Multilevel superposition for deciphering the conformational variability of protein ensembles.

The dynamics and variability of protein conformations are directly linked to their functions. Many comparative studies of X-ray protein structures have been conducted to elucidate the relevant conformational changes, dynamics and heterogeneity. The rapid increase in the number of experimentally determined structures has made comparison an effective tool for investigating protein structures. For example, it is now possible to compare structural ensembles formed by enzyme species, variants or the type of ligands bound to them. In this study, the author developed a multilevel model for estimating two covariance matrices that represent inter- and intra-ensemble variability in the Cartesian coordinate space. Principal component analysis using the two estimated covariance matrices identified the inter-/intra-enzyme variabilities, which seemed to be important for the enzyme functions, with the illustrative examples of cytochrome P450 family 2 enzymes and class A $\beta$-lactamases. In P450, in which each enzyme has its own active site of a distinct size, an active-site motion shared universally between the enzymes was captured as the first principal mode of the intra-enzyme covariance matrix. In this case, the method was useful for understanding the conformational variability after adjusting for the differences between enzyme sizes. The developed method is advantageous in small ensemble-size problems and hence promising for use in comparative studies on experimentally determined structures where ensemble sizes are smaller than those generated, for example, by molecular dynamics simulations.

A joint normal-ordinal (probit) model for ordinal and continuous longitudinal data.

In biomedical studies, continuous and ordinal longitudinal variables are frequently encountered. In many of these studies it is of interest to estimate the effect of one of these longitudinal variables on the other. Time-dependent covariates have, however, several limitations; they can, for example, not be included when the data is not collected at fixed intervals. The issues can be circumvented by implementing joint models, where two or more longitudinal variables are treated as a response and modeled with a correlated random effect. Next, by conditioning on these response(s), we can study the effect of one or more longitudinal variables on another. We propose a normal-ordinal(probit) joint model. First, we derive closed-form formulas to estimate the model-based correlations between the responses on their original scale. In addition, we derive the marginal model, where the interpretation is no longer conditional on the random effects. As a consequence, we can make predictions for a subvector of one response conditional on the other response and potentially a subvector of the history of the response. Next, we extend the approach to a high-dimensional case with more than two ordinal and/or continuous longitudinal variables. The methodology is applied to a case study where, among others, a longitudinal ordinal response is predicted with a longitudinal continuous variable.

Multi-trait analysis of gene-by-environment interactions in large-scale genetic studies.

Identifying genotype-by-environment interaction (GEI) is challenging because the GEI analysis generally has low power. Large-scale consortium-based studies are ultimately needed to achieve adequate power for identifying GEI. We introduce Multi-Trait Analysis of Gene-Environment Interactions (MTAGEI), a powerful, robust, and computationally efficient framework to test gene-environment interactions on multiple traits in large data sets, such as the UK Biobank (UKB). To facilitate the meta-analysis of GEI studies in a consortium, MTAGEI efficiently generates summary statistics of genetic associations for multiple traits under different environmental conditions and integrates the summary statistics for GEI analysis. MTAGEI enhances the power of GEI analysis by aggregating GEI signals across multiple traits and variants that would otherwise be difficult to detect individually. MTAGEI achieves robustness by combining complementary tests under a wide spectrum of genetic architectures. We demonstrate the advantages of MTAGEI over existing single-trait-based GEI tests through extensive simulation studies and the analysis of the whole exome sequencing data from the UKB.

Flagging unusual clusters based on linear mixed models using weighted and self-calibrated predictors.

Statistical models incorporating cluster-specific intercepts are commonly used in hierarchical settings, for example, observations clustered within patients or patients clustered within hospitals. Predicted values of these intercepts are often used to identify or "flag" extreme or outlying clusters, such as poorly performing hospitals or patients with rapid declines in their health. We consider a variety of flagging rules, assessing different predictors, and using different accuracy measures. Using theoretical calculations and comprehensive numerical evaluation, we show that previously proposed rules based on the 2 most commonly used predictors, the usual best linear unbiased predictor and fixed effects predictor, perform extremely poorly: the incorrect flagging rates are either unacceptably high (approaching 0.5 in the limit) or overly conservative (eg, much <0.05 for reasonable parameter values, leading to very low correct flagging rates). We develop novel methods for flagging extreme clusters that can control the incorrect flagging rates, including very simple-to-use versions that we call "self-calibrated." The new methods have substantially higher correct flagging rates than previously proposed methods for flagging extreme values, while controlling the incorrect flagging rates. We illustrate their application using data on length of stay in pediatric hospitals for children admitted for asthma diagnoses.

Random effects models of tumour growth for investigating interval breast cancer.

In Nordic countries and across Europe, breast cancer screening participation is high. However, a significant number of breast cancer cases are still diagnosed due to symptoms between screening rounds, termed "interval cancers". Radiologists use the interval cancer proportion as a proxy for the screening false negative rate (ie, 1-sensitivity). Our objective is to enhance our understanding of interval cancers by applying continuous tumour growth models to data from a study involving incident invasive breast cancer cases. Building upon previous findings regarding stationary distributions of tumour size and growth rate distributions in non-screened populations, we develop an analytical expression for the proportion of interval breast cancer cases among regularly screened women. Our approach avoids relying on estimated background cancer rates. We make specific parametric assumptions concerning tumour growth and detection processes (screening or symptoms), but our framework easily accommodates alternative assumptions. We also show how our developed analytical expression for the proportion of interval breast cancers within a screened population can be incorporated into an approach for fitting tumour growth models to incident case data. We fit a model on 3493 cases diagnosed in Sweden between 2001 and 2008. Our methodology allows us to estimate the distribution of tumour sizes at the most recent screening for interval cancers. Importantly, we find that our model-based expected incidence of interval breast cancers aligns closely with observed patterns in our study and in a large Nordic screening cohort. Finally, we evaluate the association between screening interval length and the interval cancer proportion. Our analytical expression represents a useful tool for gaining insights into the performance of population-based breast cancer screening programs.

A Bayesian nonparametric meta-analysis model for estimating the reference interval.

A reference interval represents the normative range for measurements from a healthy population. It plays an important role in laboratory testing, as well as in differentiating healthy from diseased patients. The reference interval based on a single study might not be applicable to a broader population. Meta-analysis can provide a more generalizable reference interval based on the combined population by synthesizing results from multiple studies. However, the assumptions of normally distributed underlying study-specific means and equal within-study variances, which are commonly used in existing methods, are strong and may not hold in practice. We propose a Bayesian nonparametric model with more flexible assumptions to extend random effects meta-analysis for estimating reference intervals. We illustrate through simulation studies and two real data examples the performance of our proposed approach when the assumptions of normally distributed study means and equal within-study variances do not hold.

Risk factors for herpes zoster infections: a systematic review and meta-analysis unveiling common trends and heterogeneity patterns.

PURPOSE: The burden of herpes zoster (HZ) is substantial and numerous chronic underlying conditions are known as predisposing risk factors for HZ onset. Thus, a comprehensive study is needed to synthesize existing evidence. This study aims to comprehensively identify these risk factors. METHODS: A systematic literature search was done using MEDLINE via PubMed, EMBASE and Web of Science for studies published from January 1, 2003 to January 1, 2023. A random-effects model was used to estimate pooled Odds Ratios (OR). Heterogeneity was assessed using the I2 statistic. For sensitivity analyses basic outlier removal, leave-one-out validation and Graphic Display of Heterogeneity (GOSH) plots with different algorithms were employed to further analyze heterogeneity patterns. Finally, a multiple meta-regression was conducted. RESULTS: Of 6392 considered records, 80 were included in the meta-analysis. 21 different conditions were identified as potential risk factors for HZ: asthma, autoimmune disorders, cancer, cardiovascular disorders, chronic heart failure (CHF), chronic obstructive pulmonary disorder (COPD), depression, diabetes, digestive disorders, endocrine and metabolic disorders, hematological disorders, HIV, inflammatory bowel disease (IBD), mental health conditions, musculoskeletal disorders, neurological disorders, psoriasis, renal disorders, rheumatoid arthritis (RA), systemic lupus erythematosus (SLE) and transplantation. Transplantation was associated with the highest risk of HZ (OR = 4.51 (95% CI [1.9-10.7])). Other risk factors ranged from OR = 1.17-2.87, indicating an increased risk for all underlying conditions. Heterogeneity was substantial in all provided analyses. Sensitivity analyses showed comparable results regarding the pooled effects and heterogeneity. CONCLUSIONS: This study showed an increased risk of HZ infections for all identified factors.

Meta-analysis prediction intervals are under reported in sport and exercise medicine.

AIM: Prediction intervals are a useful measure of uncertainty for meta-analyses that capture the likely effect size of a new (similar) study based on the included studies. In comparison, confidence intervals reflect the uncertainty around the point estimate but provide an incomplete summary of the underlying heterogeneity in the meta-analysis. This study aimed to estimate (i) the proportion of meta-analysis studies that report a prediction interval in sports medicine; and (ii) the proportion of studies with a discrepancy between the reported confidence interval and a calculated prediction interval. METHODS: We screened, at random, 1500 meta-analysis studies published between 2012 and 2022 in highly ranked sports medicine and medical journals. Articles that used a random effect meta-analysis model were included in the study. We randomly selected one meta-analysis from each article to extract data from, which included the number of estimates, the pooled effect, and the confidence and prediction interval. RESULTS: Of the 1500 articles screened, 866 (514 from sports medicine) used a random effect model. The probability of a prediction interval being reported in sports medicine was 1.7% (95% CI = 0.9%, 3.3%). In medicine the probability was 3.9% (95% CI = 2.4%, 6.6%). A prediction interval was able to be calculated for 220 sports medicine studies. For 60% of these studies, there was a discrepancy in study findings between the reported confidence interval and the calculated prediction interval. Prediction intervals were 3.4 times wider than confidence intervals. CONCLUSION: Very few meta-analyses report prediction intervals and hence are prone to missing the impact of between-study heterogeneity on the overall conclusions. The widespread misinterpretation of random effect meta-analyses could mean that potentially harmful treatments, or those lacking a sufficient evidence base, are being used in practice. Authors, reviewers, and editors should be aware of the importance of prediction intervals.

Postpartum pain and the risk of postpartum depression: A meta-analysis of observational studies.

OBJECTIVE: This meta-analysis of observational studies aimed to derive a more precise estimation of the relationship between postpartum pain and postpartum depression (PPD). METHODS: A systematic literature search was completed in the following databases from inception to September 26, 2022: PubMed, Embase, and Web of Science. Quality evaluation of each study was achieved through Newcastle-Ottawa scale (NOS) assessment. Heterogeneity across studies was evaluated by Cochran's Q test and I2 test. Pooled estimates of odds ratios (ORs) and corresponding 95% confidence intervals (CIs) were analyzed using fixed-effects model or random-effects model, according to heterogeneity. Subgroup analysis, sensitivity analysis, and Egger's test were also performed. RESULTS: From the identified 1884 articles, a total of 8 studies involving 3973 participants were included in the final meta-analysis. Seven of the 8 studies were evaluated as high-quality, with NOS scores ≥7. A significant heterogeneity was observed (I2 = 66.5%, p = 0.004) among eight studies. Therefore, the performed random-effect model suggested a significant association between postpartum pain and PPD risk (OR 1.29, 95% CI 1.10-1.52, p = 0.002). However, the subgroup analyses did not define the source of heterogeneity. Moreover, the sensitivity analysis showed the stability of the pooled results, but the significant publication bias was identified (p = 0.009). The trim and fill method was performed and resulted in an OR of 1.14 (95% CI 0.95-1.37, p = 0.162). CONCLUSIONS: This meta-analysis found a potential association between postpartum pain and PPD. Further researches are needed to provide more robust evidences.

Individual Mobility across Clusters: The Impact of Ignoring Cross-Classified Data Structures in Discrete-Time Survival Analysis.

A multilevel-discrete time survival model may be appropriate for purely hierarchical data, but when data are non-purely hierarchical due to individual mobility across clusters, a cross-classified discrete time survival model may be necessary. The purpose of this research was to investigate the performance of a cross-classified discrete-time survival model and assess the impact of ignoring a cross-classified data structure on the model parameters of a conventional discrete-time survival model and a multilevel discrete-time survival model. A Monte Carlo simulation was used to examine the performance of three discrete-time survival models when individuals are mobile across clusters. Simulation factors included the value of the between-clusters variance, number of clusters, within-cluster sample size, Weibull scale parameter, and mobility rate. The results suggest that substantial relative parameter bias, unacceptable coverage of the 95% confidence intervals, and severely biased standard errors are possible for all model parameters when a discrete-time survival model is used that ignores the cross-classified data structure. The findings presented in this study are useful for methodologists and practitioners in educational research, public health, and other social sciences where discrete-time survival analysis is a common methodological technique for analyzing event-history data.

Go Multivariate: Recommendations on Bayesian Multilevel Hidden Markov Models with Categorical Data.

The multilevel hidden Markov model (MHMM) is a promising method to investigate intense longitudinal data obtained within the social and behavioral sciences. The MHMM quantifies information on the latent dynamics of behavior over time. In addition, heterogeneity between individuals is accommodated with the inclusion of individual-specific random effects, facilitating the study of individual differences in dynamics. However, the performance of the MHMM has not been sufficiently explored. We performed an extensive simulation to assess the effect of the number of dependent variables (1-8), number of individuals (5-90), and number of observations per individual (100-1600) on the estimation performance of a Bayesian MHMM with categorical data including various levels of state distinctiveness and separation. We found that using multivariate data generally alleviates the sample size needed and improves the stability of the results. Moreover, including variables only consisting of random noise was generally not detrimental to model performance. Regarding the estimation of group-level parameters, the number of individuals and observations largely compensate for each other. However, only the former drives the estimation of between-individual variability. We conclude with guidelines on the sample size necessary based on the level of state distinctiveness and separation and study objectives of the researcher.

Health Care Provider Clustering Using Fusion Penalty in Quasi-Likelihood.

There has been growing research interest in developing methodology to evaluate the health care providers' performance with respect to a patient outcome. Random and fixed effects models are traditionally used for such a purpose. We propose a new method, using a fusion penalty to cluster health care providers based on quasi-likelihood. Without any priori knowledge of grouping information, our method provides a desirable data-driven approach for automatically clustering health care providers into different groups based on their performance. Further, the quasi-likelihood is more flexible and robust than the regular likelihood in that no distributional assumption is needed. An efficient alternating direction method of multipliers algorithm is developed to implement the proposed method. We show that the proposed method enjoys the oracle properties; namely, it performs as well as if the true group structure were known in advance. The consistency and asymptotic normality of the estimators are established. Simulation studies and analysis of the national kidney transplant registry data demonstrate the utility and validity of our method.

Factor-Analytic Variance-Covariance Structures for Prediction Into a Target Population of Environments.

Finlay-Wilkinson regression is a popular method for modeling genotype-environment interaction in plant breeding and crop variety testing. When environment is a random factor, this model may be cast as a factor-analytic variance-covariance structure, implying a regression on random latent environmental variables. This paper reviews such models with a focus on their use in the analysis of multi-environment trials for the purpose of making predictions in a target population of environments. We investigate the implication of random versus fixed effects assumptions, starting from basic analysis-of-variance models, then moving on to factor-analytic models and considering the transition to models involving observable environmental covariates, which promise to provide more accurate and targeted predictions than models with latent environmental variables.

When Space and Time Matter in Environmental Injustice: A Bayesian Analysis of the Association between Socio-economic Disadvantage and Air Pollution in Greater Mexico City.

Environmental injustice refers to the unequal burden of pollutants on groups with lower socioeconomic status. An increasing number of studies have identified associations between high levels of pollution and socioeconomic disadvantage. However, few studies have controlled adequately for spatio-temporal variations in pollution. This study uses a Bayesian approach to explore the association between socioeconomic disadvantage and pollution in Mexico City Metropolitan Area. We quantify the association of socioeconomic disadvantage with PM10 and ozone and evaluate the impact of accounting for spatio-temporal structure of the pollution data. We find a significant positive association between socio-economic disadvantage and pollution for levels of PM10, but not ozone. The inclusion of the spatio-temporal element in the modeling results in improved weaker estimates of this association but this does not alter results substantially. These findings confirm the robustness of previous studies that found signs of environmental injustice where spatio-temporal variations have not been explicitly considered, confirming that targeted policies to reduce pollution in socio-economically disadvantaged areas are required.

Semiparametric regression analysis of bivariate censored events in a family study of Alzheimer's disease.

Assessing disease comorbidity patterns in families represents the first step in gene mapping for diseases and is central to the practice of precision medicine. One way to evaluate the relative contributions of genetic risk factor and environmental determinants of a complex trait (e.g., Alzheimer's disease [AD]) and its comorbidities (e.g., cardiovascular diseases [CVD]) is through familial studies, where an initial cohort of subjects are recruited, genotyped for specific loci, and interviewed to provide extensive disease history in family members. Because of the retrospective nature of obtaining disease phenotypes in family members, the exact time of disease onset may not be available such that current status data or interval-censored data are observed. All existing methods for analyzing these family study data assume single event subject to right-censoring so are not applicable. In this article, we propose a semiparametric regression model for the family history data that assumes a family-specific random effect and individual random effects to account for the dependence due to shared environmental exposures and unobserved genetic relatedness, respectively. To incorporate multiple events, we jointly model the onset of the primary disease of interest and a secondary disease outcome that is subject to interval-censoring. We propose nonparametric maximum likelihood estimation and develop a stable Expectation-Maximization (EM) algorithm for computation. We establish the asymptotic properties of the resulting estimators and examine the performance of the proposed methods through simulation studies. Our application to a real world study reveals that the main contribution of comorbidity between AD and CVD is due to genetic factors instead of environmental factors.

Accounting for total variation and robustness in profiling health care providers.

Monitoring outcomes of health care providers, such as patient deaths, hospitalizations, and hospital readmissions, helps in assessing the quality of health care. We consider a large database on patients being treated at dialysis facilities in the United States, and the problem of identifying facilities with outcomes that are better than or worse than expected. Analyses of such data have been commonly based on random or fixed facility effects, which have shortcomings that can lead to unfair assessments. A primary issue is that they do not appropriately account for variation between providers that is outside the providers' control due, for example, to unobserved patient characteristics that vary between providers. In this article, we propose a smoothed empirical null approach that accounts for the total variation and adapts to different provider sizes. The linear model provides an illustration that extends easily to other non-linear models for survival or binary outcomes, for example. The empirical null method is generalized to allow for some variation being due to quality of care. These methods are examined with numerical simulations and applied to the monitoring of survival in the dialysis facility data.

MRCIP: a robust Mendelian randomization method accounting for correlated and idiosyncratic pleiotropy.

Mendelian randomization (MR) is a powerful instrumental variable (IV) method for estimating the causal effect of an exposure on an outcome of interest even in the presence of unmeasured confounding by using genetic variants as IVs. However, the correlated and idiosyncratic pleiotropy phenomena in the human genome will lead to biased estimation of causal effects if they are not properly accounted for. In this article, we develop a novel MR approach named MRCIP to account for correlated and idiosyncratic pleiotropy simultaneously. We first propose a random-effect model to explicitly model the correlated pleiotropy and then propose a novel weighting scheme to handle the presence of idiosyncratic pleiotropy. The model parameters are estimated by maximizing a weighted likelihood function with our proposed PRW-EM algorithm. Moreover, we can also estimate the degree of the correlated pleiotropy and perform a likelihood ratio test for its presence. Extensive simulation studies show that the proposed MRCIP has improved performance over competing methods. We also illustrate the usefulness of MRCIP on two real datasets. The R package for MRCIP is publicly available at https://github.com/siqixu/MRCIP.

Negative Binomial mixed models estimated with the maximum likelihood method can be used for longitudinal RNAseq data.

Time-course RNAseq experiments, where tissues are repeatedly collected from the same subjects, e.g. humans or animals over time or under several different experimental conditions, are becoming more popular due to the reducing sequencing costs. Such designs offer the great potential to identify genes that change over time or progress differently in time across experimental groups. Modelling of the longitudinal gene expression in such time-course RNAseq data is complicated by the serial correlations, missing values due to subject dropout or sequencing errors, long follow up with potentially non-linear progression in time and low number of subjects. Negative Binomial mixed models can address all these issues. However, such models under the maximum likelihood (ML) approach are less popular for RNAseq data due to convergence issues (see, e.g. [1]). We argue in this paper that it is the use of an inaccurate numerical integration method in combination with the typically small sample sizes which causes such mixed models to fail for a great portion of tested genes. We show that when we use the accurate adaptive Gaussian quadrature approach to approximate the integrals over the random-effects terms, we can successfully estimate the model parameters with the maximum likelihood method. Moreover, we show that the boostrap method can be used to preserve the type I error rate in small sample settings. We evaluate empirically the small sample properties of the test statistics and compare with state-of-the-art approaches. The method is applied on a longitudinal mice experiment to study the dynamics in Duchenne Muscular Dystrophy. Contact:s.tsonaka@lumc.nl Roula Tsonaka is an assistant professor at the Medical Statistics, Department of Biomedical Data Sciences, Leiden University Medical Center. Her research focuses on statistical methods for longitudinal omics data. Pietro Spitali is an assistant professor at the Department of Human Genetics, Leiden University Medical Center. His research focuses on the identification of biomarkers for neuromuscular disorders.

Heritability Estimation of Cognitive Phenotypes in the ABCD Study® Using Mixed Models.

Twin and family studies have historically aimed to partition phenotypic variance into components corresponding to additive genetic effects (A), common environment (C), and unique environment (E). Here we present the ACE Model and several extensions in the Adolescent Brain Cognitive Development℠ Study (ABCD Study®), employed using the new Fast Efficient Mixed Effects Analysis (FEMA) package. In the twin sub-sample (n = 924; 462 twin pairs), heritability estimates were similar to those reported by prior studies for height (twin heritability = 0.86) and cognition (twin heritability between 0.00 and 0.61), respectively. Incorporating SNP-derived genetic relatedness and using the full ABCD Study® sample (n = 9,742) led to narrower confidence intervals for all parameter estimates. By leveraging the sparse clustering method used by FEMA to handle genetic relatedness only for participants within families, we were able to take advantage of the diverse distribution of genetic relatedness within the ABCD Study® sample.

Neural networks for clustered and longitudinal data using mixed effects models.

Although most statistical methods for the analysis of longitudinal data have focused on retrospective models of association, new advances in mobile health data have presented opportunities for predicting future health status by leveraging an individual's behavioral history alongside data from similar patients. Methods that incorporate both individual-level and sample-level effects are critical to using these data to its full predictive capacity. Neural networks are powerful tools for prediction, but many assume input observations are independent even when they are clustered or correlated in some way, such as in longitudinal data. Generalized linear mixed models (GLMM) provide a flexible framework for modeling longitudinal data but have poor predictive power particularly when the data are highly nonlinear. We propose a generalized neural network mixed model that replaces the linear fixed effect in a GLMM with the output of a feed-forward neural network. The model simultaneously accounts for the correlation structure and complex nonlinear relationship between input variables and outcomes, and it utilizes the predictive power of neural networks. We apply this approach to predict depression and anxiety levels of schizophrenic patients using longitudinal data collected from passive smartphone sensor data.