Streamlined Variational Inference for Linear Mixed Models with Crossed Random Effects.

We derive streamlined mean field variational Bayes algorithms for fitting linear mixed models with crossed random effects. In the most general situation, where the dimensions of the crossed groups are arbitrarily large, streamlining is hindered by lack of sparseness in the underlying least squares system. Because of this fact we also consider a hierarchy of relaxations of the mean field product restriction. The least stringent product restriction delivers a high degree of inferential accuracy. However, this accuracy must be mitigated against its higher storage and computing demands. Faster sparse storage and computing alternatives are also provided, but come with the price of diminished inferential accuracy. This article provides full algorithmic details of three variational inference strategies, presents detailed empirical results on their pros and cons and, thus, guides the users on their choice of variational inference approach depending on the problem size and computing resources.

Alcohol drinking and head and neck cancer risk: the joint effect of intensity and duration.

BACKGROUND: Alcohol is a well-established risk factor for head and neck cancer (HNC). This study aims to explore the effect of alcohol intensity and duration, as joint continuous exposures, on HNC risk. METHODS: Data from 26 case-control studies in the INHANCE Consortium were used, including never and current drinkers who drunk ≤10 drinks/day for ≤54 years (24234 controls, 4085 oral cavity, 3359 oropharyngeal, 983 hypopharyngeal and 3340 laryngeal cancers). The dose-response relationship between the risk and the joint exposure to drinking intensity and duration was investigated through bivariate regression spline models, adjusting for potential confounders, including tobacco smoking. RESULTS: For all subsites, cancer risk steeply increased with increasing drinks/day, with no appreciable threshold effect at lower intensities. For each intensity level, the risk of oral cavity, hypopharyngeal and laryngeal cancers did not vary according to years of drinking, suggesting no effect of duration. For oropharyngeal cancer, the risk increased with durations up to 28 years, flattening thereafter. The risk peaked at the higher levels of intensity and duration for all subsites (odds ratio = 7.95 for oral cavity, 12.86 for oropharynx, 24.96 for hypopharynx and 6.60 for larynx). CONCLUSIONS: Present results further encourage the reduction of alcohol intensity to mitigate HNC risk.

Joint effects of intensity and duration of cigarette smoking on the risk of head and neck cancer: A bivariate spline model approach.

OBJECTIVES: This study aimed at re-evaluating the strength and shape of the dose-response relationship between the combined (or joint) effect of intensity and duration of cigarette smoking and the risk of head and neck cancer (HNC). We explored this issue considering bivariate spline models, where smoking intensity and duration were treated as interacting continuous exposures. MATERIALS AND METHODS: We pooled individual-level data from 33 case-control studies (18,260 HNC cases and 29,844 controls) participating in the International Head and Neck Cancer Epidemiology (INHANCE) consortium. In bivariate regression spline models, exposures to cigarette smoking intensity and duration (compared with never smokers) were modeled as a linear piecewise function within a logistic regression also including potential confounders. We jointly estimated the optimal knot locations and regression parameters within the Bayesian framework. RESULTS: For oral-cavity/pharyngeal (OCP) cancers, an odds ratio (OR) >5 was reached after 30 years in current smokers of ∼20 or more cigarettes/day. Patterns of OCP cancer risk in current smokers differed across strata of alcohol intensity. For laryngeal cancer, ORs >20 were found for current smokers of ≥20 cigarettes/day for ≥30  years. In former smokers who quit ≥10  years ago, the ORs were approximately halved for OCP cancers, and ∼1/3 for laryngeal cancer, as compared to the same levels of intensity and duration in current smokers. CONCLUSION: Referring to bivariate spline models, this study better quantified the joint effect of intensity and duration of cigarette smoking on HNC risk, further stressing the need of smoking cessation policies.