The Weibull distribution, with shape parameter $k>0$ and scale parameter $\lambda>0$, is one of the most popular parametric distributions in survival analysis with complete or censored data. Although inference of the parameters of the Weibull distribution is commonly done through maximum likelihood, it is well established that the maximum likelihood estimate of the shape parameter is inadequate due to the associated large bias when the sample size is small or the proportion of censored data is large. This manuscript demonstrates how the Bayesian information-theoretic minimum message length principle coupled with a suitable choice of weakly informative prior distributions, can be used to infer Weibull distribution parameters given complete data or data with type I censoring. Empirical experiments show that the proposed minimum message length estimate of the shape parameter is superior to the maximum likelihood estimate and appears superior to other recently proposed modified maximum likelihood estimates in terms of Kullback-Leibler risk. Lastly, we derive an extension of the proposed method to data with type II censoring.

In this short note, we derive a new bias adjusted maximum likelihood estimate for the shape parameter of the Weibull distribution with complete data and type I censored data. The proposed estimate of the shape parameter is significantly less biased and more efficient than the corresponding maximum likelihood estimate, while being simple to compute using existing maximum likelihood software procedures.

The aim of this manuscript is to introduce the Bayesian minimum message length principle of inductive inference to a general statistical audience that may not be familiar with information theoretic statistics. We describe two key minimum message length inference approaches and demonstrate how the principle can be used to develop a new Bayesian alternative to the frequentist $t$-test as well as new approaches to hypothesis testing for the correlation coefficient. Lastly, we compare the minimum message length approach to the closely related minimum description length principle and discuss similarities and differences between both approaches to inference.

Principal component analysis (PCA) is perhaps the most widely method for data dimensionality reduction. A key question in PCA decomposition of data is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting the number of principal components based on the Bayesian minimum message length method of inductive inference. We also derive a new estimate of the isotropic residual variance and demonstrate, via numerical experiments, that it improves on the usual maximum likelihood approach.

The Weibull distribution, with shape parameter $k>0$ and scale parameter $\lambda>0$, is one of the most popular parametric distributions in survival analysis with complete or censored data. Although inference of the parameters of the Weibull distribution is commonly done through maximum likelihood, it is well established that the maximum likelihood estimate of the shape parameter is inadequate due to the associated large bias when the sample size is small or the proportion of censored data is large. This manuscript demonstrates how the Bayesian information-theoretic minimum message length principle coupled with a suitable choice of weakly informative prior distributions, can be used to infer Weibull distribution parameters given complete data or data with type I censoring. Empirical experiments show that the proposed minimum message length estimate of the shape parameter is superior to the maximum likelihood estimate and appears superior to other recently proposed modified maximum likelihood estimates in terms of Kullback-Leibler risk. Lastly, we derive an extension of the proposed method to data with type II censoring.

Abstract Limited evidence exists on the link between inflammation and epigenetic aging. We aimed to (a) assess the cross-sectional and prospective associations of 22 inflammation-related plasma markers and a signature of inflammaging with epigenetic aging and (b) determine whether epigenetic aging and inflammaging are independently associated with mortality. Blood samples from 940 participants in the Melbourne Collaborative Cohort Study collected at baseline (1990–1994) and follow-up (2003–2007) were assayed for DNA methylation and 22 inflammation-related markers, including well-established markers (eg, interleukins and C-reactive protein) and metabolites of the tryptophan–kynurenine pathway. Four measures of epigenetic aging (PhenoAge, GrimAge, DunedinPoAm, and Zhang) and a signature of inflammaging were considered, adjusted for age, and transformed to Z scores. Associations were assessed using linear regression, and mortality hazard ratios (HR) and 95% confidence intervals (95% CI) were estimated using Cox regression. Cross-sectionally, most inflammation-related markers were associated with epigenetic aging measures, although with generally modest effect sizes (regression coefficients per SD ≤ 0.26) and explaining altogether between 1% and 11% of their variation. Prospectively, baseline inflammation-related markers were not, or only weakly, associated with epigenetic aging after 11 years of follow-up. Epigenetic aging and inflammaging were strongly and independently associated with mortality, for example, inflammaging: HR = 1.41, 95% CI = 1.27–1.56, p = 2 × 10−10, which was only slightly attenuated after adjustment for 4 epigenetic aging measures: HR = 1.35, 95% CI = 1.22–1.51, p = 7 × 10−9). Although cross-sectionally associated with epigenetic aging, inflammation-related markers accounted for a modest proportion of its variation. Inflammaging and epigenetic aging are essentially nonoverlapping markers of biological aging and may be used jointly to predict mortality.

Identifying tumor DNA mismatch repair deficiency (dMMR) is important for precision medicine. We assessed tumor features, individually and in combination, in whole-exome sequenced (WES) colorectal cancers (CRCs) and in panel sequenced CRCs, endometrial cancers (ECs) and sebaceous skin tumors (SSTs) for their accuracy in detecting dMMR. CRCs (n=300) with WES, where MMR status was determined by immunohistochemistry, were assessed for microsatellite instability (MSMuTect, MANTIS, MSIseq, MSISensor), COSMIC tumor mutational signatures (TMS) and somatic mutation counts. A 10-fold cross-validation approach (100 repeats) evaluated the dMMR prediction accuracy for 1) individual features, 2) Lasso statistical model and 3) an additive feature combination approach. Panel sequenced tumors (29 CRCs, 22 ECs, 20 SSTs) were assessed for the top performing dMMR predicting features/models using these three approaches. For WES CRCs, 10 features provided >80% dMMR prediction accuracy, with MSMuTect, MSIseq, and MANTIS achieving [≥]99% accuracy. The Lasso model achieved 98.3%. The additive feature approach with [≥]3/6 of MSMuTect, MANTIS, MSIseq, MSISensor, INDEL count or TMS ID2+ID7 achieved 99.7% accuracy. For the panel sequenced tumors, the additive feature combination approach of [≥]3/6 achieved accuracies of 100%, 95.5% and 100%, for CRCs, ECs, and SSTs, respectively. The microsatellite instability calling tools performed well in WES CRCs, however, an approach combining tumor features may improve dMMR prediction in both WES and panel sequenced data across tissue types.

Genetic variants in FOXO3 are associated with longevity. Here, we assessed whether blood DNA methylation at FOXO3 was associated with cancer risk, survival, and mortality. We used data from eight prospective case–control studies of breast (n = 409 cases), colorectal (n = 835), gastric (n = 170), kidney (n = 143), lung (n = 332), prostate (n = 869), and urothelial (n = 428) cancer and B-cell lymphoma (n = 438). Case–control pairs were matched on age, sex, country of birth, and smoking (lung cancer study). Conditional logistic regression was used to assess associations between cancer risk and methylation at 45 CpGs of FOXO3 included on the HumanMethylation450 assay. Mixed-effects Cox models were used to estimate hazard ratios (HR) and 95% confidence intervals (CI) for associations with cancer survival (total n = 2286 deaths). Additionally, using data from 1088 older participants, we assessed associations of FOXO3 methylation with overall and cause-specific mortality (n = 354 deaths). Methylation at a CpG in the first exon region of FOXO3 (6:108882981) was associated with gastric cancer survival (HR = 2.39, 95% CI: 1.60–3.56, p = 1.9 × 10−5). Methylation at three CpGs in TSS1500 and gene body was associated with lung cancer survival (p < 6.1 × 10−5). We found no evidence of associations of FOXO3 methylation with cancer risk and mortality. Our findings may contribute to understanding the implication of FOXO3 in longevity.

An increasing number of studies have revealed that dysregulated lipid homeostasis is associated with the pathological processes that lead to Alzheimer’s disease (AD). If changes in key lipid species could be detected in the periphery, it would advance our understanding of the disease and facilitate biomarker discovery. Global lipidomic profiling of sera/blood however has proved challenging with limited disease or tissue specificity. Small extracellular vesicles (EV) in the central nervous system, can pass the blood‐brain barrier and enter the periphery, carrying a subset of lipids that could reflect lipid homeostasis in brain. This makes EVs uniquely suited for peripheral biomarker exploration.

Data with censoring is common in many areas of science and the associated statistical models are generally estimated with the method of maximum likelihood combined with a model selection criterion such as Akaike’s information criterion. This manuscript demonstrates how the information theoretic minimum message length principle can be used to estimate statistical models in the presence of type I random and fixed censoring data. The exponential distribution with fixed and random censoring is used as an example to demonstrate the process where we observe that the minimum message length estimate of mean survival time has some advantages over the standard maximum likelihood estimate.

ABSTRACT Lifestyle-related phenotypes have been shown to be heritable and associated with DNA methylation. We aimed to investigate whether genetic predisposition to tobacco smoking, alcohol consumption, and higher body mass index (BMI) moderates the effect of these phenotypes on blood DNA methylation. We calculated polygenic scores (PGS) to quantify genetic predisposition to these phenotypes using training (N = 7,431) and validation (N = 4,307) samples. Using paired genetic-methylation data (N = 4,307), gene–environment interactions (i.e., PGS × lifestyle) were assessed using linear mixed-effects models with outcomes: 1) methylation at sites found to be strongly associated with smoking (1,061 CpGs), alcohol consumption (459 CpGs), and BMI (85 CpGs) and 2) two epigenetic ageing measures, PhenoAge and GrimAge. In the validation sample, PGS explained ~1.4% (P = 1 × 10−14), ~0.6% (P = 2 × 10−7), and ~8.7% (P = 7 × 10−87) of variance in smoking initiation, alcohol consumption, and BMI, respectively. Nominally significant interaction effects (P < 0.05) were found at 61, 14, and 7 CpGs for smoking, alcohol consumption, and BMI, respectively. There was strong evidence that all lifestyle-related phenotypes were positively associated with PhenoAge and GrimAge, except for alcohol consumption with PhenoAge. There was weak evidence that the association of smoking with GrimAge was attenuated in participants genetically predisposed to smoking (interaction term: −0.022, standard error [SE] = 0.012, P = 0.058) and that the association of alcohol consumption with PhenoAge was attenuated in those genetically predisposed to drink alcohol (interaction term: −0.030, SE = 0.015, P = 0.041). In conclusion, genetic susceptibility to unhealthy lifestyles did not strongly modify the association between observed lifestyle behaviour and blood DNA methylation. Potential associations were observed for epigenetic ageing measures, which should be replicated in additional studies.

We examined demographic and lifestyle risk factors for incidence of gastroesophageal reflux disease (GERD) and Barrett's esophagus (BE) in an Australian cohort of 20,975 participants aged 40-63 at recruitment (1990-1994). Information on GERD and BE was collected between 2007 and 2010. GERD symptoms were defined as self-reported heartburn or acid regurgitation. BE was defined as endoscopically confirmed columnar-lined esophagus. Risk factors for developing GERD symptoms, BE diagnosis, age at symptom onset, and age at BE diagnosis were quantified using regression. During a mean follow-up of 15.8 years, risk of GERD symptoms was 7.5% (n = 1,318) for daily, 7.5% (n = 1,333) for 2-6 days/week, and 4.3% (n = 751) for 1 day/week. There were 210 (1.0%) endoscopically diagnosed BE cases, of whom 141 had histologically confirmed esophageal intestinal metaplasia. Female sex, younger age, lower socioeconomic position (SEP) and educational attainment, and former smoking were associated with higher GERD risk. Male sex and smoking were associated with earlier GERD symptom onset. Men, older participants, those with higher SEP, and former smokers were at higher BE risk. There was some evidence higher SEP was associated with earlier BE diagnosis. GERD and BE had different demographic risk factors but shared similar lifestyle factors. Earlier GERD symptom onset for men and smokers might have contributed to higher BE risk. The SEP patterns observed for GERD and BE suggest potential inequity in access to care. These findings would be important in the development of clinical risk prediction models for early detection of BE.

Background: Self-reported information may not accurately capture smoking exposure. We aimed to evaluate whether smoking-associated DNA methylation markers improve urothelial cell carcinoma (UCC) risk prediction. Methods: Conditional logistic regression was used to assess associations between blood-based methylation and UCC risk using two matched case–control samples: 404 pairs from the Melbourne Collaborative Cohort Study (MCCS) and 440 pairs from the Women's Health Initiative (WHI) cohort. Results were pooled using fixed-effects meta-analysis. We developed methylation-based predictors of UCC and evaluated their prediction accuracy on two replication data sets using the area under the curve (AUC). Results: The meta-analysis identified associations (P < 4.7 × 10−5) for 29 of 1,061 smoking-associated methylation sites, but these were substantially attenuated after adjustment for self-reported smoking. Nominally significant associations (P < 0.05) were found for 387 (36%) and 86 (8%) of smoking-associated markers without/with adjustment for self-reported smoking, respectively, with same direction of association as with smoking for 387 (100%) and 79 (92%) markers. A Lasso-based predictor was associated with UCC risk in one replication data set in MCCS [N = 134; odds ratio per SD (OR) = 1.37; 95% CI, 1.00–1.90] after confounder adjustment; AUC = 0.66, compared with AUC = 0.64 without methylation information. Limited evidence of replication was found in the second testing data set in WHI (N = 440; OR = 1.09; 95% CI, 0.91–1.30). Conclusions: Combination of smoking-associated methylation marks may provide some improvement to UCC risk prediction. Our findings need further evaluation using larger data sets. Impact: DNA methylation may be associated with UCC risk beyond traditional smoking assessment and could contribute to some improvements in stratification of UCC risk in the general population.