Noninformative priors for linear combinations of normal means with unequal variances

For normal populations with unequal variances, we develop matching priors and reference priors for a linear combination of the means. Here, we find three second-order matching priors: a highest posterior density (HPD) matching prior, a cumulative distribution function (CDF) matching prior, and a likelihood ratio (LR) matching prior. Furthermore, we show that the reference priors are all first-order matching priors, but that they do not satisfy the second-order matching criterion that establishes the symmetry and the unimodality of the posterior under the developed priors. The results of a simulation indicate that the second-order matching prior outperforms the reference priors in terms of matching the target coverage probabilities, in a frequentist sense. Finally, we compare the Bayesian credible intervals based on the developed priors with the confidence intervals derived from real data.     

Development of predictive signatures for treatment selection in precision medicine with survival outcomes

For survival endpoints in subgroup selection, a score conversion model is often used to convert the set of biomarkers for each patient into a univariate score and using the median of the univariate scores to divide the patients into biomarker‐positive and biomarker‐negative subgroups. However, this may lead to bias in patient subgroup identification regarding the 2 issues: (1) treatment is equally effective for all patients and/or there is no subgroup difference; (2) the median value of the univariate scores as a cutoff may be inappropriate if the sizes of the 2 subgroups are differ substantially. We utilize a univariate composite score method to convert the set of patient's candidate biomarkers to a univariate response score. We propose applying the likelihood ratio test (LRT) to assess homogeneity of the sampled patients to address the first issue. In the context of identification of the subgroup of responders in adaptive design to demonstrate improvement of treatment efficacy (adaptive power), we suggest that subgroup selection is carried out if the LRT is significant. For the second issue, we utilize a likelihood‐based change‐point algorithm to find an optimal cutoff. Our simulation study shows that type I error generally is controlled, while the overall adaptive power to detect treatment effects sacrifices approximately 4.5% for the simulation designs considered by performing the LRT; furthermore, the change‐point algorithm outperforms the median cutoff considerably when the subgroup sizes differ substantially.     

Ethical Numbers: Ethics Training in U.S. Graduate Statistics Programs, 2013–2014

As important members of research teams, statisticians bear an ethical responsibility to analyze, interpret, and report data honestly and objectively. One way of reinforcing ethical responsibilities is through required courses covering a variety of ethics-related topics at the graduate level. We assessed ethics requirements for graduate-level statistics training programs in the United States for the 2013–2014 academic year using the websites of 88 universities, examining 103 biostatistics programs, and 136 statistics degree programs. We categorized programs’ ethics training requirements as required or not required. Thirty-one (35.1%) universities required an ethics course for at least some degree students. Sixty-two (25.5%) degree programs required an ethics course for at least some students. The majority (77.4%) of required courses were worth 0 or 1 credit. Of the 177 programs without an ethics requirement, 19 (10.7%) listed an ethics elective. Although a single ethics course is insufficient for instilling an ethical approach to science, degree programs that model expectations through coursework point to the value of ethics in science. More training programs should prepare statisticians to consider the ethical dimensions of their work through required coursework. Supplementary materials for this article are available online.     

A biclustering algorithm for binary matrices based on penalized Bernoulli likelihood

We propose a new biclustering method for binary data matrices using the maximum penalized Bernoulli likelihood estimation. Our method applies a multi-layer model defined on the logits of the success probabilities, where each layer represents a simple bicluster structure and the combination of multiple layers is able to reveal complicated, multiple biclusters. The method allows for non-pure biclusters, and can simultaneously identify the 1-prevalent blocks and 0-prevalent blocks. A computationally efficient algorithm is developed and guidelines are provided for specifying the tuning parameters, including initial values of model parameters, the number of layers, and the penalty parameters. Missing-data imputation can be handled in the EM framework. The method is tested using synthetic and real datasets and shows good performance.     

Influence Diagnostics for Simultaneous Equations Models

This paper presents influence diagnostics for simultaneous equations models. It proposes residuals, leverage and other influence measures. A missing data method is adopted to minimize the masking effect due to case deletions. The assessment of local influence is also considered. The paper shows how to evaluate the effects that perturbations to the endogenous variables, predetermined variables and case weights may have on the parameter estimates. The diagnostics are illustrated with two examples.     

Social Contagion and General Diffusion Models of Adolescent Religious Transitions: A Tutorial,and EMOSA Applications

Epidemic Models of the Onset of Social Activities (EMOSA) describe behaviors that spread through social networks. Two social influence methods are represented, social contagion (one-to-one spread) and general diffusion (spread through cultural channels). Past models explain problem behaviors—smoking, drinking, sexuality, and delinquency. We provide review, and a tutorial (including examples). Following, we present new EMOSA models explaining changes in adolescent and young adult religious participation. We fit the model to 10 years of data from the 1997 U.S. National Longitudinal Survey of Youth. Innovations include a three-stage bi-directional model, Bayesian Markov Chain Monte Carlo (MCMC) estimation, graphical innovations, and empirical validation. General diffusion dominated rapid reduction in church attendance during adolescence; both diffusion and social contagion explained church attendance stability in early adulthood.     

Posterior consistency for the spectral density of non-Gaussian stationary time series

Various nonparametric approaches for Bayesian spectral density estimation of stationary time series have been suggested in the literature, mostly based on the Whittle likelihood approximation. A generalization of this approximation involving a nonparametric correction of a parametric likelihood has been proposed in the literature with a proof of posterior consistency for spectral density estimation in combination with the Bernstein–Dirichlet process prior for Gaussian time series. In this article, we will extend the posterior consistency result to non-Gaussian time series by employing a general consistency theorem for dependent data and misspecified models. As a special case, posterior consistency for the spectral density under the Whittle likelihood is also extended to non-Gaussian time series. Small sample properties of this approach are illustrated with several examples of non-Gaussian time series.     

Conventional and expanded adverse childhood experiences (ACEs) and maternal functioning among low-income Black mothers

A paucity of research has examined the individual and cumulative effects of conventional and expanded adverse childhood experiences (ACEs) on maternal functioning, especially among low-income Black mothers. Using self-report data from a subsample of Black mothers (N = 157) who participated in a larger study to evaluate the effectiveness of an urban public prekindergarten program in the mid-Atlantic region of the United States, we examined the prevalence of ACEs and the individual and cumulative effects of conventional (i.e., family trauma and dysfunction) and expanded (i.e., community stressors) ACEs on depression and health among low-income Black mothers. Findings indicated that Black mothers had more exposure to expanded than conventional ACEs. Hierarchical regression analyses revealed that experience of physical neglect was significantly associated with depression and physical abuse with compromised health, and perceived experience of racism was a predictor of depression and compromised health. More conventional and expanded ACEs were associated with clinical levels of depression and compromised health. Findings highlight the need for more research related to the impact of ACEs, especially expanded ACEs, on mental and behavioural health outcomes. Additionally, our findings indicate the need for more trauma-informed care to reduce and address the impact of individual and community-level adversities on low-income Black mothers.     

Generating inclusive services for children,youth and families: A shift to using complex systems theory

Service systems for children and families have been shaped by standard approaches to knowledge-building, which reflect a reductionist approach and assume linearity and/or that individuals and experiences are normally distributed. Yet, these approaches may be inadequate for clients most at-risk, especially those who would be analytic ‘outliers’. A complexity lens focuses on the whole system and seeks to identify patterns, including the dynamic interactions between components of the system. Social work scholars have begun to apply complexity theory to social work research efforts, demonstrating the conceptual potential of incorporating this theoretical approach into social work theories and models such as the person-in-environment framework and the ecosystems perspective. Yet, frameworks informed by complexity theory may require ontological and epistemological shifts in thinking and new methodological approaches in order to fully embody a complexity approach. Complexity theory offers the opportunity to consider social work clients who are most at-risk, as it is better suited for power law distributions. We can, therefore, reconceptualize the most ‘at-risk’ clients as being in a state of transition, which is also the space of most creativity and possibility.