Mixture Model Research Articles

Gaussian mixture model and Bayesian convolutional neural network for abnormal musculoskeletal radiographs classification

Gaussian mixture model and Bayesian convolutional neural network for abnormal musculoskeletal radiographs classification

Models of Fluctuating Selection Between Generations: A Solution for the Theoretical Inconsistency.

The theory of selection fluctuation between generations has been a topic with much activities in population genetics and molecular evolution in 1970's. Most studies suggested that, as the result of fluctuating selection between generations, the frequency of an (on average) neutral mutation may fluctuate around 0.5 during the long-term evolution before it was ultimately fixed or lost. However, this pattern can only be derived from a specific type Wright-Fisher additive model, coined by the Nei-Yokoyama puzzle. In this commentary, I revisited this issue and figured out a theoretical assumption that has never been claimed explicitly, the notion of reference phenotype. Consider one locus with two-alleles: A is the wildtype allele and A' is the mutation. The fluctuating selection model actually requires a constraint that one of three genotypes (AA, AA', or A'A') must maintain a constant fitness without fluctuating between generations. It appears that the balancing selection at a frequency of 0.5 emerges only when the heterozygote (AA') is the reference genotype. Because it is difficult to determine which genotype could be the reference genotype in a real population, a desirable population genetics model should take all three possibilities into account. To this end, I propose a mixture model, where each genotype has a certain chance to be the reference genotype. My analysis showed that the emergence of balancing selection depends on the relative proportions of three different reference genotypes.

A Divide-and-Conquer Approach to Nanoparticle Global Optimisation Using Machine Learning.

Global optimization of the structure of atomic nanoparticles is often hampered by the presence of many funnels on the potential energy surface. While broad funnels are readily encountered and easily exploited by the search, narrow funnels are more difficult to locate and explore, presenting a problem if the global minimum is situated in such a funnel. Here, a divide-and-conquer approach is applied to overcome the issue posed by the multifunnel effect using a machine learning approach, without using a priori knowledge of the potential energy surface. This approach begins with a truncated exploration to gather coarse-grained knowledge of the potential energy surface. This is then used to train a machine learning Gaussian mixture model to divide up the potential energy surface into separate regions, with each region then being explored in more detail (or conquered) separately. This scheme was tested on a variety of multifunnel systems and yielded significant improvements to the times taken to locate the global minima of Lennard-Jones (LJ) nanoparticles, LJ75 and LJ104, as well as two metallic systems, Au55 and Pd88. However, difficulties were encountered for LJ98, providing insight into how the scheme could be further improved.

PICZL : Image-based photometric redshifts for AGN

Computing reliable photometric redshifts (photo-z) for active galactic nuclei (AGN) is a challenging task, primarily due to the complex interplay between the unresolved relative emissions associated with the supermassive black hole and its host galaxy. Spectral energy distribution (SED) fitting methods, while effective for galaxies and AGN in pencil-beam surveys, face limitations in wide or all-sky surveys with fewer bands available, lacking the ability to accurately capture the AGN contribution to the SED, hindering reliable redshift estimation. This limitation is affecting the many tens of millions of AGN detected in existing datasets, such as those AGN clearly singled out and identified by SRG/eROSITA. Our goal is to enhance photometric redshift performance for AGN in all-sky surveys while simultaneously simplifying the approach by avoiding the need to merge multiple data sets. Instead, we employ readily available data products from the 10th Data Release of the Imaging Legacy Survey for the Dark Energy Spectroscopic Instrument, which covers > 20,000 deg of extragalactic sky with deep imaging and catalog-based photometry in the grizW1-W4 bands. We fully utilize the spatial flux distribution in the vicinity of each source to produce reliable photo-z. We introduce PICZL a machine-learning algorithm leveraging an ensemble of convolutional neural networks. Utilizing a cross-channel approach, the algorithm integrates distinct SED features from images with those obtained from catalog-level data. Full probability distributions are achieved via the integration of Gaussian mixture models. On a validation sample of 8098 AGN PICZL achieves an accuracy $ NMAD $ of 4.5<!PCT!> with an outlier fraction eta of 5.6<!PCT!>. These results significantly outperform previous attempts to compute accurate photo-z for AGN using machine learning. We highlight that the model's performance depends on many variables, predominantly the depth of the data and associated photometric error. A thorough evaluation of these dependencies is presented in the paper. Our streamlined methodology maintains consistent performance across the entire survey area, when accounting for differing data quality. The same approach can be adopted for future deep photometric surveys such as LSST and Euclid, showcasing its potential for wide-scale realization. With this paper, we release updated photo-z (including errors) for the XMM-SERVS W-CDF-S, ELAIS-S1 and LSS fields.

Understanding the transdiagnostic mechanisms underlying emerging psychopathology in adolescence: study protocol of a 1-year prospective epidemiological (EMERGE) study

IntroductionAdolescent mental health is a global public health challenge as most cases remain undetected and untreated, and consequently, have a high likelihood of persistence or recurrence. It is critical to...

Preconception exposure to bisphenol A and its alternatives: Effects on female fecundity mediated by oxidative stress and ovarian reserve.

Various 'Bisphenol A (BPA)-free' alternatives have emerged in numerous personal products in recent years. However, it remains unclear whether BPA analogs affect female fecundity and possible biological mechanisms. We aimed to evaluate the relationships of bisphenol analogs with female fecundability and infertility and whether oxidative stress, inflammation, and ovarian reserve may play a mediation role in such associations. This prospective preconception cohort study included 957 couples who attempted pregnancy. BPA and six alternatives were measured in women's urine samples. Bisphenol analogs-outcome associations were estimated using discrete-time Cox hazards and logistic regression models. A quantile g-computation (QGC) methodology was further applied to assess the joint effects of co-exposure to bisphenol analogs on fecundity. We also quantified three biomarkers, including malondialdehyde (MDA), C-reactive protein and Anti-Müllerian hormone (AMH), to explore possible biological pathways. Using an integrated analytical approach consisting of both single-pollutant and mixture models, we found that BPA and bisphenol AP (BPAP) were significantly associated with decreased fecundability (adjusted fecundability ratio (aFR) = 0.87, 95%CI:0.81, 0.94 for BPA; aFR = 0.64, 95%CI: 0.48, 0.84 for BPAP) and increased risk of infertility (adjusted odd ratio (aOR) = 1.23, 95%CI:1.06, 1.44 for BPA; aOR = 2.27, 95%CI:1.29, 3.99 for BPAP) after controlling for other bisphenol analogs. The link between BPA and prolonged time to pregnancy was more prominent in overweight or obese women and those who had regular menstrual cycles. Bisphenol AF was associated with impaired fecundity in women aged 35 years or older. The mixed effects of bisphenol analogs on fecundity were statistically non-significant. Mediation analysis revealed a significant indirect effect of urinary MDA and serum AMH in bisphenol analogs-induced impaired fecundity, with all average causal mediation effects (ACME) showing statistical significance (PACME < 0.05). Our prospective preconception cohort study suggests that BPA and BPAP may be associated with impaired female fecundity. Increased oxidative stress and decreased ovarian reserve may be the underlying pathways.

Process–Material–Performance Trade-off Exploration of Materials Sintering with Machine Learning Models

AbstractProcess-induced porosity, defects, and residual stresses lead to mechanical performance degradation in fiber-reinforced composite and other heterogeneous structures. Physical and chemical processes create complex process–material–performance relationships. Predicting porosity and residual stresses in this context requires computationally burdensome forward simulations and obtaining optimal process settings and calibrating properties of new materials requires solving inverse problems with predictions from the forward simulations. In this paper, we parameterized the process–material–performance space and created a dataset based on physics models that are valid for sintering ceramic powders. The dataset was used to train several machine learning models that captured the process–material–performance relationships. The trained ML models were applied in process optimization, calibration of properties for new material systems, and estimating performance for a given process and material. Support vector regression (SVR), convolutional neural networks (CNNs), and a Gaussian mixture model (GMM) called REPAIRS were selected, and their prediction accuracy was determined. While the SVR and CNN models require training several models, we show that the GMM model captures the process–material–performance relationships with a single machine-learned model and partial system completion methods. The paper describes root-mean-square error and mean absolute percentage errors of the inferences from the models on a validation dataset.

Abstract 4121812: Longitudinal Trajectory-Based Classification of Heart Failure with preserved Ejection Fraction: A Machine Learning Approach

Background: Heart failure (HF) with preserved ejection fraction (HFpEF) is a complex syndrome characterized by heterogeneous pathophysiology and dynamic changes in cardiac structure and function. Current research predominantly focuses on left ventricular ejection fraction (LVEF) or left ventricular structures with predefined categories. This study hypothesized that applying unsupervised methodologies to longitudinal echocardiography will reveal distinct trajectory patterns in cardiac structure and function related to clinical outcomes in HFpEF patients. Methods: This retrospective cohort study, conducted at UC Davis Medical Center (2014 to 2022), consisted of adult patients with HFpEF. The inclusion criteria included ICD HF codes, a left ventricular ejection fraction (LVEF) ≥50%, and a Brain natriuretic peptide (BNP) ≥100 pg/ml or N-terminal-pro BNP (NT-proBNP) ≥225 pg/ml. Longitudinal data were analyzed using unsupervised machine learning, including UMAP for dimensionality reduction and Gaussian Mixture Models for clustering. Primary and secondary outcomes included all-cause mortality and changes in BNP levels, respectively. Results: The study included 1,626 patients. The cohort had a median age of 69 years, was 57.5% female, and 51.8% white. Three distinct echocardiographic trajectory patterns emerged (p&lt;.05) among the HFpEF cohort. Trajectory #1 (n=568) exhibited a high-stable pattern with the highest mortality rates, Trajectory #2 (n=512) showed a high-decreasing pattern with high mortality rates, and Trajectory #3 (n=546) had a low-increasing pattern with the lowest mortality rates. Trajectories varied significantly in baseline characteristics and longitudinal echocardiographic changes, with Trajectory #3 having a lower baseline left ventricular mass index (p&lt;.001) and a higher mean arterial pressure ( p =.001) compared to the other trajectories. Kaplan-Meier survival analysis indicated significant differences in survival among the trajectories ( p =.004). Conclusion: The study utilized unsupervised analysis of longitudinal echocardiographic data to identify three distinct HFpEF trajectories, each associated with unique clinical features and outcomes. These findings underscore the heterogeneity of HFpEF and highlight the potential trajectory-based patient stratification to improve targeted intervention strategies. Future validation in larger, multicenter cohorts is warranted to enhance HFpEF management and patient prognosis.

Abstract 4121890: Resting Heart Rate Trajectories over 25 Years: Patterns, Predictors, and Prognostic Impact in the Atherosclerosis Risk in Communities (ARIC) Study

Background: Abnormal resting heart rate (RHR) is associated with cardiovascular events and mortality. Longitudinal RHR trajectories may offer unique prognostic, but research exploring these trajectories over extended periods and their prognostic implications is limited. Methods: Using data from 5,794 participants in the Atherosclerosis Risk in Communities (ARIC) study, we first characterized RHR trajectories over 25 years (from visit 1 [1987-89] to visit 5 [2011-13]) with latent class growth mixture models. Then, we determined the predictors of those trajectories using multinomial logistic regression (n=5,432 with data on predictors of interest). We ran Cox models to quantify the associations between RHR trajectories with cardiovascular outcomes (coronary heart disease, heart failure, stroke) and all-cause mortality (n=4,329 free of cardiovascular disease at baseline). Results: We identified one typical pattern (stable/slight decline, 88.4%) and three atypical patterns (stable-slight increase, 9.2%; increase-decrease, 2.0%; stable-sharp increase, 0.4%) (Figure-Left panel). Obesity, ever smoking, a history of heart failure, and lower education levels predicted the atypical patterns. The stable-increase (combined for slight and sharp) trajectory was significantly and robustly associated with heart failure and all-cause mortality (Figure-Right panel). The increase-decrease trajectory showed a hazard ratio of ~2 for coronary heart disease, although statistical significance was restricted in the demographically adjusted model. Conclusions: We identified one typical (stable/slight decline) and three atypical (increase-decrease, stable-slight increase, and stable-sharp increase) RHR trajectories over 25 years. The atypical trajectories, particularly the stable-increase pattern, were associated with poorer prognosis. These findings highlight the value of monitoring long-term RHR trajectories for cardiovascular risk assessment.

Abstract 4127413: High-normal Blood Pressure (130-139/85-89mmHg) is Associated with an Increased Risk of Mortality

Background: The relationship between high-normal blood pressure (BP) and mortality lacks high-quality evidence based on large population cohort. The aim of this study was to comprehensively investigate the association of high-normal BP and its trajectory with all-cause and cause-specific mortality. Methods: In a community-based population cohort from the China Health Evaluation And risk Reduction through nationwide Teamwork (ChinaHEART) project, 3,598,940 participants aged 35-75 years with baseline BP were included. High-normal BP was defined as a systolic blood pressure (SBP) of 130-139 mmHg and/or a diastolic blood pressure (DBP) of 85-89 mmHg at baseline. Four trajectories of BP change were identified in 105,894 participants included in the study, who had more than 2 follow-up BP measurements, using latent mixture modeling. Among them, high-normal-increasing was defined as an increase in SBP from 130-139 at baseline to over 140 at the last follow-up. Findings: Compared with the optimal BP group (SBP &lt; 120 mmHg and DBP &lt; 80 mmHg, [18.1%]), participants with high-normal BP (18.7%) had a 4% increase in all-cause mortality risk (hazard ratio [HR] 1.04, 95% confidence interval [CI]: 1.01-1.07) and a 28% increase in CVD mortality risk (HR 1.28, 95% CI: 1.21-1.34), with the greatest increase in mortality risk observed from hemorrhagic stroke (HR 1.75, 95% CI: 1.55-1.98). Among BP trajectories, compared with participants with optimal-stable BP (25.3%), those with high-normal-increasing BP (3.5%) had a 25% increase in all-cause mortality risk (HR 1.25, 95% CI: 1.00-1.54) and a 67% increase in CVD mortality risk (HR 1.66, 95% CI: 1.21-2.30), with the greatest increase in mortality risk also observed from hemorrhagic stroke (HR 3.15, 95% CI: 1.38-7.20). In our study cohort, approximately 0.7% and 1.3% of all-cause mortality was attributable to the high-normal BP at baseline and high-normal-increasing BP trajectory, respectively. Interpretation: Individuals presenting high-normal BP at baseline or high-normal-increasing BP trajectory afterward exhibited a significantly elevated mortality risk, which is most pronounced for hemorrhagic stroke. Early management of BP in patients with high-normal BP is crucial for the prevention and treatment of hypertension.

Latent characterisation of the complete BATSE gamma ray bursts catalogue using Gaussian mixture of factor analysers and model-estimated overlap-based syncytial clustering

Abstract Characterising and distinguishing gamma-ray bursts (GRBs) has interested astronomers for many decades. While some authors have found two or three groups of GRBs by analyzing only a few parameters, recent work identified five ellipsoidally-shaped groups upon considering nine parameters T50, T90, F1, F2, F3, F4, P64, P256, P1024. Yet others suggest sub-classes within the two or three groups found earlier. Using a mixture model of Gaussian factor analysers, we analysed 1150 GRBs, that had nine parameters observed, from the current Burst and Transient Source Experiment (BATSE) catalogue, and again established five ellipsoidal-shaped groups to describe the GRBs. These five groups are characterised in terms of their average duration, fluence and spectrum as shorter-faint-hard, long-intermediate-soft, long-intermediate-intermediate, long-bright-intermediate and short-faint-hard. The use of factor analysers in describing individual group densities allows for a more thorough group-wise characterisation of the parameters in terms of a few latent features. However, given the discrepancy with many other existing studies that advocated for two or three groups, we also performed model-estimated overlap-based syncytial clustering (MOBSynC) that successively merges poorer-separated groups. The five ellipsoidal groups merge into three and then into two groups, one with GRBs of low durations and the other having longer duration GRBs. These groups are also characterised in terms of a few latent factors made up of the nine parameters. Our analysis provides context for all three sets of results, and in doing so, details a multi-layered characterisation of the BATSE GRBs, while also explaining the structure in their variability.

Gaussian Mixture Model Based Voronoi Partitioning Scheme in Multi-Beam Satellites

With advances in technology and growing user needs, satellite communication is changing over time. Efficiently managing resources across diverse satellite coverage areas can be significantly enhanced through the application of Artificial Intelligence (AI) and Machine Learning (ML). The intended project seeks to employ fundamental machine learning algorithms, including Weighted k-means and Gaussian Mixture Model (GMM), to cluster user demands within a designated geographical region. This approach aims to optimize the utilization of satellite bandwidth in a multi-beam satellite system. A comparison of the results obtained using two techniques indicates improved performance of the GMM in terms of allocating the user demands. To ensure effective coverage, the clusters are transformed into shapes that match the coverage areas of the satellite. A technique called Voronoi Tessellation is used to create irregular polygons, and then these polygons are approximated as ellipses to cover the clusters more effectively.

Excess Mortality and its Determinants During the COVID-19 Pandemic in 21 Countries: An Ecological Study from the C-MOR Project, 2020 and 2021.

The COVID-19 pandemic overwhelmed health systems, resulting in a surge in excess deaths. This study clustered countries based on excess mortality to understand their response to the pandemic and the influence of various factors on excess mortality within each cluster. This ecological study is part of the COVID-19 MORtality (C-MOR) Consortium. Mortality data were gathered from 21 countries and were previously used to calculate weekly all-cause excess mortality. Thirty exposure variables were considered in five categories as factors potentially associated with excess mortality: population factors, health care resources, socioeconomic factors, air pollution, and COVID-19 policy. Estimation of Latent Class Linear Mixed Model (LCMM) was used to cluster countries based on response trajectory and Generalized Linear Mixture Model (GLMM) for each cluster was run separately. Using LCMM, two clusters were reached. Among 21 countries, Brazil, the USA, Georgia, and Poland were assigned to a separate cluster, with the mean of excess mortality z-score in 2020 and 2021 around 4.4, compared to 1.5 for all other countries assigned to the second cluster. In both clusters the population incidence of COVID-19 had the greatest positive relationship with excess mortality while interactions between the incidence of COVID-19, fully vaccinated people, and stringency index were negatively associated with excess mortality. Moreover, governmental variables (government revenue and government effectiveness) were the most protective against excess mortality. This study highlighted that clustering countries based on excess mortality can provide insights to gain a broader understanding of countries' responses to the pandemic and their effectiveness.

Association between body mass index trajectories and type 2 diabetes incidence over an 18-year follow-up in the Tehran Lipid and Glucose Study.

Body mass index (BMI) is a well-known risk factor for type 2 diabetes mellitus (T2DM). We aimed to identify BMI trajectory patterns and evaluate their association with T2DM during 18 years of follow-up. We included 6026 participants aged 20 to 65 from the prospective population-based Tehran Lipid and Glucose Study (TLGS). The BMI trajectory patterns were identified using latent growth mixture modeling (LGMM) during the measurement period. The association between the BMI trajectory patterns and future T2DM was evaluated using the Cox proportional hazard regression models. Three BMI trajectory patterns of low-increasing (38.6%), medium-increasing (47.1%), and high-increasing (14.3%) were detected. The participants in the medium-increasing and high-increasing BMI trajectory groups had HRs of 1.87 (95% CI 1.53-2.28) and 3.41(95% CI 2.71-4.29) for T2DM incidence, respectively. Within the normoglycemic subpopulation, the high-increasing BMI group had an HR of 3.82 (95% CI 2.79-5.24) compared to the low-increasing BMI group, while in the prediabetic subpopulation, the high-increasing BMI group had an HR of 2.93 (95% CI 2.04-4.19) compared to the low-increasing BMI group. Body weight varies in a relatively stable pattern in adulthood over the long-term period. Medium and high-increasing BMI trajectory patterns have a significantly increased risk for future T2DM in both normoglycemic and prediabetic individuals. Identifying BMI trajectory patterns can help healthcare providers in early prediction, risk assessment, and monitoring strategies development for the prevention of T2DM.

BIOM-48. UTILITY OF CIRCULATING TUMOR DNA (CTDNA) FROM CEREBROSPINAL FLUID (CSF) FOR PROGNOSIS OF PATIENTS WITH RECURRENT HIGH-GRADE GLIOMA

Abstract High-grade gliomas (HGGs) are the most aggressive primary brain tumors, and molecular characterization is vital for their diagnosis and treatment. Due to their location, tumor sampling is often challenging. Therefore, developing minimally invasive diagnostic methods is urgently needed. Here we report that circulating tumor DNA (ctDNA) from cerebrospinal fluid (CSF) can identify key genomic alterations and track clonal evolution in HGGs. Detection of CSF ctDNA correlates with leptomeningeal disease and overall survival, indicating its potential for integration into clinical decision-making. Our study includes 313 samples from 253 patients with recurrent glioma treated at MSKCC who underwent CSF collection using the MSK-IMPACT targeted sequencing assay. 37% of genomic alterations were detected using our less stringent variant calling criteria and Gaussian Mixture Model to call copy number events. CSF ctDNA positivity was determined by the presence of at least one oncogenic disease-defining alteration or any shared alteration with the tumor. We found 212 CSF ctDNA positive (68%) and 101 CSF ctDNA negative (32%) samples. CSF ctDNA positivity was the highest amongst histone mutant tumors (96%). We noticed 44% of alterations shared between the tumor and the CSF, additionally, we noted considerable tumor evolution particularly within the growth signaling pathways (e.g. PDGFRA). Our cohort demonstrated that patients with positive CSF ctDNA had a significantly shorter overall survival compared to those who were CSF ctDNA negative (4.83 months vs 14.14 months, HR 2.4, p &amp;lt; 0.001). Radiographic findings such as enhancing disease and contact of the tumor with the ventricular space were positively associated with CSF ctDNA positivity. Additionally, CSF ctDNA was associated with positive cytology in 12/12 cases (100%). With our improved pipeline, we hypothesize CSF ctDNA may be used as a prognostic biomarker for survival, but confirmation requires further validation in a prospective study.

Model-Based Clustering of Categorical Data Based on the Hamming Distance

A model-based approach is developed for clustering categorical data with no natural ordering. The proposed method exploits the Hamming distance to define a family of probability mass functions to model the data. The elements of this family are then considered as kernels of a finite mixture model with an unknown number of components. Conjugate Bayesian inference has been derived for the parameters of the Hamming distribution model. The mixture is framed in a Bayesian nonparametric setting, and a transdimensional blocked Gibbs sampler is developed to provide full Bayesian inference on the number of clusters, their structure, and the group-specific parameters, facilitating the computation with respect to customary reversible jump algorithms. The proposed model encompasses a parsimonious latent class model as a special case when the number of components is fixed. Model performances are assessed via a simulation study and reference datasets, showing improvements in clustering recovery over existing approaches. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

A Data-Driven Model for Classification of Traditional Chinese Medicine Materials

This paper proposes a data-driven classification model for traditional Chinese medicinal herbs based on mid-infrared spectral data. Addressing the limitations of traditional identification methods when the herbs’ appearance is damaged or incomplete, this study employs machine learning techniques to achieve accurate classification of medicinal herb types through spectral data preprocessing and feature extraction. Firstly, the Savitzky-Golay convolution smoothing method and Standard Normal Variate (SNV) transformation were used for denoising the spectral data. Then, Principal Component Analysis (PCA) was employed to reduce the dimensionality of the high-dimensional spectral data and extract the key features. Finally, the Gaussian Mixture Model (GMM) was applied to cluster the reduced data, categorizing the medicinal herbs into six classes. The results show that this method produces the accurate and stable classification. The constructed model is not only applicable to the classification and origin identification of medicinal herbs but also provides an important reference value for the classification and origin identification of other plant species.

Examining what works for whom and how in mindfulness-based cognitive therapy (MBCT) for recurrent depression: moderated-mediation analysis in the PREVENT trial.

Personalised management of recurrent depression, considering individual patient characteristics, is crucial. This study evaluates the potentially different mediating role of mindfulness skills in managing recurrent depression using mindfulness-based cognitive therapy (MBCT) among people with varying depression severity. Data from the Prevention of Depressive Relapse or Recurrence (PREVENT) trial, comparing MBCT (with antidepressant medication (ADM) tapering support, MBCT-tapering support) versus maintenance-ADM, were used. The study included pre, post, 9-, 12-, 18- and 24-month follow-ups. Adults with ≥3 previous major depressive episodes, in full/partial remission (below threshold for a current episode), on ADM, were assessed for eligibility in primary care practices in the UK. People were randomised (1:1) to MBCT-tapering support or maintenance-ADM. We used the Beck Depression Inventory-II to evaluate depressive symptom changes over the six time points. Pre-post treatment, we employed the Five Facets of Mindfulness Questionnaire to gauge mindfulness skills. Baseline symptom and history variables were used to identify individuals with varying severity profiles. We conducted Latent Profile Moderated-Mediation Growth Mixture Models. A total of 424 people (mean (s.d.) age = 49.44 (12.31) years; with 325 (76.7%) self-identified as female) were included. A mediating effect of mindfulness skills, between trial arm allocation and the linear rate of depressive symptoms change over 24 months, moderated by depression severity, was observed (moderated-mediation index = -0.27, 95% CI = -0.66, -0.03). Conditional indirect effects were -0.42 (95% CI = -0.78, -0.18) for higher severity (expected mean BDI-II reduction = 10 points), and -0.15 (95% CI = -0.35, -0.02) for lower severity (expected mean BDI-II reduction = 3.5 points). Mindfulness skills constitute a unique mechanism driving change in MBCT (versus maintenance-ADM). Individuals with higher depression severity may benefit most from MBCT-tapering support for residual symptoms. It is unclear if these effects apply to those with a current depressive episode. Future research should investigate individuals who are not on medication. This study provides preliminary evidence for personalised management of recurrent depression. ISRCTN26666654.

Stochastic Comparisons for Finite Mixtures from Location-scale Family of Distributions

In this study, we consider two finite mixture models (FMMs) with location-scale family distributed components, in which ordering results are established in various stochastic senses. For heterogeneity in one parameter, the comparisons are obtained with respect to usual stochastic order, hazard rate order, reversed hazard rate order and likelihood ratio order. Further, for heterogeneity in two parameters, we derive sufficient conditions for the stochastic comparison of FMMs with respect to usual stochastic order and hazard rate order. Various examples and counterexamples are presented to illustrate the proposed results.

Symptom Shifting From Nonsuicidal Self-Injury to Substance Use and Borderline Personality Pathology

A decline in nonsuicidal self-injury (NSSI) behavior is often viewed as an indication of mental health improvement when treating adolescents and young adults with borderline personality pathology. However, evidence shows that an initial decrease in NSSI behavior does not always signal recovery, and potential symptom shifting needs to be considered. To examine the codevelopment of NSSI and substance use in adolescents and young adults receiving treatment for NSSI behavior and to explore whether shifting from NSSI behavior to substance use is associated with emerging or persistent borderline personality pathology. This cohort study used data from the AtR!Sk study. The study included a consecutive sample of adolescents and young adults with NSSI behavior who presented to a specialized outpatient clinic for early intervention of borderline personality pathology. A baseline assessment (between May 3, 2016, and December 19, 2019) and 2 annual follow-up assessments were conducted. Data were analyzed from April 15, 2023, to September 5, 2024. The frequencies of NSSI behavior and substance use were self-reported. Diagnostic interviews were carried out to assess borderline personality pathology. Growth mixture models were specified to identify latent classes with different joint trajectories of NSSI behavior and substance use, and the classes were compared for the number of fulfilled borderline personality disorder (BPD) diagnostic criteria. Overall, 277 adolescents and young adults (249 [89.9%] female; mean [SD] age at baseline, 14.9 [1.5] years) were included in the study (number at first follow-up, 135; number at second follow-up, 82). Three latent classes were extracted from the data. A decline in NSSI behavior following treatment was common. Class 1 (estimated class count: 32.5; 11.7% of participants) was further characterized by a decline in substance use; class 2 (210.1; 75.9% of participants), by a moderate increase in substance use; and class 3 (34.4; 12.4% of participants), by a strong increase in substance use. The number of fulfilled BPD diagnostic criteria in class 1 (mean [SE], 4.64 [0.40]; comparison: χ2, 11.64; P < .001) and class 3 (mean [SE], 4.29 [0.41]; comparison: χ2, 5.98; P = .01) was greater than that in class 2 (mean [SE], 3.18 [0.15]) at baseline. The number of fulfilled BPD criteria remained high at the second follow-up assessment in class 3 (mean [SE], 5.15 [0.84]) but not in class 1 (mean [SE], 2.05 [0.54]). In this cohort study of adolescent patients with NSSI behavior, a decline in this behavior was commonly paired with an increase in substance use. This finding suggests that a decrease in NSSI behavior alone may be insufficient to indicate treatment success. Monitoring the joint trajectories of NSSI behavior and substance use may be a promising avenue toward early detection and targeted treatment of adolescent borderline personality pathology.