Advances in statistical methods for cancer surveillance research: an age-period-cohort perspective

Background

Analysis of Lexis diagrams (population-based cancer incidence and mortality rates indexed by age group and calendar period) requires specialized statistical methods. However, existing methods have limitations that can now be overcome using new approaches.

Methods

We assembled a "toolbox" of novel methods to identify trends and patterns by age group, calendar period, and birth cohort. We evaluated operating characteristics across 152 cancer incidence Lexis diagrams compiled from United States (US) Surveillance, Epidemiology and End Results Program data for 21 leading cancers in men and women in four race and ethnicity groups (the "cancer incidence panel").

Results

Nonparametric singular values adaptive kernel filtration (SIFT) decreased the estimated root mean squared error by 90% across the cancer incidence panel. A novel method for semi-parametric age-period-cohort analysis (SAGE) provided optimally smoothed estimates of age-period-cohort (APC) estimable functions and stabilized estimates of lack-of-fit (LOF). SAGE identified statistically significant birth cohort effects across the entire cancer panel; LOF had little impact. As illustrated for colon cancer, newly developed methods for comparative age-period-cohort analysis can elucidate cancer heterogeneity that would otherwise be difficult or impossible to discern using standard methods.

Conclusions

Cancer surveillance researchers can now identify fine-scale temporal signals with unprecedented accuracy and elucidate cancer heterogeneity with unprecedented specificity. Birth cohort effects are ubiquitous modulators of cancer incidence in the US. The novel methods described here can advance cancer surveillance research.

Comparative age-period-cohort analysis

BACKGROUND

Cancer surveillance researchers analyze incidence or mortality rates jointly indexed by age group and calendar period using age-period-cohort models. Many studies consider age- and period-specific rates in two or more strata defined by sex, race/ethnicity, etc. A comprehensive characterization of trends and patterns within each stratum can be obtained using age-period-cohort (APC) estimable functions (EF). However, currently available approaches for joint analysis and synthesis of EF are limited.

METHODS

We develop a new method called Comparative Age-Period-Cohort Analysis to quantify similarities and differences of EF across strata. Comparative Analysis identifies whether the stratum-specific hazard rates are proportional by age, period, or cohort.

RESULTS

Proportionality imposes natural constraints on the EF that can be exploited to gain efficiency and simplify the interpretation of the data. Comparative Analysis can also identify differences or diversity in proportional relationships between subsets of strata ("pattern heterogeneity"). We present three examples using cancer incidence from the United States Surveillance, Epidemiology, and End Results Program: non-malignant meningioma by sex; multiple myeloma among men stratified by race/ethnicity; and in situ melanoma by anatomic site among white women.

CONCLUSIONS

For studies of cancer rates with from two through to around 10 strata, which covers many outstanding questions in cancer surveillance research, our new method provides a comprehensive, coherent, and reproducible approach for joint analysis and synthesis of age-period-cohort estimable functions.

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.

Past, present, and future trends of overweight and obesity in Belgium using Bayesian age-period-cohort models

Background

Overweight and obesity are one of the most significant risk factors of the twenty-first century related to an increased risk in the occurrence of non-communicable diseases and associated increased healthcare costs. To estimate the future impact of overweight, the current study aimed to project the prevalence of overweight and obesity to the year 2030 in Belgium using a Bayesian age-period-cohort (APC) model, supporting policy planning.

Methods

Height and weight of 58,369 adults aged 18+ years, collected in six consecutive cross-sectional health interview surveys between 1997 and 2018, were evaluated. Criteria used for overweight and obesity were defined as body mass index (BMI) ≥ 25, and BMI ≥ 30. Past trends and projections were estimated with a Bayesian hierarchical APC model.

Results

The prevalence of overweight and obesity has increased between 1997 and 2018 in both men and women, whereby the highest prevalence was observed in the middle-aged group. It is likely that a further increase in the prevalence of obesity will be seen by 2030 with a probability of 84.1% for an increase in cases among men and 56.0% for an increase in cases among women. For overweight, it is likely to see an increase in cases in women (57.4%), while a steady state in cases among men is likely. A prevalence of 52.3% [21.2%; 83.2%] for overweight, and 27.6% [9.9%; 57.4%] for obesity will likely be achieved in 2030 among men. Among women, a prevalence of 49,1% [7,3%; 90,9%] for overweight, and 17,2% [2,5%; 61,8%] for obesity is most likely.

Conclusions

Our projections show that the WHO target to halt obesity by 2025 will most likely not be achieved. There is an urgent necessity for policy makers to implement effective prevent policies and other strategies in people who are at risk for developing overweight and/or obesity.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12889-022-13685-w.

Variance partitioning in spatio-temporal disease mapping models

Bayesian disease mapping, yet if undeniably useful to describe variation in risk over time and space, comes with the hurdle of prior elicitation on hard-to-interpret random effect precision parameters. We introduce a reparametrized version of the popular spatio-temporal interaction models, based on Kronecker product intrinsic Gaussian Markov random fields, that we name the variance partitioning model. The variance partitioning model includes a mixing parameter that balances the contribution of the main and interaction effects to the total (generalized) variance and enhances interpretability. The use of a penalized complexity prior on the mixing parameter aids in coding prior information in an intuitive way. We illustrate the advantages of the variance partitioning model using two case studies.

Projections of the future burden of cancer in Australia using Bayesian age-period-cohort models

BACKGROUND

Accurate forecasts of cancer incidence, with appropriate estimates of uncertainty, are crucial for planners and policy makers to ensure resource availability and prioritize interventions. We used Bayesian age-period-cohort (APC) models to project the future incidence of cancer in Australia.

METHODS

Bayesian APC models were fitted to counts of cancer diagnoses in Australia from 1982 to 2016 and projected to 2031 for seven key cancer types: breast, colorectal, liver, lung, non-Hodgkin lymphoma, melanoma and stomach. Aggregate cancer data from population-based cancer registries were sourced from the Australian Institute of Health and Welfare.

RESULTS

Over the projection period, total counts for these cancer types increased on average by 3 % annually to 100 385 diagnoses in 2031, which is a 50 % increase over 2016 numbers, although there is considerable uncertainty in this estimate. Counts for each cancer type and sex increased over the projection period, whereas decreases in the age-standardized incidence rates (ASRs) were projected for stomach, colorectal and male lung cancers. Large increases in ASRs were projected for liver and female lung cancer. Increases in the percentage of colorectal cancer diagnoses among younger age groups were projected. Retrospective one-step-ahead projections indicated both the incidence and its uncertainty were successfully forecast.

CONCLUSIONS

Increases in the projected incidence counts of key cancer types are in part attributable to the increasing and ageing population. The projected increases in ASRs for some cancer types should increase motivation to reduce sedentary behaviour, poor diet, overweight and undermanagement of infections. The Bayesian paradigm provides useful measures of the uncertainty associated with these projections.

Spatially varying age-period-cohort analysis with application to US mortality, 2002-2016

Many public health databases index disease counts by age groups and calendar periods within geographic regions (e.g., states, districts, or counties). Issues around relative risk estimation in small areas are well-studied; however, estimating trend parameters that vary across geographic regions has received less attention. Additionally, small counts (e.g., $<10$) in most publicly accessible databases are censored, further complicating age-period-cohort (APC) analysis in small areas. Here, we present a novel APC model with left-censoring and spatially varying intercept and trends, estimated with correlations among contiguous geographic regions. Like traditional models, our model captures population-scale trends, but it can also be used to characterize geographic disparities in relative risk and age-adjusted trends over time. To specify the joint distribution of our three spatially varying parameters, we adapt the generalized multivariate conditional autoregressive prior, previously used for multivariate disease mapping. Specified in this manner, region-specific parameters are correlated spatially, and also to one another. Estimation is performed using the No-U-Turn Hamiltonian Monte Carlo sampler in Stan. We conduct a simulation study to assess the performance of the proposed model relative to the standard model, and conclude with an application to US state-level opioid overdose mortality in men and women aged 15-64 years.

Using additive and coupled spatiotemporal SPDE models: a flexible illustration for predicting occurrence of Culicoides species

This paper formulates and compares a general class of spatiotemporal models for univariate space-time geostatistical data. The implementation of stochastic partial differential equation (SPDE) approach combined with integrated nested Laplace approximation into the R-INLA package makes it computationally feasible to use spatiotemporal models. However, the impact of specifying models with and without space-time interaction is unclear. We formulate an extensive class of additive and coupled spatiotemporal SPDE models and investigate the distinction between them by (1) Extending their temporal effect, allowing a random walk process in time, (2) varying the spatial correlation function and (3) running a simulation study to assess the effect of misspecifying the spatial and temporal models, and to assess the generalizability of our results to a higher number of locations. Our methods are illustrated with Culicoides data from Belgium. The Bayesian spatial predictions showed that the highest prevalence of Culicoides species was found in the Northeastern and central parts of Belgium during summer.

Identification and forecasting in mortality models

Mortality models often have inbuilt identification issues challenging the statistician. The statistician can choose to work with well-defined freely varying parameters, derived as maximal invariants in this paper, or with ad hoc identified parameters which at first glance seem more intuitive, but which can introduce a number of unnecessary challenges. In this paper we describe the methodological advantages from using the maximal invariant parameterisation and we go through the extra methodological challenges a statistician has to deal with when insisting on working with ad hoc identifications. These challenges are broadly similar in frequentist and in Bayesian setups. We also go through a number of examples from the literature where ad hoc identifications have been preferred in the statistical analyses.

Evaluating space-time models for short-term cancer mortality risk predictions in small areas

Current cancer mortality data are available with a delay of roughly three years due to the administrative procedure necessary to create the registries. Therefore, health agencies rely on forecast cancer deaths. In this context, statistical procedures providing mortality/incidence risk predictions for different regions or health areas are very useful. These predictions are essential for defining priorities for cancer prevention and treatment. The main objective of this work is to evaluate the predictive performance of alternative spatio-temporal models for short-term cancer risk/counts prediction in small areas. All the models analyzed here are presented under a general-mixed model framework, providing a unified structure of presentation and facilitating the use of similar tools for computing the prediction mean squared error. Prostate cancer mortality data are used to illustrate the behavior of the different models in Spanish provinces.

Bayesian shared spatial-component models to combine and borrow strength across sparse disease surveillance sources

When analyzing the geographical variations of disease risk, one common problem is data sparseness. In such a setting, we investigate the possibility of using Bayesian shared spatial component models to strengthen inference and correct for any spatially structured sources of bias, when distinct data sources on one or more related diseases are available. Specifically, we apply our models to analyze the spatial variation of risk of two forms of scrapie infection affecting sheep in Wales (UK) using three surveillance sources on each disease. We first model each disease separately from the combined data sources and then extend our approach to jointly analyze diseases and data sources. We assess the predictive performances of several nested joint models through pseudo cross-validatory predictive model checks.

A conditional approach for inference in multivariate age-period-cohort models

Age-period-cohort (APC) models are used to analyse data from disease registers given by age and time. When data are stratified by one further variable, for example geographical location, multivariate APC (MAPC) models can be applied to identify and estimate heterogeneous time trends across the different strata. In such models, outcomes share a set of parameters, typically the age effects, while the remaining parameters may differ across strata. In this article, we propose a conditional approach for inference to directly model relative time trends. We show that in certain situations the conditional approach can handle unmeasured confounding so that relative risks might be estimated with higher precision. Furthermore, we propose an extension for data with more stratification levels. Maximum likelihood estimation is performed using software for multinomial logistic regression. The usage of smoothing splines is suggested to stabilise estimates of relative time trends, if necessary. We apply the methodology to chronic obstructive pulmonary disease mortality data in England & Wales, stratified by three different areas and gender.