Testing for marginal covariate effect when the subgroup size induced by the covariate is informative.

In many cluster-correlated data analyses, informative cluster size poses a challenge that can potentially introduce bias in statistical analyses. Different methodologies have been introduced in statistical literature to address this bias. In this study, we consider a complex form of informativeness where the number of observations corresponding to latent levels of a unit-level continuous covariate within a cluster is associated with the response variable. This type of informativeness has not been explored in prior research. We present a novel test statistic designed to evaluate the effect of the continuous covariate while accounting for the presence of informativeness. The covariate induces a continuum of latent subgroups within the clusters, and our test statistic is formulated by aggregating values from an established statistic that accounts for informative subgroup sizes when comparing group-specific marginal distributions. Through carefully designed simulations, we compare our test with four traditional methods commonly employed in the analysis of cluster-correlated data. Only our test maintains the size across all data-generating scenarios with informativeness. We illustrate the proposed method to test for marginal associations in periodontal data with this distinctive form of informativeness.

Homogeneity pursuit and variable selection in regression models for multivariate abundance data.

When building regression models for multivariate abundance data in ecology, it is important to allow for the fact that the species are correlated with each other. Moreover, there is often evidence species exhibit some degree of homogeneity in their responses to each environmental predictor, and that most species are informed by only a subset of predictors. We propose a generalized estimating equation (GEE) approach for simultaneous homogeneity pursuit (ie, grouping species with similar coefficient values while allowing differing groups for different covariates) and variable selection in regression models for multivariate abundance data. Using GEEs allows us to straightforwardly account for between-response correlations through a (reduced-rank) working correlation matrix. We augment the GEE with both adaptive fused lasso- and adaptive lasso-type penalties, which aim to cluster the species-specific coefficients within each covariate and encourage differing levels of sparsity across the covariates, respectively. Numerical studies demonstrate the strong finite sample performance of the proposed method relative to several existing approaches for modeling multivariate abundance data. Applying the proposed method to presence-absence records collected along the Great Barrier Reef in Australia reveals both a substantial degree of homogeneity and sparsity in species-environmental relationships. We show this leads to a more parsimonious model for understanding the environmental drivers of seabed biodiversity, and results in stronger out-of-sample predictive performance relative to methods that do not accommodate such features.

Interval estimation of relative risks for combined unilateral and bilateral correlated data.

Measurements are generally collected as unilateral or bilateral data in clinical trials, epidemiology, or observational studies. For example, in ophthalmology studies, the primary outcome is often obtained from one eye or both eyes of an individual. In medical studies, the relative risk is usually the parameter of interest and is commonly used. In this article, we develop three confidence intervals for the relative risk for combined unilateral and bilateral correlated data under the equal dependence assumption. The proposed confidence intervals are based on maximum likelihood estimates of parameters derived using the Fisher scoring method. Simulation studies are conducted to evaluate the performance of proposed confidence intervals with respect to the empirical coverage probability, the mean interval width, and the ratio of mesial non-coverage probability to the distal non-coverage probability. We also compare the proposed methods with the confidence interval based on the method of variance estimates recovery and the confidence interval obtained from the modified Poisson regression model with correlated binary data. We recommend the score confidence interval for general applications because it best controls converge probabilities at the 95% level with reasonable mean interval width. We illustrate the methods with a real-world example.

Nonparametric bootstrap methods for interval estimation of the area under the ROC curve with correlated diagnostic test data: application to whole-virus ELISA testing in swine.

Developing and evaluating novel diagnostic assays are crucial components of contemporary diagnostic research. The receiver operating characteristic (ROC) curve and the area under the ROC curve (AUC) are frequently used to evaluate diagnostic assays' performance. The variation in AUC estimation can be quantified nonparametrically using resampling methods, such as bootstrapping, and then used to construct interval estimation for the AUC. When multiple observations are observed from the same subject, which is very common in veterinary diagnostic tests evaluation experiments, a traditional bootstrap-based method can fail to provide valid interval estimations of AUC. In particular, the traditional method does not account for the correlation among data observations and could result in interval estimation that fails to cover the true AUC adequately at the desired confidence level. In this paper, we proposed two novel methods to calculate the confidence interval of the AUC for correlated diagnostic test data based on cluster bootstrapping and hierarchical bootstrapping, respectively. Our simulation studies showed that both proposed methods had adequate coverage probabilities which were higher than the existing traditional method when there were intra-subject correlations. We also discussed applying the proposed methods to evaluate a novel whole-virus ELISA (wv-ELISA) diagnostic assay in detecting porcine parainfluenza virus type-1 antibodies in swine serum.

Evaluation of Risk Prediction with Hierarchical Data: Dependency Adjusted Confidence Intervals for the AUC.

The area under the true ROC curve (AUC) is routinely used to determine how strongly a given model discriminates between the levels of a binary outcome. Standard inference with the AUC requires that outcomes be independent of each other. To overcome this limitation, a method was developed for the estimation of the variance of the AUC in the setting of two-level hierarchical data using probit-transformed prediction scores generated from generalized estimating equation models, thereby allowing for the application of inferential methods. This manuscript presents an extension of this approach so that inference for the AUC may be performed in a three-level hierarchical data setting (e.g., eyes nested within persons and persons nested within families). A method that accounts for the effect of tied prediction scores on inference is also described. The performance of 95% confidence intervals around the AUC was assessed through the simulation of three-level clustered data in multiple settings, including ones with tied data and variable cluster sizes. Across all settings, the actual 95% confidence interval coverage varied from 0.943 to 0.958, and the ratio of the theoretical variance to the empirical variance of the AUC varied from 0.920 to 1.013. The results are better than those from existing methods. Two examples of applying the proposed methodology are presented.

A latent functional approach for modeling the effects of multidimensional exposures on disease risk.

Understanding the relationships between exposure and disease incidence is an important problem in environmental epidemiology. Typically, a large number of these exposures are measured, and it is found either that a few exposures transmit risk or that each exposure transmits a small amount of risk, but, taken together, these may pose a substantial disease risk. Further, these exposure effects can be nonlinear. We develop a latent functional approach, which assumes that the individual effect of each exposure can be characterized as one of a series of unobserved functions, where the number of latent functions is less than or equal to the number of exposures. We propose Bayesian methodology to fit models with a large number of exposures and show that existing Bayesian group LASSO approaches are a special case of the proposed model. An efficient Markov chain Monte Carlo sampling algorithm is developed for carrying out Bayesian inference. The deviance information criterion is used to choose an appropriate number of nonlinear latent functions. We demonstrate the good properties of the approach using simulation studies. Further, we show that complex exposure relationships can be represented with only a few latent functional curves. The proposed methodology is illustrated with an analysis of the effect of cumulative pesticide exposure on cancer risk in a large cohort of farmers.

Avoiding Blunders When Analyzing Correlated Data, Clustered Data, or Repeated Measures.

Rheumatology research often involves correlated and clustered data. A common error when analyzing these data occurs when instead we treat these data as independent observations. This can lead to incorrect statistical inference. The data used are a subset of the 2017 study from Raheel et al consisting of 633 patients with rheumatoid arthritis (RA) between 1988 and 2007. RA flare and the number of swollen joints served as our binary and continuous outcomes, respectively. Generalized linear models (GLM) were fitted for each, while adjusting for rheumatoid factor (RF) positivity and sex. Additionally, a generalized linear mixed model with a random intercept and a generalized estimating equation were used to model RA flare and the number of swollen joints, respectively, to take additional correlation into account. The GLM's ß coefficients and their 95% confidence intervals (CIs) are then compared to their mixed-effects equivalents. The ß coefficients compared between methodologies are very similar. However, their standard errors increase when correlation is accounted for. As a result, if the additional correlations are not considered, the standard error can be underestimated. This results in an overestimated effect size, narrower CIs, increased type I error, and a smaller P value, thus potentially producing misleading results. It is important to model the additional correlation that occurs in correlated data.

A random effect regression based on the odd log-logistic generalized inverse Gaussian distribution.

In recent decades, the use of regression models with random effects has made great progress. Among these models' attractions is the flexibility to analyze correlated data. In various situations, the distribution of the response variable presents asymmetry or bimodality. In these cases, it is possible to use the normal regression with random effect at the intercept. In light of these contexts, i.e. the desire to analyze correlated data in the presence of bimodality or asymmetry, in this paper we propose a regression model with random effect at the intercept based onthe generalized inverse Gaussian distribution model with correlated data. The maximum likelihood is adopted to estimate the parameters and various simulations are performed for correlated data. A type of residuals for the new regression is proposed whose empirical distribution is close to normal. The versatility of the new regression is demonstrated by estimating the average price per hectare of bare land in 10 municipalities in the state of São Paulo (Brazil). In this context, various databases are constantly emerging, requiring flexible modeling. Thus, it is likely to be of interest to data analysts, and can make a good contribution to the statistical literature.

Clinical trial design and analysis for comparing three treatments with intra-individual right- and left-hand data.

BACKGROUND: Chemotherapy-induced peripheral neuropathy can occur in the right and left hand. Studies on prevention treatments for chemotherapy-induced peripheral neuropathy have largely adopted either self-controlled designs or parallel designs to compare two preventive treatments. When three treatment options (two experimental treatments and a control treatment) are available, both designs can be extended. However, no clinical trials have adopted a self-controlled design to compare three prevention treatments for chemotherapy-induced peripheral neuropathy. The incomplete block crossover design for more than two treatments can be extended to compare three treatments in the self-controlled design. In simple extension, some of the participants receive two experimental treatments in both hands; however, it may be difficult to administer different experimental treatments in both hands for practical reasons, such as a concern for the different types of unexpected adverse events. This study proposes a design and analysis method appropriate for the situation where only one experimental treatment is provided to each participant. METHODS: We assume clinical trials to compare each of the two experimental treatments (E1 and E2) with the control treatment (C) and between two experimental treatments only when both experimental treatments are superior to the control treatment. We propose a self-controlled design, which equally randomizes to four arms to adjust for the dominant hand effect: Arm 1: E1 for right hand, C for left hand; Arm 2: C for right hand, E1 for left hand; Arm 3: E2 for right hand, C for left hand; and Arm 4: C for right hand, E2 for left hand. We compare operating characteristics of the proposed design with the three-arm parallel design in which the same treatment is performed in both hands by participants. We also assess three proposed analysis methods for comparisons between experimental treatments in the self-controlled design under several conditions of correlations between right and left hands using simulation studies. RESULTS: The simulation studies showed that the proposed design was more powerful than the three-arm parallel design when correlation was 0.3 or higher. For comparisons between experimental treatments, the methods based on the regression model, including the outcome of hands with C as a covariate, had the highest power under modest to high correlation among the analysis methods in the self-controlled design. CONCLUSION: The proposed design can improve the power for comparing between two experimental treatments and the control treatment. Our design is useful in situations where it is undesirable for participants to receive different experimental treatments in both hands for practical reasons.

Comparing Generalized Estimating Equation and Linear Mixed Effects Model for Estimating Marginal Association with Bivariate Continuous Outcomes.

PURPOSE: Both linear regression with generalized estimating equations (GEE) and linear mixed-effects models (LMEM) can be used to estimate the marginal association of an exposure with clustered continuous outcomes. This study compares their performance for bivariate continuous outcomes which are common in eye studies. METHODS: Parametric and non-parametric simulations were used to compare the GEE models including independent, exchangeable, and unstructured working correlation structures and LMEM including random intercept only and random intercept and slope models in R and SAS. Data generation referenced the data distributions from a real-world study for estimating ocular structure-visual function relationships in patients with retinitis pigmentosa. RESULTS: From both parametric and non-parametric simulations, comparing the random intercept LMEM and GEE exchangeable model, bias was similar; coverage probability of the 95% confidence interval (CI) from the random intercept LMEM was often closer to 95%, especially when the sample size was small; the power for testing the association of the exposure was higher from the GEE exchangeable model, but its type-I error rate might be inflated especially when the sample size was small. The type-I error rate from the random intercept LMEM was closer to 0.05, but it might be under 0.05 and coverage probability might be over 95%. The GEE independent model performed worst and the LMEM with both random intercept and slope might not converge. CONCLUSION: To estimate marginal exposure-outcome association with bivariate continuous outcomes, the random intercept LMEM may be preferred. It has the best coverage probability of 95% CI and is the only model with correct type-I error rates in this study. However, it may have low power and overly wide CI in studies with small sample size or low inter-eye correlation.

A model selection criterion for clustered survival analysis with informative cluster size.

We propose a model selection criterion for correlated survival data when the cluster size is informative to the outcome. This approach, called Resampling Cluster Survival Information Criterion (RCSIC), uses the Cox proportional hazards model that is weighted with the inverse of the cluster size. The RCSIC based on the within-cluster resampling idea takes into account the possible variability of the within-cluster subsampling and the possible informativeness of cluster sizes. The RCSIC allows for easy execution for the within-cluster resampling idea without a large number of resamples of the data. In contrast with the traditional model selection method in survival analysis, the RCSIC has an additional penalization for the within-cluster subsampling variability. Our simulations show the satisfactory results where the RCSIC provides a more robust power for variable selection in terms of clustered survival analysis, regardless of whether informative cluster size exists or not. Applying the RCSIC method to a periodontal disease studies, we identify the tooth loss in patients associated with the risk factors, Age, Filled Tooth, Molar, Crown, Decayed Tooth, and Smoking Status, respectively.

Bottom-up uncertainty evaluation of complex measurements from correlated performance data: Determination of total Cr in yeast by ICP-MS after acid digestion.

The objective interpretation of a measurement result requires knowing the associated uncertainty. The cost-effective collection of measurement performance data on the same day produces correlated values that can affect measurement uncertainty evaluation. This work describes a novel methodology for the bottom-up evaluation of measurements based on complex sample pretreatment and the instrumental quantification of the prepared sample applicable to correlated inputs. The numerical Kragten method is used to combine the uncertainty components shared in various analyte recovery determinations. The developed methodology was applied to the determination of total chromium in yeast samples by ICP-MS after microwave-assisted acid digestion. The developed analysis of yeast samples is fit for monitoring the contamination of this product since it is associated with a relative expanded uncertainty, U', lower than 20%, ranging from 8.4% to 10.0% in determinations of Cr between 0.125 mg/kg and 305.5 mg/kg. Duplicate analyses are adequate for reference materials production (U' < 7%).

Modeling noisy time-series data of crime with stochastic differential equations.

We develop and calibrate stochastic continuous models that capture crime dynamics in the city of Valencia, Spain. From the emergency phone, data corresponding to three crime events, aggressions, stealing and women alarms, are available from the year 2010 until 2020. As the resulting time series, with monthly counts, are highly noisy, we decompose them into trend and seasonality parts. The former is modeled by geometric Brownian motions, both uncorrelated and correlated, and the latter is accommodated by randomly perturbed sine-cosine waves. Albeit simple, the models exhibit high ability to simulate the real data and show promising for crimes-interaction identification and short-term predictive policing.

A new approach to modeling positive random variables with repeated measures.

In many situations, it is common to have more than one observation per experimental unit, thus generating the experiments with repeated measures. In the modeling of such experiments, it is necessary to consider and model the intra-unit dependency structure. In the literature, there are several proposals to model positive continuous data with repeated measures. In this paper, we propose one more with the generalization of the beta prime regression model. We consider the possibility of dependence between observations of the same unit. Residuals and diagnostic tools also are discussed. To evaluate the finite-sample performance of the estimators, using different correlation matrices and distributions, we conducted a Monte Carlo simulation study. The methodology proposed is illustrated with an analysis of a real data set. Finally, we create an R package for easy access to publicly available the methodology described in this paper.

lmerSeq: an R package for analyzing transformed RNA-Seq data with linear mixed effects models.

BACKGROUND: Studies that utilize RNA Sequencing (RNA-Seq) in conjunction with designs that introduce dependence between observations (e.g. longitudinal sampling) require specialized analysis tools to accommodate this additional complexity. This R package contains a set of utilities to fit linear mixed effects models to transformed RNA-Seq counts that properly account for this dependence when performing statistical analyses. RESULTS: In a simulation study comparing lmerSeq and two existing methodologies that also work with transformed RNA-Seq counts, we found that lmerSeq was comprehensively better in terms of nominal error rate control and statistical power. CONCLUSIONS: Existing R packages for analyzing transformed RNA-Seq data with linear mixed models are limited in the variance structures they allow and/or the transformation methods they support. The lmerSeq package offers more flexibility in both of these areas and gave substantially better results in our simulations.

Evaluation of GENESIS, SAIGE, REGENIE and fastGWA-GLMM for genome-wide association studies of binary traits in correlated data.

Performing a genome-wide association study (GWAS) with a binary phenotype using family data is a challenging task. Using linear mixed effects models is typically unsuitable for binary traits, and numerical approximations of the likelihood function may not work well with rare genetic variants with small counts. Additionally, imbalance in the case-control ratios poses challenges as traditional statistical methods such as the Score test or Wald test perform poorly in this setting. In the last couple of years, several methods have been proposed to better approximate the likelihood function of a mixed effects logistic regression model that uses Saddle Point Approximation (SPA). SPA adjustment has recently been implemented in multiple software, including GENESIS, SAIGE, REGENIE and fastGWA-GLMM: four increasingly popular tools to perform GWAS of binary traits. We compare Score and SPA tests using real family data to evaluate computational efficiency and the agreement of the results. Additionally, we compare various ways to adjust for family relatedness, such as sparse and full genetic relationship matrices (GRM) and polygenic effect estimates. We use the New England Centenarian Study imputed genotype data and the Long Life Family Study whole-genome sequencing data and the binary phenotype of human extreme longevity to compare the agreement of the results and tools' computational performance. The evaluation suggests that REGENIE might not be a good choice when analyzing correlated data of a small size. fastGWA-GLMM is the most computationally efficient compared to the other three tools, but it appears to be overly conservative when applied to family-based data. GENESIS, SAIGE and fastGWA-GLMM produced similar, although not identical, results, with SPA adjustment performing better than Score tests. Our evaluation also demonstrates the importance of adjusting by full GRM in highly correlated datasets when using GENESIS or SAIGE.

Methodological Issues in Analyzing Real-World Longitudinal Occupational Health Data: A Useful Guide to Approaching the Topic.

Ever greater technological advances and democratization of digital tools such as computers and smartphones offer researchers new possibilities to collect large amounts of health data in order to conduct clinical research. Such data, called real-world data, appears to be a perfect complement to traditional randomized clinical trials and has become more important in health decisions. Due to its longitudinal nature, real-world data is subject to specific and well-known methodological issues, namely issues with the analysis of cluster-correlated data, missing data and longitudinal data itself. These concepts have been widely discussed in the literature and many methods and solutions have been proposed to cope with these issues. As examples, mixed and trajectory models have been developed to explore longitudinal data sets, imputation methods can resolve missing data issues, and multilevel models facilitate the treatment of cluster-correlated data. Nevertheless, the analysis of real-world longitudinal occupational health data remains difficult, especially when the methodological challenges overlap. The purpose of this article is to present various solutions developed in the literature to deal with cluster-correlated data, missing data and longitudinal data, sometimes overlapped, in an occupational health context. The novelty and usefulness of our approach is supported by a step-by-step search strategy and an example from the Wittyfit database, which is an epidemiological database of occupational health data. Therefore, we hope that this article will facilitate the work of researchers in the field and improve the accuracy of future studies.

A comparison of methods for multiple degree of freedom testing in repeated measures RNA-sequencing experiments.

BACKGROUND: As the cost of RNA-sequencing decreases, complex study designs, including paired, longitudinal, and other correlated designs, become increasingly feasible. These studies often include multiple hypotheses and thus multiple degree of freedom tests, or tests that evaluate multiple hypotheses jointly, are often useful for filtering the gene list to a set of interesting features for further exploration while controlling the false discovery rate. Though there are several methods which have been proposed for analyzing correlated RNA-sequencing data, there has been little research evaluating and comparing the performance of multiple degree of freedom tests across methods. METHODS: We evaluated 11 different methods for modelling correlated RNA-sequencing data by performing a simulation study to compare the false discovery rate, power, and model convergence rate across several hypothesis tests and sample size scenarios. We also applied each method to a real longitudinal RNA-sequencing dataset. RESULTS: Linear mixed modelling using transformed data had the best false discovery rate control while maintaining relatively high power. However, this method had high model non-convergence, particularly at small sample sizes. No method had high power at the lowest sample size. We found a mix of conservative and anti-conservative behavior across the other methods, which was influenced by the sample size and the hypothesis being evaluated. The patterns observed in the simulation study were largely replicated in the analysis of a longitudinal study including data from intensive care unit patients experiencing cardiogenic or septic shock. CONCLUSIONS: Multiple degree of freedom testing is a valuable tool in longitudinal and other correlated RNA-sequencing experiments. Of the methods that we investigated, linear mixed modelling had the best overall combination of power and false discovery rate control. Other methods may also be appropriate in some scenarios.

Statistical Evaluation of Correlated Measurement Data in Longitudinal Setting Based on Bilateral Corneal Cross-Linking.

PURPOSE: In ophthalmology, data from both eyes of a person are frequently included in the statistical evaluation. This violates the requirement of data independence for classical statistical tests (e.g. t-Test or analysis of variance (ANOVA)) because it is correlated data. Linear mixed models (LMM) were used as a possibility to include the data of both eyes in the statistical evaluation. METHODS: The LMM is available for a variety of statistical software such as SPSS or R. The application was applied to a retrospective longitudinal analysis of an accelerated corneal cross-linking (ACXL (9*10)) treatment in progressive keratoconus (KC) with a follow-up period of 36 months. Forty eyes of 20 patients were included, whereas sequential bilateral CXL treatment was performed within 12 months. LMM and ANOVA for repeated measurements were used for statistical evaluation of topographical and tomographical data measured by Pentacam (Oculus, Wetzlar, Germany). RESULTS: Both eyes were classified into a worse and better eye concerning corneal topography. Visual acuity, keratometric values and minimal corneal thickness were statistically significant between them at baseline (p < 0.05). A significant correlation between worse and better eye was shown (p < 0.05). Therefore, analyzing the data at each follow-up visit using ANOVA partially led to an overestimation of the statistical effect that could be avoided by using LMM. After 36 months, ACXL has significantly improved BCVA and flattened the cornea. CONCLUSION: The evaluation of data of both eyes without considering their correlation using classical statistical tests leads to an overestimation of the statistical effect, which can be avoided by using the LMM.

A state-space approach for longitudinal outcomes: An application to neuropsychological outcomes.

Longitudinal assessments are crucial in evaluating the disease state and trajectory in patients with neurodegenerative diseases. Neuropsychological outcomes measured over time often have a non-linear trajectory with autocorrelated residuals and a skewed distribution. We propose the adjusted local linear trend model, an extended state-space model in lieu of the commonly used linear mixed-effects model in modeling longitudinal neuropsychological outcomes. Our contributed model has the capability to utilize information from the stochasticity of the data while accounting for subject-specific trajectories with the inclusion of covariates and unequally spaced time intervals. The first step of model fitting involves a likelihood maximization step to estimate the unknown variances in the model before parsing these values into the Kalman filter and Kalman smoother recursive algorithms. Results from simulation studies showed that the adjusted local linear trend model is able to attain lower bias, lower standard errors, and high power, particularly in short longitudinal studies with equally spaced time intervals, as compared to the linear mixed-effects model. The adjusted local linear trend model also outperforms the linear mixed-effects model when data is missing completely at random, missing at random, and, in certain cases, even in data with missing not at random.