Bayesian age-stratified joinpoint regression model: an application to lung and brain cancer mortality

Joinpoint regression model identifies significant changes in the trends of the incidence, mortality, and survival of a specific disease in a given population. The purpose of the present study is to develop an age-stratified Bayesian joinpoint regression model to describe mortality trend assuming that the observed counts are probabilistically characterized by the Poisson distribution. The proposed model is based on Bayesian model selection criteria with the smallest number of joinpoints that are sufficient to explain the Annual Percentage Change. The prior probability distributions are chosen in such a way that they are automatically derived from the model index contained in the model space. The proposed model and methodology estimates the age-adjusted mortality rates in different epidemiological studies to compare the trends by accounting the confounding effects of age. In developing the subject methods, we use the cancer mortality counts of adult lung and bronchus cancer, and brain and other Central Nervous System cancer patients obtained from the Surveillance Epidemiology and End Results data base of the National Cancer Institute.     

A longitudinal analysis of infant and senescent mortality using mixture models

We construct a mixture distribution including infant, exogenous and Gompertzian/non-Gompertzian senescent mortality. Using mortality data from Swedish females 1751–, we show that this outperforms models without these features, and compare its trends in cohort and period mortality over time. We find an almost complete disappearance of exogenous mortality within the last century of period mortality, with cohort mortality approaching the same limits. Both Gompertzian and non-Gompertzian senescent mortality are consistently present, with the estimated balance between them oscillating constantly. While the parameters of the latter appear to be trending over time, the parameters of the former do not.     

Bayesian inference for categorical data analysis

This article surveys Bayesian methods for categorical data analysis, with primary emphasis on contingency table analysis. Early innovations were proposed by Good (1953, 1956, 1965) for smoothing proportions in contingency tables and by Lindley (1964) for inference about odds ratios. These approaches primarily used conjugate beta and Dirichlet priors. Altham (1969, 1971) presented Bayesian analogs of small-sample frequentist tests for 2 x 2 tables using such priors. An alternative approach using normal priors for logits received considerable attention in the 1970s by Leonard and others (e.g., Leonard 1972). Adopted usually in a hierarchical form, the logit-normal approach allows greater flexibility and scope for generalization. The 1970s also saw considerable interest in loglinear modeling. The advent of modern computational methods since the mid-1980s has led to a growing literature on fully Bayesian analyses with models for categorical data, with main emphasis on generalized linear models such as logistic regression for binary and multi-category response variables.     

Empirical Bayes procedures for stabilizing maps of U.S. cancer mortality rates

"The geographic mapping of age-standardized, cause-specific death rates is a powerful tool for identifying possible etiologic factors, because the spatial distribution of mortality risks can be examined for correlations with the spatial distribution of disease-specific risk factors. This article presents a two-stage empirical Bayes procedure for calculating age-standardized cancer death rates, for use in mapping, which are adjusted for the stochasticity of rates in small area populations. Using the adjusted rates helps isolate and identify spatial patterns in the rates. The model is applied to sex-specific data on U.S. county cancer mortality in the white population for 15 cancer sites for three decades: 1950-1959, 1960-1969, and 1970-1979. Selected results are presented as maps of county death rates for white males."     

The Decline in U.S. Output Volatility

Explanations for the decline in U.S. output volatility since the mid-1980s include: “better policy,” “good luck,” and technological change. Our multiple-break estimates suggest that reductions in volatility since the mid-1980s extend not only to manufacturing inventories, but also to sales. This finding, along with a concentration of the reduction in the volatility of inventories in materials and supplies and the lack of a significant break in the inventory–sales covariance, imply that new inventory technology cannot account for most of the decline in output volatility.     

Modeling heteroscedastic age-period-cohort cancer data

The extent to which cancer will be a burden on the Canadian health-care system will be determined by future cancer rates and future population levels in the high-risk age groups. Parametric models of incidence and mortality rates for various cancers may be used to obtain medium-term forecasts of rates, which then can be used in conjunction with population projections to obtain forecasts of total incidence and mortality. Age-period-cohort cancer data often exhibit marked heteroscedasticity, which complicates the modeling of the data. Methods to allow for the effects of this heteroscedasticity on residual processes are developed and discussed in the context of modeling Canadian female breast-cancer incidence data.     

Average life expectancy of the population of the USSR

Mortality trends in the USSR from the middle of the nineteenth century to the present day are analyzed, with a focus on changes in life expectancy. The authors note that life expectancy increased up to 1964-1965, declined subsequently, and stabilized during the 1980s. Life expectancy has again started to rise since 1985. More detailed analyses of mortality differentials by sex and age and for the rural and urban populations are included. (SUMMARY IN ENG)     

Alternative models for the heterogeneity of mortality risks among the aged

The authors examine how sensitive the estimates of heterogeneity in the mortality risks in a population are to the choices of two types of function, "one describing the age-specific rate of increase of mortality risks for individuals and the other describing the distribution of mortality risks across individuals." U.S. data from published Medicare mortality rates for the period 1968-1978 are used to analyze total mortality among the aged. "In addition, national vital statistics data for the period 1950-1977 were used to analyze adult lung cancer mortality. For these data, the estimates of structural parameters were less sensitive to reasonable choices of the heterogeneity distribution (gamma vs. inverse Gaussian) than to reasonable choices of the hazard rate function (Gompertz vs. Weibull)."     

Multilevel modelling of the geographical distributions of diseases

Multilevel modelling is used on problems arising from the analysis of spatially distributed health data. We use three applications to demonstrate the use of multilevel modelling in this area. The first concerns small area all-cause mortality rates from Glasgow where spatial autocorrelation between residuals is examined. The second analysis is of prostate cancer cases in Scottish counties where we use a range of models to examine whether the incidence is higher in more rural areas. The third develops a multiple-cause model in which deaths from cancer and cardiovascular disease in Glasgow are examined simultaneously in a spatial model. We discuss some of the issues surrounding the use of complex spatial models and the potential for future developments.     

Estimating age-specific incidence of dementia using prevalent cohort data

In prospective cohort studies individuals are usually recruited according to a certain cross-sectional sampling criterion. The prevalent cohort is defined as a group of individuals who are alive but possibly with disease at the beginning of the study. It is appealing to incorporate the prevalent cases to estimate the incidence rate of disease before the enrollment. The method of back calculation of incidence rate has been used to estimate the incubation time from HIV infection to AIDS. The time origin is defined as the time of HIV infection. In aging cohort studies, the primary time scale is age of disease onset, subjects have to survive certain years to be enrolled into the study, thus creating left truncation (delay entry). The current methods usually assume that either the disease incidence is rare or the excess mortality due to disease is small compared to the healthy subjects. By far the validity of the results based on these assumptions has not been examined. In this paper, a simple alternative method is proposed to estimate dementia incidence rate before enrollment using prevalent cohort data with left truncation. Furthermore simulations are used to examine the performance of the estimation of disease incidence under different assumptions of disease incidence rates and excess mortality hazards due to disease. As application, the method is applied to the prevalent cases of dementia from the Honolulu Asia Aging Study to estimate dementia incidence rate and to assess the effect of hypertension, Apoe 4 and education on dementia onset.     

The Impact of Ovarian Cancer on Life Expectancy in Japan

The purpose of this study was to determine how life expectancy is modified by ovarian cancer from 1950-2000. The contributions of ovarian cancer to life expectancy were estimated. The age characteristics of ovarian cancer were detected using the Gompertz relational mortality model. The patterns between years of potential life lost (YPLL) and mortality were obtained by fitting a linear regression equation to the natural logarithm of their ratios. YPLLs are substantially higher in Ireland than in Japan. However, the rates of change were much higher in Japan than in Ireland. YPLLs changed from 0.02 year in 1950 to 0.12 year in 2000. In Japan, there was a sixfold increase in the proportion of YPLLs for death from ovarian cancer relative to those for death from gynaecological cancers during the last half century. The impact of ovarian cancer on life expectancy clearly increased and the age-specific mortality tend to ageing.     

Lee–Carter mortality forecasting: a parallel generalized linear modelling approach for England and Wales mortality projections

Summary. The paper presents a reinterpretation of the model underpinning the Lee–Carter methodology for forecasting mortality (and other vital) rates. A parallel methodology based on generalized linear modelling is introduced. The use of residual plots is proposed for both methods to aid the assessment of the goodness of fit. The two methods are compared in terms of structure and assumptions. They are then compared through an analysis of the gender- and age-specific mortality rates for England and Wales over the period 1950–1998 and through a consideration of the forecasts generated by the two methods. The paper also compares different approaches to the forecasting of life expectancy and considers the effectiveness of the Coale–Guo method for extrapolating mortality rates to the oldest ages.     

Poisson regression with misclassified counts: application to cervical cancer

"Errors in disease classification can give misleading inferences for covariate effects when the probability of error is itself related to the covariates. More accurate inferences are possible using supplemental data on both true and fallible disease counts at various covariate levels. We present a method for incorporating such supplemental data into disease rate regression and use it to show that, although observed intercountry differences in European cervical cancer mortality rates are exaggerated by errors in death certification, they are not completely explained by such errors." The data concern Belgium, England and Wales, France, and Italy.     

Population study and management of Atlantic Flyway Canada geese

Numbers of wintering Canada geese ( Branta canadensis ) in different regions of the Atlantic Flyway have significantly changed since the 1950s. During the 1980s, numbers increased in the mid-Atlantic and declined in the Chesapeake regions. A neckband study during the 1980s tested hypotheses that differential survival or movement caused changes in wintering numbers. The earlier studies and a reanalysis of the movement data using MSSURVIV indicated that the changes in wintering numbers did not result from differential survival or movement. A new neckband study, started in 1991, was designed to test hypotheses that the increases in wintering geese in the mid-Atlantic resulted from increasing numbers of resident geese and that the decline in migrants was related to higher harvest rates. Numbers of wintering geese continued to increase in the mid-Atlantic and declined in the Chesapeake region. Analyses of winter-banded, migrant geese indicated that 47 000 (SE = 14 000) geese per year moved from the mid-Atlantic to the Chesapeake region, thus rejecting the short-stopping hypothesis for this period. The probability of mid-Atlantic neckbanded resident geese remaining in the mid-Atlantic during winter was 0.988 (0.005). No differences in average survival were detected for migrants wintering in different regions during 1991-1994. Resident geese had higher survival than migrant geese in the Chesapeake region but not in the mid-Atlantic region. Harvest age ratios were low for Maryland and Quebec during the 1990s with record lows occurring during 1992. The only survival rate that could be estimated during the period of harvest restrictions was for 1992. Differences in survival were not detected between the periods of liberal harvest, 1985-1987, and the one year estimate under restrictive harvest. Because of the low age ratio, comparable numbers of adults were harvested during periods of restrictive and liberal regulations. Migrants appeared to be declining in all wintering regions, and residents appeared to be increasing. The different trends may be due to production differences.     

Ridge estimator in singulah oesiun with application to age-period-cohort analysis of disease rates

Ridge estimator of a singular design is considered for linear and gener¬alized linear models. Ridge penalty helps determine a unique estimator in singmar uesign. me tuning parameter o± tue penalty is seiecteu via gener¬alized cross-validation (GCV) method. It is proven that the ridge estimator lies in a special sub-parameter space and converges to the intrinsic estimator, an estimable function in singular design, as the shrinkage penalty diminishes. The expansion of the ridge estimator and its variance are also obtained. Thismethod is demonstrated through an application to age-period-cohort (APC) analysis of the incidence rates of cervical cancer in Ontario women 1980-1994     

Estimating age-specific incidence of dementia using prevalent cohort data

In prospective cohort studies, individuals are usually recruited according to a certain cross-sectional sampling criterion. The prevalent cohort is defined as a group of individuals who are alive but possibly with disease at the beginning of the study. It is appealing to incorporate the prevalent cases to estimate the incidence rate of disease before the enrollment. The method of back calculation of incidence rate has been used to estimate the incubation time from human immunodeficiency virus (HIV) infection to AIDS. The time origin is defined as the time of HIV infection. In aging cohort studies, the primary time scale is age of disease onset, subjects have to survive certain years to be enrolled into the study, thus creating left truncation (delay entry). The current methods usually assume that either the disease incidence is rare or the excess mortality due to disease is small compared with the healthy subjects. So far the validity of the results based on these assumptions has not been examined. In this paper, a simple alternative method is proposed to estimate dementia incidence rate before enrollment using prevalent cohort data with left truncation. Furthermore, simulations are used to examine the performance of the estimation of disease incidence under different assumptions of disease incidence rates and excess mortality hazards due to disease. As application, the method is applied to the prevalent cases of dementia from the Honolulu-Asia Aging Study to estimate the dementia incidence rate and to assess the effect of hypertension, Apoe 4 and education on dementia onset.     

Statistical materials. Part 3: fertility,mortality, and natural increase

In this one-page statistical summary, data are presented for the USSR as a whole on fertility, mortality, and natural increase. The data are for five-year intervals from 1940 to 1980 and for single years from 1980 and are presented in terms of both totals and rates.     

Change point-cure models with application to estimating the change-point effect of age of diagnosis among prostate cancer patients

Previous research on prostate cancer survival trends in the United States National Cancer Institute's Surveillance Epidemiology and End Results database has indicated a potential change-point in the age of diagnosis of prostate cancer around age 50. Identifying a change-point value in prostate cancer survival and cure could have important policy and health care management implications. Statistical analysis of this data has to address two complicating features: (1) change-point models are not smooth functions and so present computational and theoretical difficulties; and (2) models for prostate cancer survival need to account for the fact that many men diagnosed with prostate cancer can be effectively cured of their disease with early treatment. We develop a cure survival model that allows for change-point effects in covariates to investigate a potential change-point in the age of diagnosis of prostate cancer. Our results do not indicate that age under 50 is associated with increased hazard of death from prostate cancer.     

Statistical materials: natural increase of population in the USSR

Data on the population of the USSR by sex and Union republic as of January 1, 1982, are presented. Data are included on population by sex; birth, death, and natural growth rates, 1980 and 1981; distribution of births, deaths, and marriages by month, 1981; distribution of births by birth order, 1981; age-specific birth rates for rural and urban areas, 1980 and 1981; mortality from cardiovascular disease and cancer, 1980 and 1981; marriages by age of bride and groom, 1981; and divorces by duration of marriage and age of husband and wife, 1981.     

Estimating the cure fraction in population-based cancer studies by using finite mixture models

Summary.  The cure fraction (the proportion of patients who are cured of disease) is of interest to both patients and clinicians and is a useful measure to monitor trends in survival of curable disease. The paper extends the non-mixture and mixture cure fraction models to estimate the proportion cured of disease in population-based cancer studies by incorporating a finite mixture of two Weibull distributions to provide more flexibility in the shape of the estimated relative survival or excess mortality functions. The methods are illustrated by using public use data from England and Wales on survival following diagnosis of cancer of the colon where interest lies in differences between age and deprivation groups. We show that the finite mixture approach leads to improved model fit and estimates of the cure fraction that are closer to the empirical estimates. This is particularly so in the oldest age group where the cure fraction is notably lower. The cure fraction is broadly similar in each deprivation group, but the median survival of the 'uncured' is lower in the more deprived groups. The finite mixture approach overcomes some of the limitations of the more simplistic cure models and has the potential to model the complex excess hazard functions that are seen in real data.