The association between aging and cancer is complex. Recent studies have developed measures of biological aging based on DNA methylation and called them “age acceleration.” We aimed to assess the associations of age acceleration with risk of and survival from seven common cancers. Seven case–control studies of DNA methylation and colorectal, gastric, kidney, lung, prostate and urothelial cancer and B‐cell lymphoma nested in the Melbourne Collaborative Cohort Study were conducted. Cancer cases, vital status and cause of death were ascertained through linkage with cancer and death registries. Conditional logistic regression and Cox models were used to estimate odds ratios (OR) and hazard ratios (HR) and 95% confidence intervals (CI) for associations of five age acceleration measures derived from the Human Methylation 450 K Beadchip assay with cancer risk (N = 3,216 cases) and survival (N = 1,726 deaths), respectively. Epigenetic aging was associated with increased cancer risk, ranging from 4% to 9% per five‐year age acceleration for the 5 measures considered. Heterogeneity by study was observed, with stronger associations for risk of kidney cancer and B‐cell lymphoma. An associated increased risk of death following cancer diagnosis ranged from 2% to 6% per five‐year age acceleration, with no evidence of heterogeneity by cancer site. Cancer risk and mortality were increased by 15–30% for the fourth versus first quartile of age acceleration. DNA methylation‐based measures of biological aging are associated with increased cancer risk and shorter cancer survival, independently of major health risk factors.

Measures of biological age based on blood DNA methylation, referred to as age acceleration (AA), have been developed. We examined whether AA was associated with health risk factors and overall and cause-specific mortality. At baseline (1990-1994), blood samples were drawn from 2,818 participants in the Melbourne Collaborative Cohort Study (Melbourne, Victoria, Australia). DNA methylation was determined using the Infinium HumanMethylation450 BeadChip array (Illumina Inc., San Diego, California). Mixed-effects models were used to examine the association of AA with health risk factors. Cox models were used to assess the association of AA with mortality. A total of 831 deaths were observed during a median 10.7 years of follow-up. Associations of AA were observed with male sex, Greek nationality (country of birth), smoking, obesity, diabetes, lower education, and meat intake. AA measures were associated with increased mortality, and this was only partly accounted for by known determinants of health (hazard ratios were attenuated by 20%-40%). Weak evidence of heterogeneity in the association was observed by sex (P = 0.06) and cause of death (P = 0.07) but not by other factors. DNA-methylation-based AA measures are associated with several major health risk factors, but these do not fully explain the association between AA and mortality. Future research should investigate what genetic and environmental factors determine AA.

This paper applies the minimum message length principle to inference of linear regression models with Student-t errors. A new criterion for variable selection and parameter estimation in Student-t regression is proposed. By exploiting properties of the regression model, we derive a suitable non-informative proper uniform prior distribution for the regression coefficients that leads to a simple and easy-to-apply criterion. Our proposed criterion does not require specification of hyperparameters and is invariant under both full rank transformations of the design matrix and linear transformations of the outcomes. We compare the proposed criterion with several standard model selection criteria, such as the Akaike information criterion and the Bayesian information criterion, on simulations and real data with promising results.

Global-local shrinkage hierarchies are an important innovation in Bayesian estimation. We propose the use of log-scale distributions as a novel basis for generating familes of prior distributions for local shrinkage hyperparameters. By varying the scale parameter one may vary the degree to which the prior distribution promotes sparsity in the coefficient estimates. By examining the class of distributions over the logarithm of the local shrinkage parameter that have log-linear, or sub-log-linear tails, we show that many standard prior distributions for local shrinkage parameters can be unified in terms of the tail behaviour and concentration properties of their corresponding marginal distributions over the coefficients $\beta_j$. We derive upper bounds on the rate of concentration around $|\beta_j|=0$, and the tail decay as $|\beta_j| \to \infty$, achievable by this wide class of prior distributions. We then propose a new type of ultra-heavy tailed prior, called the log-$t$ prior with the property that, irrespective of the choice of associated scale parameter, the marginal distribution always diverges at $\beta_j = 0$, and always possesses super-Cauchy tails. We develop results demonstrating when prior distributions with (sub)-log-linear tails attain Kullback--Leibler super-efficiency and prove that the log-$t$ prior distribution is always super-efficient. We show that the log-$t$ prior is less sensitive to misspecification of the global shrinkage parameter than the horseshoe or lasso priors. By incorporating the scale parameter of the log-scale prior distributions into the Bayesian hierarchy we derive novel adaptive shrinkage procedures. Simulations show that the adaptive log-$t$ procedure appears to always perform well, irrespective of the level of sparsity or signal-to-noise ratio of the underlying model.

Global-local shrinkage hierarchies are an important, recent innovation in Bayesian estimation of regression models. In this paper we propose to use log-scale distributions as a basis for generating familes of flexible prior distributions for the local shrinkage hyperparameters within such hierarchies. An important property of the log-scale priors is that by varying the scale parameter one may vary the degree to which the prior distribution promotes sparsity in the coefficient estimates, all the way from the simple proportional shrinkage ridge regression model up to extremely heavy tailed, sparsity inducing prior distributions. By examining the class of distributions over the logarithm of the local shrinkage parameter that have log-linear, or sub-log-linear tails, we show that many of standard prior distributions for local shrinkage parameters can be unified in terms of the tail behaviour and concentration properties of their corresponding marginal distributions over the coefficients $\beta_j$. We use these results to derive upper bounds on the rate of concentration around $|\beta_j|=0$, and the tail decay as $|\beta_j| \to \infty$, achievable by this class of prior distributions. We then propose a new type of ultra-heavy tailed prior, called the log-$t$ prior, which exhibits the property that, irrespective of the choice of associated scale parameter, the induced marginal distribution over $\beta_j$ always diverge at $\beta_j = 0$, and always possesses super-Cauchy tails. Finally, we propose to incorporate the scale parameter in the log-scale prior distributions into the Bayesian hierarchy and derive an adaptive shrinkage procedure. Simulations show that in contrast to a number of standard prior distributions, our adaptive log-$t$ procedure appears to always perform well, irrespective of the level of sparsity or signal-to-noise ratio of the underlying model.

Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of attention in the problem of estimating sparse, high-dimensional linear models. This paper extends these ideas, and presents a Bayesian grouped model with continuous global-local shrinkage priors to handle complex group hierarchies that include overlapping and multilevel group structures. As the posterior mean is never a sparse estimate of the linear model coefficients, we extend the recently proposed decoupled shrinkage and selection (DSS) technique to the problem of selecting groups of variables from posterior samples. To choose a final, sparse model, we also adapt generalised information criteria approaches to the DSS framework. To ensure that sparse groups, in which only a few predictors are active, can be effectively identified, we provide an alternative degrees of freedom estimator for sparse Bayesian linear models that takes into account the effects of shrinkage on the model coefficients. Simulations and real data analysis using our proposed method show promising performance in terms of correct identification of active and inactive groups, and prediction, in comparison with a Bayesian grouped slab-and-spike approach.

Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of attention in the problem of estimating sparse, high-dimensional linear models. This paper extends these ideas, and presents a Bayesian grouped model with continuous global-local shrinkage priors to handle complex group hierarchies that include overlapping and multilevel group structures. As the posterior mean is never a sparse estimate of the linear model coefficients, we extend the recently proposed decoupled shrinkage and selection (DSS) technique to the problem of selecting groups of variables from posterior samples. To choose a final, sparse model, we also adapt generalised information criteria approaches to the DSS framework. To ensure that sparse groups, in which only a few predictors are active, can be effectively identified, we provide an alternative degrees of freedom estimator for sparse, Bayesian linear models that takes into account the effects of shrinkage on the model coefficients. Simulations and real data analysis using our proposed method show promising performance in terms of correct identification of active and inactive groups, and prediction, in comparison with a Bayesian grouped slab-and-spike approach.