Comparison of statistical models to predict age-standardized cancer incidence in Switzerland

This study compares the performance of statistical methods for predicting age-standardized cancer incidence, including Poisson generalized linear models, age-period-cohort (APC) and Bayesian age-period-cohort (BAPC) models, autoregressive integrated moving average (ARIMA) time series, and simple linear models. The methods are evaluated via leave-future-out cross-validation, and performance is assessed using the normalized root mean square error, interval score, and coverage of prediction intervals. Methods were applied to cancer incidence from the three Swiss cancer registries of Geneva, Neuchatel, and Vaud combined, considering the five most frequent cancer sites: breast, colorectal, lung, prostate, and skin melanoma and bringing all other sites together in a final group. Best overall performance was achieved by ARIMA models, followed by linear regression models. Prediction methods based on model selection using the Akaike information criterion resulted in overfitting. The widely used APC and BAPC models were found to be suboptimal for prediction, particularly in the case of a trend reversal in incidence, as it was observed for prostate cancer. In general, we do not recommend predicting cancer incidence for periods far into the future but rather updating predictions regularly.

Penalized smoothing splines resolve the curvature identifiability problem in age-period-cohort models with unequal intervals

Age-period-cohort (APC) models are frequently used in a variety of health and demographic-related outcomes. Fitting and interpreting APC models to data in equal intervals (equal age and period widths) is nontrivial due to the structural link between the three temporal effects (given two, the third can always be found) causing the well-known identification problem. The usual method for resolving the structural link identification problem is to base a model on identifiable quantities. It is common to find health and demographic data in unequal intervals, this creates further identification problems on top of the structural link. We highlight the new issues by showing that curvatures which were identifiable for equal intervals are no longer identifiable for unequal data. Furthermore, through extensive simulation studies, we show how previous methods for unequal APC models are not always appropriate due to their sensitivity to the choice of functions used to approximate the true temporal functions. We propose a new method for modeling unequal APC data using penalized smoothing splines. Our proposal effectively resolves the curvature identification issue that arises and is robust to the choice of the approximating function. To demonstrate the effectiveness of our proposal, we conclude with an application to UK all-cause mortality data from the Human mortality database.

Trends in "Deaths of Despair" Among Working-Aged White and Black Americans, 1990-2017

Life expectancy for US White men and women declined between 2013 and 2017. Initial explanations for the decline focused on increases in "deaths of despair" (i.e., deaths from suicide, drug use, and alcohol use), which have been interpreted as a cohort-based phenomenon afflicting middle-aged White Americans. There has been less attention on Black mortality trends from these same causes, and whether the trends are similar or different by cohort and period. We complement existing research and contend that recent mortality trends in both the US Black and White populations most likely reflect period-based exposures to 1) the US opioid epidemic and 2) the Great Recession. We analyzed cause-specific mortality trends in the United States for deaths from suicide, drug use, and alcohol use among non-Hispanic Black and non-Hispanic White Americans, aged 20-64 years, over 1990-2017. We employed sex-, race-, and cause-of-death-stratified Poisson rate models and age-period-cohort models to compare mortality trends. Results indicate that rising "deaths of despair" for both Black and White Americans are overwhelmingly driven by period-based increases in drug-related deaths since the late 1990s. Further, deaths related to alcohol use and suicide among both White and Black Americans changed during the Great Recession, despite some racial differences across cohorts.

A Survivorship-Period-Cohort Model for Cancer Survival: Application to Liver Cancer in Taiwan, 1997-2016

Monitoring survival in cancer is a common concern for patients, physicians, and public health researchers. The traditional cohort approach for monitoring cancer prognosis has a timeliness problem. In this paper, we propose a survivorship-period-cohort (SPC) model for examining the effects of survivorship, period, and year-of-diagnosis cohort on cancer prognosis and for predicting future trends in cancer survival. We used the developed SPC model to evaluate the relative survival (RS) of patients with liver cancer in Taiwan (diagnosed from 1997 to 2016) and to predict future trends in RS by imputing incomplete follow-up data for recently diagnosed patient cohorts. We used cross-validation to select the extrapolation method and bootstrapping to estimate the 95% confidence interval for RS. We found that 5-year cumulative RS increased for both men and women with liver cancer diagnosed after 2003. For patients diagnosed before 2010, the 5-year cumulative RS rate for men was lower than that for women; thereafter, the rates were better for men than for women. The SPC model can help elucidate the effects of survivorship, period, and year-of-diagnosis cohort effects on cancer prognosis. Moreover, the SPC model can be used to monitor cancer prognosis in real time and predict future trends; thus, we recommend its use.

A simplified approach for establishing estimable functions in fixed effect age-period-cohort multiple classification models

Estimable functions play an important role in learning about certain aspects of the impact of ages, periods, and cohorts in age-period-cohort multiple classification (APCMC) models. The advantage of these estimates is that they are unbiased estimates of, for example, the deviations of age, period, and cohort effects from their linear trends, or changes in the linear trends of cohort effects within cohorts, or the residuals of fixed effect APCMC models. If the fixed effect APCMC model contains the relevant variables (is well specified), these estimable functions are unbiased estimates of functions of the parameters that generated the dependent variable data, even though the parameters that generated that data are not identified. I provide a simplified approach to establishing which functions are estimable in fixed effect APCMC models that provides an intuitive understanding of estimable functions by showing clearly and simply why they are estimable. This approach involves the partitioning of the age, period, and cohort effects into linear components and deviations from the linear components; the use of the "line of solutions"; and of the "extended null vector."

CP*Trends: An Online Tool for Comparing Cohort and Period Trends Across Cancer Sites

Cohort or period components of trends can provide a rationale for new research or point to clues on the effectiveness of control strategies. Graphical display of trends guides models that quantify the experience of a population. In this paper, a method for smoothing rates by single year of age and year is developed and displayed to show the contributions of period and cohort to trends. The magnitude of the contribution of period and/or cohort in a model for trends may be assessed by the percentage of deviance explained and the relative contributions of cohort (C) and period (P) individually, known as the C-P score. The method is illustrated using Surveillance, Epidemiology, and End Results data (1975-2014) on lung and bronchial cancer mortality in females and prostate and colorectal cancer incidence in males. Smoothed age-period and age-cohort rates provide a useful first step in studies of etiology and the impact of disease control without imposing a restrictive model. We found that, in this data set, cohort predominates for female lung and bronchial cancer and period predominates for male prostate cancer. However, the effects change with age for male colorectal cancer incidence, indicating an age shift in relevant exposures. These methods are applied on an interactive website for both incidence and mortality at over 20 cancer sites in the United States.

Biased estimation of trends in cohort effects: the problems with age-period-cohort models in ecology

Environmental variation can generate life-long similarities among individuals born in the same breeding event, so-called cohort effects. Studies of cohort effects have to account for the potentially confounding effects of current conditions (observation year) and age of individuals. However, estimation of such models is hampered by inherent collinearity, as age is the difference between observation year (period) and cohort year. The difficulties of separating linear trends in any of the three variables in Age-Period-Cohort (APC) models are the subject of ongoing debate in social sciences and medicine but have remained unnoticed in ecology. After reviewing the use of APC models, we investigate the consequences of model specification on the estimation of cohort effects, using both simulated data and empirical data from a long-term individual-based study of reindeer in Svalbard. We demonstrate that APC models are highly sensitive to the model's treatment of age, period and cohort, which may generate spurious temporal trends in cohort effects. Avoiding grouping ages and using environmental covariates believed to be drivers of temporal variation reduces the APC identification problem. Nonetheless, ecologists should use caution, given that the specification issues in APC models may have substantial impacts on estimated effect sizes and therefore conclusions.

Lung Cancer Mortality Trends in China from 1988 to 2013: New Challenges and Opportunities for the Government

Background: As lung cancer has shown a continuously increasing trend in many countries, it is essential to stay abreast of lung cancer mortality information and take informed actions with a theoretical basis derived from appropriate and practical statistical methods. Methods: Age-specific rates were collected by gender and region (urban/rural) and analysed with descriptive methods and age-period-cohort models to estimate the trends in lung cancer mortality in China from 1988 to 2013. Results: Descriptive analysis revealed that the age-specific mortality rates of lung cancer in rural residents increased markedly over the last three decades, and there was no obvious increase in urban residents. APC analysis showed that the lung cancer mortality rates significantly increased with age (20–84), rose slightly with the time period, and decreased with the cohort, except for the rural cohorts born during the early years (1909–1928). The trends in the patterns of the period and cohort effects showed marked disparities between the urban and rural residents. Conclusions: Lung cancer mortality remains serious and is likely to continue to rise in China. Some known measures are suggested to be decisive factors in mitigating lung cancer, such as environmental conservation, medical security, and tobacco control, which should be implemented more vigorously over the long term in China, especially in rural areas.

Invited Commentary: A-P-C... It's Easy as 1-2-3!

Investigations of age, period, and cohort effects are difficult because the 3 factors are linearly dependent. In a novel application, Kramer et al. (Am J Epidemiol. 2015;182(4):302-312) have used graphical analysis and statistical models to estimate the impact that age, period, and cohort effects have had on trends in black-white inequalities in heart disease mortality. Using a constrained regression approach (with the first 2 periods' effects constrained to zero), Kramer et al. find evidence that age and cohort effects figure more prominently than do period effects in contributing to relative black-white mortality differences, and they argue that early-life exposures should be given greater consideration for mitigation of racial differences in heart disease. In this invited commentary, I argue that the utility of age-period-cohort models for understanding health inequalities depends on the plausibility of the assumptions used to break the link between the 3 factors. Based on the existing age-period-cohort literature, alternative assumptions seem likely to produce substantially different results. I also argue that interpretations of the impacts of age, period, and cohort effects on racial inequalities in heart disease mortality may depend on whether inequalities are assessed on the absolute scale or the relative scale.

Decomposing Black-White Disparities in Heart Disease Mortality in the United States, 1973-2010: An Age-Period-Cohort Analysis

Against the backdrop of late 20th century declines in heart disease mortality in the United States, race-specific rates diverged because of slower declines among blacks compared with whites. To characterize the temporal dynamics of emerging black-white racial disparities in heart disease mortality, we decomposed race-sex-specific trends in an age-period-cohort (APC) analysis of US mortality data for all diseases of the heart among adults aged ≥35 years from 1973 to 2010. The black-white gap was largest among adults aged 35-59 years (rate ratios ranged from 1.2 to 2.7 for men and from 2.3 to 4.0 for women) and widened with successive birth cohorts, particularly for men. APC model estimates suggested strong independent trends across generations ("cohort effects") but only modest period changes. Among men, cohort-specific black-white racial differences emerged in the 1920-1960 birth cohorts. The apparent strength of the cohort trends raises questions about life-course inequalities in the social and health environments experienced by blacks and whites which could have affected their biomedical and behavioral risk factors for heart disease. The APC results suggest that the genesis of racial disparities is neither static nor restricted to a single time scale such as age or period, and they support the importance of equity in life-course exposures for reducing racial disparities in heart disease.

50 years of screening in the Nordic countries: quantifying the effects on cervical cancer incidence

BACKGROUND

Nordic countries' data offer a unique possibility to evaluate the long-term benefit of cervical cancer screening in a context of increasing risk of human papillomavirus infection.

METHODS

Ad hoc-refined age-period-cohort models were applied to the last 50-year incidence data from Denmark, Finland, Norway and Sweden to project expected cervical cancer cases in a no-screening scenario.

RESULTS

In the absence of screening, projected incidence rates for 2006-2010 in Nordic countries would have been between 3 and 5 times higher than observed rates. Over 60,000 cases or between 41 and 49% of the expected cases of cervical cancer may have been prevented by the introduction of screening in the late 1960s and early 1970s.

CONCLUSIONS

Our study suggests that screening programmes might have prevented a HPV-driven epidemic of cervical cancer in Nordic countries. According to extrapolations from cohort effects, cervical cancer incidence rates in the Nordic countries would have been otherwise comparable to the highest incidence rates currently detected in low-income countries.

Age-period-cohort effects on mortality from cerebrovascular disease in southern Spain

BACKGROUND

The aim of this article is to evaluate the age-period-cohort effects on mortality from cerebrovascular disease in Andalusia (southern Spain) as a whole and in each of its 8 provinces during the period 1981-2008.

METHODS

A population-based ecologic study was conducted. In all, 145,867 deaths were analyzed for individuals between the ages of 15 and 84 years who died in Andalusia in the period of study. A nonlinear regression model was estimated for each gender group and geographic area. The effects of age, year of death, and birth cohort were parameterized using spline smoothing functions.

RESULTS

There is an upward trend in mortality from the age of 25 years. The risk of death was downward for cohorts born after 1896, decreasing after 1970 with steep slope. The analysis of the period effect showed that death rate first declined from 1981 to 1995 and then increased between 1995 and 2000, only to decrease again until 2008.

CONCLUSIONS

There is a similar age-period-cohort effect on male and female mortality from cerebrovascular disease in all the provinces of Andalusia and for Andalusia as a whole. A significant reduction of male and female mortality has been observed during the last decade.

Divergent estrogen receptor-positive and -negative breast cancer trends and etiologic heterogeneity in Denmark

Long-term breast cancer trends in incidence in the United States (US) show rising estrogen receptor (ER)-positive rates and falling ER-negative rates. We hypothesized that these divergent trends reflect etiologic heterogeneity and that comparable trends should be observed in other countries with similar risk factor profiles. Therefore, we analyzed invasive female breast cancers in Denmark, a country with similar risk factors as the US. We summarized the overall trend in age-standardized rates with the estimated annual percentage change (EAPC) statistic (1993-2010) and used age-period-cohort models to estimate age-specific EAPCs, cohort rate ratios and projections for future time periods (2011-2018). In Denmark, the overall rate of ER-positive cancers rose between 1993 and 2010 by 3.0% per year (95% CI: 2.8-3.3% per year), whereas the overall rate of ER-negative cancers fell by 2.1% per year (95% CI: -2.5 to -1.6% per year). The ER-positive rate increased fastest among postmenopausal women and the ER-negative rate decreased fastest among premenopausal women, reflecting that cohorts born after 1944 were at relatively higher risk of ER-positive tumors and lower risk of ER-negative tumors. If current trends continue, ER-positive cancers will increase at least 13% by 2018 in Denmark, ER-negative cancers will fall 15% by 2018, and breast cancer overall will increase at least 7% by 2018. Divergent ER-specific trends are consistent with distinct etiologic pathways. If trends in known risk factors are responsible, the Danish and US experience may foreshadow a common pattern worldwide.

Trends in cancer of the cervix uteri in Sweden following cytological screening

Trends in cervical cancer incidence following the introduction of screening have mostly been studied using cross-sectional data and not analysed separately for squamous cell cancer and adenocarcinomas. Using Swedish nationwide data on incidence and mortality, we analysed trends during more than 3 decades and fitted Poisson-based age-period-cohort models, and also investigated whether screening has reduced the incidence of adenocarcinomas of the cervix. The incidence of reported cancer in situ increased rapidly during 1958-1967. Incidence rates of squamous cell cancer, fairly stable before 1968, decreased thereafter by 4-6% yearly in women aged 40-64, with a much smaller magnitude in younger and older women. An age-cohort model indicated a stable 70-75% reduction in incidence for women born 1940 and later compared with those born around 1923. The incidence of adenocarcinomas doubled during the 35-year study period. The mortality rate increased by 3.6% before 1968 and decreased by 4.0% yearly thereafter. Although a combination of organized and opportunistic screening can reduce the incidence of squamous cell cancer substantially, the incidence of adenocarcinomas appears uninfluenced by screening.