Mean field variational bayes for elaborate distributions

We develop strategies for mean field variational Bayes approximate inference for Bayesian hierarchical models containing elaborate distributions. We loosely define elaborate distributions to be those having more complicated forms compared with common distributions such as those in the Normal and Gamma families. Examples are Asymmetric Laplace, Skew Normal and Generalized Extreme Value distributions. Such models suffer from the difficulty that the parameter updates do not admit closed form solutions. We circumvent this problem through a combination of (a) specially tailored auxiliary variables, (b) univariate quadrature schemes and (c) finite mixture approximations of troublesome density functions. An accuracy assessment is conducted and the new methodology is illustrated in an application. © 2011 International Society for Bayesian Analysis

Association between age at disease onset of anti-neutrophil cytoplasmic antibody-associated vasculitis and clinical presentation and short-term outcomes

Objectives: ANCA-associated vasculitis (AAV) can affect all age groups. We aimed to show that differences in disease presentation and 6 month outcome between younger- A nd older-onset patients are still incompletely understood. Methods: We included patients enrolled in the Diagnostic and Classification Criteria for Primary Systemic Vasculitis (DCVAS) study between October 2010 and January 2017 with a diagnosis of AAV. We divided the population according to age at diagnosis: <65 years or ≥65 years. We adjusted associations for the type of AAV and the type of ANCA (anti-MPO, anti-PR3 or negative). Results: A total of 1338 patients with AAV were included: 66% had disease onset at <65 years of age [female 50%; mean age 48.4 years (s.d. 12.6)] and 34% had disease onset at ≥65 years [female 54%; mean age 73.6 years (s.d. 6)]. ANCA (MPO) positivity was more frequent in the older group (48% vs 27%; P = 0.001). Younger patients had higher rates of musculoskeletal, cutaneous and ENT manifestations compared with older patients. Systemic, neurologic,cardiovascular involvement and worsening renal function were more frequent in the older-onset group. Damage accrual, measured with the Vasculitis Damage Index (VDI), was significantly higher in older patients, 12% of whom had a 6 month VDI ≥5, compared with 7% of younger patients (P = 0.01). Older age was an independent risk factor for early death within 6 months from diagnosis [hazard ratio 2.06 (95% CI 1.07, 3.97); P = 0.03]. Conclusion: Within 6 months of diagnosis of AAV, patients >65 years of age display a different pattern of organ involvement and an increased risk of significant damage and mortality compared with younger patients

Mixed model-based additive models for sample extremes

We consider additive models fitting and inference when the response variable is a sample extreme. Non-linear covariate effects are handled using the mixed model representation of penalised splines. A fitting algorithm based on likelihood approximations is derived. The efficacy of the resulting methodology is demonstrated via application to simulated and real data. © 2008 Elsevier B.V. All rights reserved