular design. Our method provides a novel approach to studying asymptotics of multiple estimators with a diverging number of nuisance parameters.

Hyperlink-Embedded Journal Articles Improve Statistical Knowledge and Reader Satisfaction.

To practice evidence-based medicine, physicians should have a solid understanding of fundamental epidemiological and biostatistical concepts. Research suggests that only a minority of physicians have such an understanding of biostatistics. To collect pilot data on a novel biostatistical educational tool, a hyperlink-embedded journal article, which is aimed at improving knowledge in biostatistics. Forty-four physicians-in-training participated in this pilot study. Participants completed a pretest consisting of 5 questions about biostatistical terms that would be encountered in the article. They were randomized to either an unmodified journal article or to the same article with hyperlinked biostatistical terms. All participants then completed a posttest that was identical to the pretest. Having access to hyperlinked information had a positive association with the number of improved test answers (P = .05). Use of hyperlinks varied, and were seemingly dependent on user comfort with terms; well-understood definitions ("average") were clicked on a few times (5.5% of participants), whereas more obscure method terms ("Lexis diagram") were clicked on by 94% of participants. While only 42% of participants stated they would have looked up definitions of the biostatistical terms if they had not been provided in the hyperlinked article, 94% of participants identified the hyperlink tool as something they would use if readily available to them when reading journal articles. Results of this pilot study of a novel educational intervention suggest that embedded hyperlinks within journal articles may be a useful tool to teach biostatistical terms to physicians.

Smoothed Lexis Diagrams With Applications to Lung and Breast Cancer Trends in Taiwan

Cancer surveillance research often begins with a rate matrix, also called a Lexis diagram, of cancer incidence derived from cancer registry and census data. Lexis diagrams with 3- or 5-year intervals for age group and for calendar year of diagnosis are often considered. This simple smoothing approach suffers from a significant limitation; important details useful in studying time trends may be lost in the averaging process involved in generating a summary rate. This article constructs a smoothed Lexis diagram and indicates its use in cancer surveillance research. Specifically, we use a Poisson model to describe the relationship between the number of new cases, the number of people at risk, and a smoothly varying incidence rate for the study of the incidence rate function. Based on the Poisson model, we use the standard Lexis diagram to introduce priors through the coefficients of Bernstein polynomials and propose a Bayesian approach to construct a smoothed Lexis diagram for the study of the effects of age, period, and cohort on incidence rates in terms of straightforward graphical displays. These include the age-specific rates by year of birth, age-specific rates by year of diagnosis, year-specific rates by age of diagnosis, and cohort-specific rates by age of diagnosis. We illustrate our approach by studying the trends in lung and breast cancer incidence in Taiwan. We find that for nearly every age group the incidence rates for lung adenocarcinoma and female invasive breast cancer increased rapidly in the past two decades and those for male lung squamous cell carcinoma started to decrease, which is consistent with the decline in the male smoking rate that began in 1985. Since the analyses indicate strong age, period, and cohort effects, it seems that both lung cancer and breast cancer will become more important public health problems in Taiwan. Supplementary materials for this article are available online.

Selection bias due to parity-conditioning in studies of time trends in fertility.

Studies of couple fertility over time have often examined study populations with broad age ranges at a cross-section of time. An increase in fertility has been observed in studies that followed episodes of fertility events either prospectively among nulliparous women or retrospectively among parous women. Fertility has a biological effect on parity. If defined at a cross-section of time, parity will also be affected by year of birth, and thus becomes a collider. Conditioning (stratifying, restricting, or adjusting) on a collider may cause selection bias in the studied association. A study with prospective follow-up was taken as the model to assess the validity of fertility studies. We demonstrate the potential for selection bias using causal graphs and nationwide birth statistics and other demographic data. We tested the existence of parity-conditioning bias in data including both parous and nulliparous women. We also used a simulation approach to assess the strength of the bias in populations with prior at-risk cycles. Finally, we evaluated the potential for selection bias due to conditioning on parity in various sampling frames. Analyses indicate that the observed increase in fertility over time can be entirely explained by selection bias due to parity-conditioning. Heterogeneity in fertility and differential success in prior at-risk cycles are the ultimate factors behind the selection bias. The potential for selection bias due to parity-conditioning varies by sampling frame. A prospective multidecade study with representative sampling of birth cohorts and follow-up from menarche to menopause would bypass the described bias.

Modeling and forecasting duration-dependent mortality rates

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.

Lexis diagram and illness-death model: simulating populations in chronic disease epidemiology.

Chronic diseases impose a tremendous global health problem of the 21st century. Epidemiological and public health models help to gain insight into the distribution and burden of chronic diseases. Moreover, the models may help to plan appropriate interventions against risk factors. To provide accurate results, models often need to take into account three different time-scales: calendar time, age, and duration since the onset of the disease. Incidence and mortality often change with age and calendar time. In many diseases such as, for example, diabetes and dementia, the mortality of the diseased persons additionally depends on the duration of the disease. The aim of this work is to describe an algorithm and a flexible software framework for the simulation of populations moving in an illness-death model that describes the epidemiology of a chronic disease in the face of the different times-scales. We set up a discrete event simulation in continuous time involving competing risks using the freely available statistical software R. Relevant events are birth, the onset (or diagnosis) of the disease and death with or without the disease. The Lexis diagram keeps track of the different time-scales. Input data are birth rates, incidence and mortality rates, which can be given as numerical values on a grid. The algorithm manages the complex interplay between the rates and the different time-scales. As a result, for each subject in the simulated population, the algorithm provides the calendar time of birth, the age of onset of the disease (if the subject contracts the disease) and the age at death. By this means, the impact of interventions may be estimated and compared.

Exploring the use of the Lexis diagram for monitoring lead times in health care: the illustrative case of an outpatient referral process

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.

Analysis of age–period–cohort effects on overall mortality in Andalusia (Southern Spain)

ObjectivesTo evaluate the age–period–cohort effects on overall mortality in Andalusia (Spain). Study designAn ecological study was implemented with a Lexis diagram triangle comprising each annual age group, year of death and year of birth as the unit of analysis. MethodsIn all 1,384,899 deaths from all causes were analysed for individuals between the ages of 1 and 84 years who died in Andalusia in the period 1981–2008. A non-linear regression model was estimated for each gender group and geographical area. The effects of age, year of death and birth cohort were parameterized using B-spline smoothing functions. ResultsThere is a downward trend in mortality by age to around the age of 15 years, from which point the trend turned upwards. For cohorts born between 1945 and 1965, the rate climbed steadily. From 1965, the rate turned downwards. Death rates increased between 1995 and 2000, only to turn down again until the end of the period. Broadly, these results were similar for both men and women, in all the provinces of Andalusia and for Andalusia as a whole. ConclusionsThis study points to an age–period–cohort effect on deaths from all causes in all the geographic areas studied.

Age‐period‐cohort models using smoothing splines: a generalized additive model approach

Age-period-cohort (APC) models are used to analyze temporal trends in disease or mortality rates, dealing with linear dependency among associated effects of age, period, and cohort. However, the nature of sparseness in such data has severely limited the use of APC models. To deal with these practical limitations and issues, we advocate cubic smoothing splines. We show that the methods of estimable functions proposed in the framework of generalized linear models can still be considered to solve the non-identifiability problem when the model fitting is within the framework of generalized additive models with cubic smoothing splines. Through simulation studies, we evaluate the performance of the cubic smoothing splines in terms of the mean squared errors of estimable functions. Our results support the use of cubic smoothing splines for APC modeling with sparse but unaggregated data from a Lexis diagram.

Age–period–cohort analysis in the 1870s: Diagrams, stereograms, and the basic differential equation

AbstractThe period 1868–1880 saw a dramatic development in analytical and graphical descriptions of mortality, varying with time and age; this took place almost entirely in the German language. This report attempts a survey of these developments with brief notes on other graphical representations and on how they evolved into the Lexis diagram and the McKendrick–Von Foerster equation of the present time. The Canadian Journal of Statistics 39: 405–420; 2011 © 2011 Statistical Society of Canada

The Nature of Demography

In The Nature of Demography, the eminent French demographer Herve Le Bras presents an imaginative and compelling vision of what demography might become if it were to take seriously the scientific task of theory building and codification. Ranging across a wide array of substantive areas – mortality, fertility, marriage, migration, population projections, population and economic development, life-cycle economics and pensions, social mobility, settlement patterns, population density – Le Bras constructs simple (but not simplistic) mathematical models of population processes. The focus on process is central to his vision. Demographic measurement (a sort of land surveying applied to populations) is important, but secondary to the development of demography as an independent scientific discipline: Demography is a science of processes (p.345). It is necessary to get down to individual behaviour in real cohorts (time-lines in the language of the Lexis diagram), in short, to provide micro explanations for macro-demographic period observations. The latter are seen as unreliable guides to what is really going on, as a consequence of censoring (to which Le Bras devotes three chapters) and of wrong perspective: this interpretation reverses the true direction of the process, attempting to derive causes from their consequences (p.94). Le Bras works almost exclusively with mathematical models, spending little time on less rigorous conceptual or visual models. The models are constructed with an eye to specific empirical observations, and are solved analytically if possible, or by micro-simulation where necessary. A model is considered interesting and useful if it provides insight into the workings of the demographic system. A model is deemed empirically adequate if it can closely reproduce the original empirical observations. Le Bras does not speak of validity or truth of a model or theory. He avoids the logical fallacy of affirming the consequent by taking an ecumenical view of theory. Commenting on the large array of ________________________________ ________________________________ ________________________________

Hervé Le Bras: The Nature of Demography

Hervé Le Bras: The Nature of Demography