A default prior for regression coefficients

Preoperative cognitive profile predictive of cognitive decline after subthalamic deep brain stimulation in Parkinson's disease

Cognitive decline represents a severe non-motor symptom of Parkinson's disease (PD) that can significantly reduce the benefits of subthalamic deep brain stimulation (STN DBS). Here, we aimed to describe post-surgery cognitive decline and identify pre-surgery cognitive profile associated with faster decline in STN DBS-treated PD patients. A retrospective observational study of 126 PD patients treated by STN DBS combined with oral dopaminergic therapy followed for 3.54 years on average (SD = 2.32) with repeated assessments of cognition was conducted. Pre-surgery cognitive profile was obtained via a comprehensive neuropsychological examination and data analysed using exploratory factor analysis and Bayesian generalized linear mixed models. On the whole, we observed a mild annual cognitive decline of 0.90 points from a total of 144 points in the Mattis Dementia Rating Scale (95% posterior probability interval [-1.19, -0.62]) with high inter-individual variability. However, true score changes did not reach previously reported reliable change cut-offs. Executive deficit was the only pre-surgery cognitive variable to reliably predict the rate of post-surgery cognitive decline. On the other hand, exploratory analysis of electrode localization did not yield any statistically clear results. Overall, our data and models imply mild gradual average annual post-surgery cognitive decline with high inter-individual variability in STN DBS-treated PD patients. Nonetheless, patients with worse long-term cognitive prognosis can be reliably identified via pre-surgery examination of executive functions. To further increase the utility of our results, we demonstrate how our models can help with disentangling true score changes from measurement error in future studies of post-surgery cognitive changes.

Prevalence of personality disorders in adults with binge eating disorder-A systematic review and Bayesian meta-analysis

Binge eating disorder (BED) is a complex mental health problem entailing high risk for obesity, overweight, and other psychiatric disorders. However, there is still unclear evidence of the prevalence of personality disorders (PDs) in BED patients. We conducted a systematic review and a Bayesian meta-analysis for studies examining the prevalence of any PD in adult BED patients. Data sources included PubMed, Cochrane library, EBSCO, PsycINFO, and Science Direct. A Bayesian meta-analysis was conducted to estimate effect sizes for the prevalence of any PD in BED patients. Twenty eligible articles were examined with a total of 2945 BED patients. Borderline personality disorder and "Cluster C" PD, particularly obsessive-compulsive and avoidant PD, were the most frequent PD found in BED patients. BED diagnosis was associated with 28% probability of a comorbid diagnosis of any PD (0.279, 95%CrI: [0.22, 0.34]), with high levels of between-study heterogeneity (τ = 0.61, 95% CrI [0.40, 0.90]). Sensitivity analysis suggested effect sizes ranging from 0.27 to 0.28. The high comorbidity of PDs in BED patients draws attention to the potential complexity of BED clinical presentations, including those that might also be comorbid with obesity. Clinical practice should address this complexity to improve care for BED and obesity patients.

Effect of model space priors on statistical inference with model uncertainty

Bayesian model averaging (BMA) provides a coherent way to account for model uncertainty in statistical inference tasks. BMA requires specification of model space priors and parameter space priors. In this article we focus on comparing different model space priors in presence of model uncertainty. We consider eight reference model space priors used in the literature and three adaptive parameter priors recommended by Porwal and Raftery [37]. We assess the performance of these combinations of prior specifications for variable selection in linear regression models for the statistical tasks of parameter estimation, interval estimation, inference, point and interval prediction. We carry out an extensive simulation study based on 14 real datasets representing a range of situations encountered in practice. We found that beta-binomial model space priors specified in terms of the prior probability of model size performed best on average across various statistical tasks and datasets, outperforming priors that were uniform across models. Recently proposed complexity priors performed relatively poorly.

Type D Personality as a Risk Factor for Adverse Outcome in Patients With Cardiovascular Disease: An Individual Patient-Data Meta-analysis

OBJECTIVE

Type D personality, a joint tendency toward negative affectivity and social inhibition, has been linked to adverse events in patients with heart disease, although with inconsistent findings. Here, we apply an individual patient-data meta-analysis to data from 19 prospective cohort studies ( N = 11,151) to investigate the prediction of adverse outcomes by type D personality in patients with acquired cardiovascular disease.

METHOD

For each outcome (all-cause mortality, cardiac mortality, myocardial infarction, coronary artery bypass grafting, percutaneous coronary intervention, major adverse cardiac event, any adverse event), we estimated type D's prognostic influence and the moderation by age, sex, and disease type.

RESULTS

In patients with cardiovascular disease, evidence for a type D effect in terms of the Bayes factor (BF) was strong for major adverse cardiac event (BF = 42.5; odds ratio [OR] = 1.14) and any adverse event (BF = 129.4; OR = 1.15). Evidence for the null hypothesis was found for all-cause mortality (BF = 45.9; OR = 1.03), cardiac mortality (BF = 23.7; OR = 0.99), and myocardial infarction (BF = 16.9; OR = 1.12), suggesting that type D had no effect on these outcomes. This evidence was similar in the subset of patients with coronary artery disease (CAD), but inconclusive for patients with heart failure (HF). Positive effects were found for negative affectivity on cardiac and all-cause mortality, with the latter being more pronounced in male than female patients.

CONCLUSION

Across 19 prospective cohort studies, type D predicts adverse events in patients with CAD, whereas evidence in patients with HF was inconclusive. In both patients with CAD and HF, we found evidence for a null effect of type D on cardiac and all-cause mortality.

Informative g-Priors for Mixed Models

Zellner’s objective g-prior has been widely used in linear regression models due to its simple interpretation and computational tractability in evaluating marginal likelihoods. However, the g-prior further allows portioning the prior variability explained by the linear predictor versus that of pure noise. In this paper, we propose a novel yet remarkably simple g-prior specification when a subject matter expert has information on the marginal distribution of the response yi. The approach is extended for use in mixed models with some surprising but intuitive results. Simulation studies are conducted to compare the model fitting under the proposed g-prior with that under other existing priors.

Comparing methods for statistical inference with model uncertainty

Probability models are used for many statistical tasks, notably parameter estimation, interval estimation, inference about model parameters, point prediction, and interval prediction. Thus, choosing a statistical model and accounting for uncertainty about this choice are important parts of the scientific process. Here we focus on one such choice, that of variables to include in a linear regression model. Many methods have been proposed, including Bayesian and penalized likelihood methods, and it is unclear which one to use. We compared 21 of the most popular methods by carrying out an extensive set of simulation studies based closely on real datasets that span a range of situations encountered in practical data analysis. Three adaptive Bayesian model averaging (BMA) methods performed best across all statistical tasks. These used adaptive versions of Zellner’s g-prior for the parameters, where the prior variance parameter g is a function of sample size or is estimated from the data. We found that for BMA methods implemented with Markov chain Monte Carlo, 10,000 iterations were enough. Computationally, we found two of the three best methods (BMA with g=√n and empirical Bayes-local) to be competitive with the least absolute shrinkage and selection operator (LASSO), which is often preferred as a variable selection technique because of its computational efficiency. BMA performed better than Bayesian model selection (in which just one model is selected).

The Relationship Between Income Inequality and the Palliative Function of Meritocracy Belief: The Micro- and the Macro-Levels Both Count

In the current paper, we report the analysis of the relationship between meritocracy belief and subjective well-being using two large international databases, the European Social Survey Program (N = 44,387) and the European Values Study Program (N = 51,752), involving data gathered from 36 countries in total. We investigated whether low status individuals are more likely to psychologically benefit from endorsing meritocratic beliefs, and the same benefits are more pronounced in more unequal societies. Since meritocracy belief can function as a justification for income differences, we assumed that the harsher the objective reality is, the higher level of subjective well-being can be maintained by justifying this harsh reality. Therefore, we hypothesized that the palliative function of meritocracy belief is stronger for both low social status (low income) individuals, and for those living in an unequal social environment (in countries with larger income differences). Our multilevel models showed a positive relationship between meritocracy belief and subjective well-being, which relationship was moderated by both individual-level income status and country-level income differences in both studies. Based on these results, we concluded that the emotional payoff of justifying income inequalities is larger if one is more strongly affected by these inequalities.

Bayesian methods for clinicians

Background: The Bayesian methods have received more attention in medical research. It is considered as a natural paradigm for dealing with applied problems in the sciences and also an alternative to the traditional frequentist approach. However, its concept is somewhat difficult to grasp by nonexperts. This study aimed to explain the foundational ideas of the Bayesian methods through an intuitive example in medical science and to illustrate some simple examples of Bayesian data analysis and the interpretation of results delivered by Bayesian analyses. In this study, data sparsity, as a problem which could be solved by this approach, was presented through an applied example. Moreover, a common sense description of Bayesian inference was offered and some illuminating examples were provided for medical investigators and nonexperts. Methods: Data augmentation prior, MCMC, and Bayes factor were introduced. Data from the Khuzestan study, a 2-phase cohort study, were applied for illustration. Also, the effect of vitamin D intervention on pregnancy outcomes was studied. Results: Unbiased estimate was obtained by the introduced methods. Conclusion: Bayesian and data augmentation as the advanced methods provide sufficient results and deal with most data problems such as sparsity.