Distribution Of Random Effects Research Articles

Maternal and Fetal Outcomes of Aplastic Anemia During Pregnancy and Delivery: Systematic Review and Meta-Analysis.

Little scientific evidence exists on maternal and fetal outcomes in aplastic anemia (AA) during pregnancy. The review was conducted to assess the maternal and fetal outcomes due to AA during pregnancy. Web of Science, EMBASE, PubMed, Scopus, Cochrane CENTRAL, and registries until May 5, 2024. Studies (prospective, retrospective cohort, cross-sectional, one arm, survey, follow-up studies) evaluating AA during pregnancy were searched as per PROSPERO registered protocol (CRD42024506668). Case reports, case series, expert opinion letters, and studies assessing less than or equal to 10 pregnant women were not considered. The primary outcome was the prevalence of preeclampsia in AA pregnancies. The secondary outcomes included spontaneous abortion, preterm premature rupture of membranes, premature rupture of membranes, fetal growth restriction, type of delivery, intrauterine fetal death, maternal and neonatal mortality, and pre and post-pregnancy remission status comparison. The quality of research was checked using the New Castle-Ottawa risk-of-bias tool. A meta-analysis model with a random effect distribution, coupled with meta-regression, sensitivity analysis, and publication bias assessment, was used in the statistical software R. Standard Equator network study reporting guidelines were followed. Seven (one prospective and six retrospective cohort) studies included patients with confirmed AA diagnosis in 248 pregnancies. The pooled prevalence of preeclampsia was 13% (95% CI, 8%-20%). Heterogeneity was low in the present meta-analysis (I2 = 26%). The secondary outcome evaluation showed a pooled prevalence of 5% (95% CI, 3%-11%) for spontaneous abortion, 4% (95% CI, 1%-11%) for preterm premature rupture of membranes, 10% (95% CI, 3%-28%) for premature rupture of membranes, 6% (95% CI, 3%-11%) for fetal growth restriction, 5% (95% CI, 2%-13%) for intrauterine fetal death, 12% (95% CI, 5%-26%) for post-partum hemorrhage, 74% (95% CI, 45%-91%) for intrapartum transfusion requirement, and 55% (95% CI, 27%-80%) for the cesarean delivery opting. The maternal mortality in pregnancies with AA was 4% (95% CI, 0.01-0.14), whereas neonatal mortality was 7% (95% CI, 0.03-0.18). The odds of AA complete remission were better in pre-pregnancy than post-pregnancy (OR = 0.36; 95% CI = 0.08-1.66), although the results remain insignificant. The leave-one-out sensitivity analysis did not change the pooled estimates for the primary outcome. A risk of developing preeclampsia was observed in every eighth pregnant woman with an AA diagnosis. AA remission status might worsen after undergoing pregnancy, considering the significant obstetric morbidity and mortality burden.

Variability in Causal Effects and Noncompliance in a Multisite Trial: A Bivariate Hierarchical Generalized Random Coefficients Model for a Binary Outcome.

Within each of 170 physicians, patients were randomized to access e-assist, an online program that aimed to increase colorectal cancer screening (CRCS), or control. Compliance was partial: of the experimental patients accessed e-assist while no controls were provided the access. Of interest are the average causal effect of assignment to treatment and the complier average causal effect as well as the variation of these causal effects across physicians. Each physician generates probabilities of screening for experimental compliers (experimental patients who accessed e-assist), control compliers (controls who would have accessed e-assist had they been assigned to e-assist), and never takers (patients who would have avoided e-assist no matter what). Estimating physician-specific probabilities jointly over physicians poses novel challenges. We address these challenges by maximum likelihood, factoring a "complete-data likelihood" uniquely into the conditional distribution of screening and partially observed compliance given random effects and the distribution of random effects. We marginalize this likelihood using adaptive Gauss-Hermite quadrature. The approach is doubly iterative in that the conditional distribution defies analytic evaluation. Because the small sample size per physician constrains estimability of multiple random effects, we reduce their dimensionality using a shared random effects model having a factor analytic structure. We assess estimators and recommend sample sizes to produce reasonably accurate and precise estimates by simulation, and analyze data from a trial of a CRCS intervention.

Joint meta-analysis of two diagnostic tests accounting for within and between studies dependence.

There is an extensive literature on methods for meta-analysis of diagnostic test accuracy, but it mainly focuses on a single test. A multinomial generalised linear mixed model was recently proposed for the joint meta-analysis of studies comparing two tests on the same participants in a paired tests design with a gold standard. In this setting, we propose a novel model for joint meta-analysis of studies comparing two diagnostic tests which assumes independent multinomial distributions for the counts of each combination of test results in diseased and non-diseased patients, conditional on the latent vector of probabilities of each combination of test results in diseased and non-diseased patients. For the random effects distribution of the latent proportions, we employ a one-truncated D-vine copula that can provide tail dependence or asymmetry. The proposed model includes the multinomial generalised linear mixed model as a special case, accounts for the within-study dependence induced because the tests are applied to the same participants, allows for between-studies dependence, and can also operate on the original scale of the latent proportions. The latter enables the derivation of summary receiver operating characteristic curves. Our methodology is demonstrated with simulation studies and a meta-analysis of screening for Down's syndrome with two tests: shortened humerus and shortened femur.

On the Addams family of discrete frailty distributions for modeling multivariate case I interval-censored data.

Random effect models for time-to-event data, also known as frailty models, provide a conceptually appealing way of quantifying association between survival times and of representing heterogeneities resulting from factors which may be difficult or impossible to measure. In the literature, the random effect is usually assumed to have a continuous distribution. However, in some areas of application, discrete frailty distributions may be more appropriate. The present paper is about the implementation and interpretation of the Addams family of discrete frailty distributions. We propose methods of estimation for this family of densities in the context of shared frailty models for the hazard rates for case I interval-censored data. Our optimization framework allows for stratification of random effect distributions by covariates. We highlight interpretational advantages of the Addams family of discrete frailty distributions and theK-point distribution as compared to other frailty distributions. A unique feature of the Addams family and the K-point distribution is that the support of the frailty distribution depends on its parameters. This feature is best exploited by imposing a model on the distributional parameters, resulting in a model with non-homogeneous covariate effects that can be analyzed using standard measures such as the hazard ratio. Our methods are illustrated with applications to multivariate case I interval-censored infection data.

A New Approach Using the Lindley Distribution in Stochastic Frontier Analysis

Abstract Stochastic Frontier Analysis plays a crucial role in assessing technical efficiency and modelling production processes across various disciplines. Traditionally, SFA assumes specific error distributions, such as the normal distribution for random effects and the half-normal distribution for technical efficiency. However, the choice of error distributions can significantly impact model estimation and interpretation. This study proposes a novel approach by incorporating the Lindley distribution as a flexible error distribution in SFA, termed Lindley Stochastic Frontier Analysis (L-SFA). This extension offers a more detailed representation of the error structure, potentially enhancing the accuracy of efficiency estimates. The derivation and solution of maximum likelihood estimators for the theoretical foundations of L-SFA are provided. Furthermore, a simulation study demonstrates the advantages of L-SFA over traditional SFA. The findings underscore the importance of flexible error distributions in capturing the complexities of production processes with this new SFA extension. Keywords: Efficiency, Error distribution, Lindley stochastic frontier analysis, Maximum likelihood estimation, Simulation

Bootstrap-based statistical inference for linear mixed effects under misspecifications

Linear mixed effects are considered excellent predictors of cluster-level parameters in various domains. However, previous research has demonstrated that their performance is affected by departures from model assumptions. Given the common occurrence of these departures in empirical studies, there is a need for inferential methods that are robust to misspecifications while remaining accessible and appealing to practitioners. Statistical tools have been developed for cluster-wise and simultaneous inference for mixed effects under distributional misspecifications, employing a user-friendly semiparametric random effect bootstrap. The merits and limitations of this approach are discussed in the general context of model misspecification. Theoretical analysis demonstrates the asymptotic consistency of the methods under general regularity conditions. Simulations show that the proposed intervals are robust to departures from modelling assumptions, including asymmetry and long tails in the distributions of errors and random effects, outperforming competitors in terms of empirical coverage probability. Finally, the methodology is applied to construct confidence intervals for household income across counties in the Spanish region of Galicia.

A sparse factor model for clustering high-dimensional longitudinal data.

Recent advances in engineering technologies have enabled the collection of a large number of longitudinal features. This wealth of information presents unique opportunities for researchers to investigate the complex nature of diseases and uncover underlying disease mechanisms. However, analyzing such kind of data can be difficult due to its high dimensionality, heterogeneity and computational challenges. In this article, we propose a Bayesian nonparametric mixture model for clustering high-dimensional mixed-type (eg, continuous, discrete and categorical) longitudinal features. We employ a sparse factor model on the joint distribution of random effects and the key idea is to induce clustering at the latent factor level instead of the original data to escape the curse of dimensionality. The number of clusters is estimated through a Dirichlet process prior. An efficient Gibbs sampler is developed to estimate the posterior distribution of the model parameters. Analysis of real and simulated data is presented and discussed. Our study demonstrates that the proposed model serves as a useful analytical tool for clustering high-dimensional longitudinal data.

Estimating the Distribution of True Rates of Visual Field Progression in Glaucoma.

The purpose of this study was to estimate the distribution of the true rates of progression (RoP) of visual field (VF) loss. We analyzed the progression of mean deviation over time in series of ≥ 10 tests from 3352 eyes (one per patient) from 5 glaucoma clinics, using a novel Bayesian hierarchical Linear Mixed Model (LMM); this modeled the random-effect distribution of RoPs as the sum of 2 independent processes following, respectively, a negative exponential distribution (the "true" distribution of RoPs) and a Gaussian distribution (the "noise"), resulting in a skewed exGaussian distribution. The exGaussian-LMM was compared to a standard Gaussian-LMM using the Watanabe-Akaike Information Criterion (WAIC). The random-effect distributions were compared to the empirical cumulative distribution function (eCDF) of linear regression RoPs using a Kolmogorov-Smirnov test. The WAIC indicated a better fit with the exGaussian-LMM (estimate [standard error]: 192174.4 [721.2]) than with the Gaussian-LMM (192595 [697.4], with a difference of 157.2 [22.6]). There was a significant difference between the eCDF and the Gaussian-LMM distribution (P < 0.0001), but not with the exGaussian-LMM distribution (P = 0.108). The estimated mean (95% credible intervals, CIs) "true" RoP (-0.377, 95% CI = -0.396 to -0.359 dB/year) was more negative than the observed mean RoP (-0.283, 95% CI = -0.299 to -0.268 dB/year), indicating a bias likely due to learning in standard LMMs. The distribution of "true" RoPs can be estimated with an exGaussian-LMM, improving model accuracy. We used these results to develop a fast and accurate analytical approximation for sample-size calculations in clinical trials using standard LMMs, which was integrated in a freely available web application.

Semiparametric accelerated failure time models under unspecified random effect distributions

Accelerated failure time (AFT) models with random effects, a useful alternative to frailty models, have been widely used for analyzing clustered (or correlated) time-to-event data. In the AFT model, the distribution of the unobserved random effect is conventionally assumed to be parametric, often modeled as a normal distribution. Although it has been known that a misspecfied random-effect distribution has little effect on regression parameter estimates, in some cases, the impact caused by such misspecification is not negligible. Particularly when our focus extends to quantities associated with random effects, the problem could become worse. In this paper, we propose a semi-parametric maximum likelihood approach in which the random-effect distribution under the AFT models is left unspecified. We provide a feasible algorithm to estimate the random-effect distribution as well as model parameters. Through comprehensive simulation studies, our results demonstrate the effectiveness of this proposed method across a range of random-effect distribution types (discrete or continuous) and under conditions of heavy censoring. The efficacy of the approach is further illustrated through simulation studies and real-world data examples.

Flexible Bayesian semiparametric mixed-effects model for skewed longitudinal data

BackgroundIn clinical trials and epidemiological research, mixed-effects models are commonly used to examine population-level and subject-specific trajectories of biomarkers over time. Despite their increasing popularity and application, the specification of these models necessitates a great deal of care when analysing longitudinal data with non-linear patterns and asymmetry. Parametric (linear) mixed-effect models may not capture these complexities flexibly and adequately. Additionally, assuming a Gaussian distribution for random effects and/or model errors may be overly restrictive, as it lacks robustness against deviations from symmetry.MethodsThis paper presents a semiparametric mixed-effects model with flexible distributions for complex longitudinal data in the Bayesian paradigm. The non-linear time effect on the longitudinal response was modelled using a spline approach. The multivariate skew-t distribution, which is a more flexible distribution, is utilized to relax the normality assumptions associated with both random-effects and model errors.ResultsTo assess the effectiveness of the proposed methods in various model settings, simulation studies were conducted. We then applied these models on chronic kidney disease (CKD) data and assessed the relationship between covariates and estimated glomerular filtration rate (eGFR). First, we compared the proposed semiparametric partially linear mixed-effect (SPPLM) model with the fully parametric one (FPLM), and the results indicated that the SPPLM model outperformed the FPLM model. We then further compared four different SPPLM models, each assuming different distributions for the random effects and model errors. The model with a skew-t distribution exhibited a superior fit to the CKD data compared to the Gaussian model. The findings from the application revealed that hypertension, diabetes, and follow-up time had a substantial association with kidney function, specifically leading to a decrease in GFR estimates.ConclusionsThe application and simulation studies have demonstrated that our work has made a significant contribution towards a more robust and adaptable methodology for modeling intricate longitudinal data. We achieved this by proposing a semiparametric Bayesian modeling approach with a spline smoothing function and a skew-t distribution.

Joint modeling of association networks and longitudinal biomarkers: An application to childhood obesity.

The prevalence of chronic non-communicable diseases such as obesity has noticeably increased in the last decade. The study of these diseases in early life is of paramount importance in determining their course in adult life and in supporting clinical interventions. Recently, attention has been drawn to approaches that study the alteration of metabolic pathways in obese children. In this work, we propose a novel joint modeling approach for the analysis of growth biomarkers and metabolite associations, to unveil metabolic pathways related to childhood obesity. Within a Bayesian framework, we flexibly model the temporal evolution of growth trajectories and metabolic associations through the specification of a joint nonparametric random effect distribution, with the main goal of clustering subjects, thus identifying risk sub-groups. Growth profiles as well as patterns of metabolic associations determine the clustering structure. Inclusion of risk factors is straightforward through the specification of a regression term. We demonstrate the proposed approach on data from the Growing Up in Singapore Towards healthy Outcomes cohort study, based in Singapore. Posterior inference is obtained via a tailored MCMC algorithm, involving a nonparametric prior with mixed support. Our analysis has identified potential key pathways in obese children that allow for the exploration of possible molecular mechanisms associated with childhood obesity.

Frailty model with change points for survival analysis.

We propose a novel frailty model with change points applying random effects to a Cox proportional hazard model to adjust the heterogeneity between clusters. In the specially focused eight Empowered Action Group (EAG) states in India, there are problems with different survival curves for children up to the age of five in different states. Therefore, when analyzing the survival times for the eight EAG states, we need to adjust for the effects among states (clusters). Because the frailty model includes random effects, the parameters are estimated using the expectation-maximization (EM) algorithm. Additionally, our model needs to estimate change points; we thus propose a new algorithm extending the conventional estimation algorithm to the frailty model with change points to solve the problem. We show a practical example to demonstrate how to estimate the change point and the parameters of the distribution of random effect. Our proposed model can be easily analyzed using the existing R package. We conducted simulation studies with three scenarios to confirm the performance of our proposed model. We re-analyzed the survival time data of the eight EAG states in India to show the difference in analysis results with and without random effect. In conclusion, we confirmed that the frailty model with change points has a higher accuracy than the model without a random effect. Our proposed model is useful when heterogeneity needs to be taken into account. Additionally, the absence of heterogeneity did not affect the estimation of the regression parameters.

Nonparametric estimation of the random effects distribution for the risk or rate ratio in rare events meta-analysis with the arm-based and contrast-based approaches.

Rare events are events which occur with low frequencies. These often arise in clinical trials or cohort studies where the data are arranged in binary contingency tables. In this article, we investigate the estimation of effect heterogeneity for the risk-ratio parameter in meta-analysis of rare events studies through two likelihood-based nonparametric mixture approaches: an arm-based and a contrast-based model. Maximum likelihood estimation is achieved using the EM algorithm. Special attention is given to the choice of initial values. Inspired by the classification likelihood, a strategy is implemented which repeatably uses random allocation of the studies to the mixture components as choice of initial values. The likelihoods under the contrast-based and arm-based approaches are compared and differences are highlighted. We use simulations to assess the performance of these two methods. Under the design of sampling studies with nested treatment groups, the results show that the nonparametric mixture model based on the contrast-based approach is more appropriate in terms of model selection criteria such as AIC and BIC. Under the arm-based design the results from the arm-based model performs well although in some cases it is also outperformed by the contrast-based model. Comparisons of the estimators are provided in terms of bias and mean squared error. Also included in the comparison is the mixed Poisson regression model as well as the classical DerSimonian-Laird model (using the Mantel-Haenszel estimator for the common effect). Using simulation, estimating effect heterogeneity in the case of the contrast-based method appears to behave better than the compared methods although differences become negligible for large within-study sample sizes. We illustrate the methodologies using several meta-analytic data sets in medicine.

Are your random effects normal? A simulation study of methods for estimating whether subjects or items come from more than one population by examining the distribution of random effects in mixed-effects logistic regression.

With mixed-effects regression models becoming a mainstream tool for every psycholinguist, there has become an increasing need to understand them more fully. In the last decade, most work on mixed-effects models in psycholinguistics has focused on properly specifying the random-effects structure to minimize error in evaluating the statistical significance of fixed-effects predictors. The present study examines a potential misspecification of random effects that has not been discussed in psycholinguistics: violation of the single-subject-population assumption, in the context of logistic regression. Estimated random-effects distributions in real studies often appear to be bi- or multimodal. However, there is no established way to estimate whether a random-effects distribution corresponds to more than one underlying population, especially in the more common case of a multivariate distribution of random effects. We show that violations of the single-subject-population assumption can usually be detected by assessing the (multivariate) normality of the inferred random-effects structure, unless the data show quasi-separability, i.e., many subjects or items show near-categorical behavior. In the absence of quasi-separability, several clustering methods are successful in determining which group each participant belongs to. The BIC difference between a two-cluster and a one-cluster solution can be used to determine that subjects (or items) do not come from a single population. This then allows the researcher to define and justify a new post hoc variable specifying the groups to which participants or items belong, which can be incorporated into regression analysis.

Fast and flexible inference for joint models of multivariate longitudinal and survival data using integrated nested Laplace approximations.

Modeling longitudinal and survival data jointly offers many advantages such as addressing measurement error and missing data in the longitudinal processes, understanding and quantifying the association between the longitudinal markers and the survival events, and predicting the risk of events based on the longitudinal markers. A joint model involves multiple submodels (one for each longitudinal/survival outcome) usually linked together through correlated or shared random effects. Their estimation is computationally expensive (particularly due to a multidimensional integration of the likelihood over the random effects distribution) so that inference methods become rapidly intractable, and restricts applications of joint models to a small number of longitudinal markers and/or random effects. We introduce a Bayesian approximation based on the integrated nested Laplace approximation algorithm implemented in the R package R-INLA to alleviate the computational burden and allow the estimation of multivariate joint models with fewer restrictions. Our simulation studies show that R-INLA substantially reduces the computation time and the variability of the parameter estimates compared with alternative estimation strategies. We further apply the methodology to analyze five longitudinal markers (3 continuous, 1 count, 1 binary, and 16 random effects) and competing risks of death and transplantation in a clinical trial on primary biliary cholangitis. R-INLA provides a fast and reliable inference technique for applying joint models to the complex multivariate data encountered in health research.

Modeling clustered binary data with nonparametric unobserved heterogeneity: An application to stock crash analysis

AbstractVarious random effects models have been developed for clustered binary data; however, traditional approaches to these models generally rely heavily on the specification of a continuous random effect distribution such as Gaussian or beta distribution. In this article, we introduce a new model that incorporates nonparametric unobserved random effects on unit interval (0,1) into logistic regression multiplicatively with fixed effects. This new multiplicative model setup facilitates prediction of our nonparametric random effects and corresponding model interpretations. A distinctive feature of our approach is that a closed‐form expression has been derived for the predictor of nonparametric random effects on unit interval (0,1) in terms of known covariates and responses. A quasi‐likelihood approach has been developed in the estimation of our model. Our results are robust against random effects distributions from very discrete binary to continuous beta distributions. We illustrate our method by analyzing recent large stock crash data in China. The performance of our method is also evaluated through simulation studies.

Ordinal categorical response with baseline response and skew-normal random effect: an application to schizophrenia data

The normal is a popular random effect distribution perceived to identify the correlation between the baseline or initial response and subsequent responses in the analysis of longitudinal data. In this article, we apply more flexible skew-normal random effects in modeling initial responses for the ordinal longitudinal data which include normal as a member. Furthermore, the correlation structure between the baseline response and the consequent responses is studied. Our results indicate that the skew-normal random effects produce the best results in modeling initial conditions for longitudinal ordinal data. Various types of simulation studies are applied to investigate the properties of the proposed model in different scenarios. We found that the baseline observation includes the pre-sample information of the process affecting the structure of random effects and explanatory variables of the proposed model. The developed model is illustrated as an application to the Schizophrenia Collaborative Study data.

Classified Mixed Model Projections

In many practical problems, there is interest in the estimation of mixed effect projections for new data that are outside the range of the training data. Examples include predicting extreme small area means for rare populations or making treatment decisions for patients who do not fit typical risk profiles. Standard methods have long been known to struggle with such problems since the training data may not provide enough information about potential model changes for these new data values (extrapolation bias). We propose a new framework called Prediction Using Random-effect Extrapolation (PURE) which involves constructing a generalized independent variable hull (gIVH) to isolate a minority training set which is “close” to the prediction space, followed by a regrouping of the minority data according to the response variable which results in a new (but misspecified) random effect distribution. This misspecification reflects “extrapolated random effects” which prove vital to capture information that is needed for accurate model projections. Projections are then made using classified mixed model prediction (CMMP) (?) with the regrouped minority data. Comprehensive simulation studies and analysis of data from the National Longitudinal Mortality Study (NLMS) demonstrate superior predictive performance in these very challenging paradigms. An asymptotic analysis reveals why PURE results in more accurate projections. Supplementary materials for this article are available online.

Improving risk classification and ratemaking using mixture‐of‐experts models with random effects

AbstractIn the underwriting and pricing of nonlife insurance products, it is essential for the insurer to utilize both policyholder information and claim history to ensure profitability and proper risk management. In this paper, we apply a flexible regression model with random effects, called theMixed Logit‐weighted Reduced Mixture‐of‐Experts, which leverages both policyholder information and their claim history, to categorize policyholders into groups with similar risk profiles, and to determine a premium that accurately captures the unobserved risks. Estimates of model parameters and the posterior distribution of random effects can be obtained by a stochastic variational algorithm, which is numerically efficient and scalable to large insurance portfolios. Our proposed framework is shown to outperform the classical benchmark models (Logistic and Lognormal GL(M)M) in terms of goodness‐of‐fit to data, while offering intuitive and interpretable characterization of policyholders' risk profiles to adequately reflect their claim history.

Smoothed simulated pseudo-maximum likelihood estimation for nonlinear mixed effects models with censored responses.

Nonlinear mixed effects models have been widely applied to analyses of data that arise from biological, agricultural, and environmental sciences. Estimation of and inference on parameters in nonlinear mixed effects models are often based on the specification of a likelihood function. Maximizing this likelihood function can be complicated by the specification of the random effects distribution, especially in the presence of multiple random effects. The implementation of nonlinear mixed effects models can be further complicated by left-censored responses, representing measurements from bioassays where the exact quantification below a certain threshold is not possible. Motivated by the need to characterize the nonlinear human immunodeficiency virus RNA viral load trajectories after the interruption of antiretroviral therapy, we propose a smoothed simulated pseudo-maximum likelihood estimation approach to fit nonlinear mixed effects models in the presence of left-censored observations. We establish the consistency and asymptotic normality of the resulting estimators. We develop testing procedures for the correlation among random effects and for testing the distributional assumptions on random effects against a specific alternative. In contrast to the existing variants of expectation-maximization approaches, the proposed methods offer flexibility in the specification of the random effects distribution and convenience in making inference about higher-order correlation parameters. We evaluate the finite-sample performance of the proposed methods through extensive simulation studies and illustrate them on a combined dataset from six AIDS Clinical Trials Group treatment interruption studies.