Meta-analysis of Proportions Using Generalized Linear Mixed Models.
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ABSTRACT:
SUBMITTER: Lin L
PROVIDER: S-EPMC7398826 | biostudies-literature |
REPOSITORIES: biostudies-literature
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Project description:The use of digital PCR for quantification of nucleic acids is rapidly growing. A major drawback remains the lack of flexible data analysis tools. Published analysis approaches are either tailored to specific problem settings or fail to take into account sources of variability. We propose the generalized linear mixed models framework as a flexible tool for analyzing a wide range of experiments. We also introduce a method for estimating reference gene stability to improve accuracy and precision of copy number and relative expression estimates. We demonstrate the usefulness of the methodology on a complex experimental setup.
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Project description:BACKGROUND:Renal transplant patients are mandated to have continuous assessment of their kidney function over time to monitor disease progression determined by changes in blood urea nitrogen (BUN), serum creatinine (Cr), and estimated glomerular filtration rate (eGFR). Multivariate analysis of these outcomes that aims at identifying the differential factors that affect disease progression is of great clinical significance. Thus our study aims at demonstrating the application of different joint modeling approaches with random coefficients on a cohort of renal transplant patients and presenting a comparison of their performance through a pseudo-simulation study. The objective of this comparison is to identify the model with best performance and to determine whether accuracy compensates for complexity in the different multivariate joint models. METHODS AND RESULTS:We propose a novel application of multivariate Generalized Linear Mixed Models (mGLMM) to analyze multiple longitudinal kidney function outcomes collected over 3 years on a cohort of 110 renal transplantation patients. The correlated outcomes BUN, Cr, and eGFR and the effect of various covariates such patient's gender, age and race on these markers was determined holistically using different mGLMMs. The performance of the various mGLMMs that encompass shared random intercept (SHRI), shared random intercept and slope (SHRIS), separate random intercept (SPRI) and separate random intercept and slope (SPRIS) was assessed to identify the one that has the best fit and most accurate estimates. A bootstrap pseudo-simulation study was conducted to gauge the tradeoff between the complexity and accuracy of the models. Accuracy was determined using two measures; the mean of the differences between the estimates of the bootstrapped datasets and the true beta obtained from the application of each model on the renal dataset, and the mean of the square of these differences. The results showed that SPRI provided most accurate estimates and did not exhibit any computational or convergence problem. CONCLUSION:Higher accuracy was demonstrated when the level of complexity increased from shared random coefficient models to the separate random coefficient alternatives with SPRI showing to have the best fit and most accurate estimates.
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Project description:BACKGROUND:Systematic reviews and meta-analyses of binary outcomes are widespread in all areas of application. The odds ratio, in particular, is by far the most popular effect measure. However, the standard meta-analysis of odds ratios using a random-effects model has a number of potential problems. An attractive alternative approach for the meta-analysis of binary outcomes uses a class of generalized linear mixed models (GLMMs). GLMMs are believed to overcome the problems of the standard random-effects model because they use a correct binomial-normal likelihood. However, this belief is based on theoretical considerations, and no sufficient simulations have assessed the performance of GLMMs in meta-analysis. This gap may be due to the computational complexity of these models and the resulting considerable time requirements. METHODS:The present study is the first to provide extensive simulations on the performance of four GLMM methods (models with fixed and random study effects and two conditional methods) for meta-analysis of odds ratios in comparison to the standard random effects model. RESULTS:In our simulations, the hypergeometric-normal model provided less biased estimation of the heterogeneity variance than the standard random-effects meta-analysis using the restricted maximum likelihood (REML) estimation when the data were sparse, but the REML method performed similarly for the point estimation of the odds ratio, and better for the interval estimation. CONCLUSIONS:It is difficult to recommend the use of GLMMs in the practice of meta-analysis. The problem of finding uniformly good methods of the meta-analysis for binary outcomes is still open.
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Project description:BACKGROUND:Power analysis becomes an inevitable step in experimental design of current biomedical research. Complex designs allowing diverse correlation structures are commonly used in RNA-Seq experiments. However, the field currently lacks statistical methods to calculate sample size and estimate power for RNA-Seq differential expression studies using such designs. To fill the gap, simulation based methods have a great advantage by providing numerical solutions, since theoretical distributions of test statistics are typically unavailable for such designs. RESULTS:In this paper, we propose a novel simulation based procedure for power estimation of differential expression with the employment of generalized linear mixed effects models for correlated expression data. We also propose a new procedure for power estimation of differential expression with the use of a bivariate negative binomial distribution for paired designs. We compare the performance of both the likelihood ratio test and Wald test under a variety of simulation scenarios with the proposed procedures. The simulated distribution was used to estimate the null distribution of test statistics in order to achieve the desired false positive control and was compared to the asymptotic Chi-square distribution. In addition, we applied the procedure for paired designs to the TCGA breast cancer data set. CONCLUSIONS:In summary, we provide a framework for power estimation of RNA-Seq differential expression under complex experimental designs. Simulation results demonstrate that both the proposed procedures properly control the false positive rate at the nominal level.
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Project description:We investigated the relationship between reported cases of influenza in Catalonia (Spain). Covariates analyzed were: population, age, data of report of influenza, and health region during 2010-2014 using data obtained from the SISAP program (Institut Catala de la Salut - Generalitat of Catalonia). Reported cases were related with the study of covariates using a descriptive analysis. Generalized Linear Models, Generalized Additive Models and Generalized Additive Mixed Models were used to estimate the evolution of the transmission of influenza. Additive models can estimate non-linear effects of the covariates by smooth functions; and mixed models can estimate data dependence and variability in factor variables using correlations structures and random effects, respectively. The incidence rate of influenza was calculated as the incidence per 100 000 people. The mean rate was 13.75 (range 0-27.5) in the winter months (December, January, February) and 3.38 (range 0-12.57) in the remaining months. Statistical analysis showed that Generalized Additive Mixed Models were better adapted to the temporal evolution of influenza (serial correlation 0.59) than classical linear models.
| S-EPMC4514424 | biostudies-other
Project description:Generalized linear mixed models (GLMMs) continue to grow in popularity due to their ability to directly acknowledge multiple levels of dependency and model different data types. For small sample sizes especially, likelihood-based inference can be unreliable with variance components being particularly difficult to estimate. A Bayesian approach is appealing but has been hampered by the lack of a fast implementation, and the difficulty in specifying prior distributions with variance components again being particularly problematic. Here, we briefly review previous approaches to computation in Bayesian implementations of GLMMs and illustrate in detail, the use of integrated nested Laplace approximations in this context. We consider a number of examples, carefully specifying prior distributions on meaningful quantities in each case. The examples cover a wide range of data types including those requiring smoothing over time and a relatively complicated spline model for which we examine our prior specification in terms of the implied degrees of freedom. We conclude that Bayesian inference is now practically feasible for GLMMs and provides an attractive alternative to likelihood-based approaches such as penalized quasi-likelihood. As with likelihood-based approaches, great care is required in the analysis of clustered binary data since approximation strategies may be less accurate for such data.
| S-EPMC2883299 | biostudies-literature
Project description:'Will my study answer my research question?' is the most fundamental question a researcher can ask when designing a study, yet when phrased in statistical terms - 'What is the power of my study?' or 'How precise will my parameter estimate be?' - few researchers in ecology and evolution (EE) try to answer it, despite the detrimental consequences of performing under- or over-powered research. We suggest that this reluctance is due in large part to the unsuitability of simple methods of power analysis (broadly defined as any attempt to quantify prospectively the 'informativeness' of a study) for the complex models commonly used in EE research. With the aim of encouraging the use of power analysis, we present simulation from generalized linear mixed models (GLMMs) as a flexible and accessible approach to power analysis that can account for random effects, overdispersion and diverse response distributions.We illustrate the benefits of simulation-based power analysis in two research scenarios: estimating the precision of a survey to estimate tick burdens on grouse chicks and estimating the power of a trial to compare the efficacy of insecticide-treated nets in malaria mosquito control. We provide a freely available R function, sim.glmm, for simulating from GLMMs.Analysis of simulated data revealed that the effects of accounting for realistic levels of random effects and overdispersion on power and precision estimates were substantial, with correspondingly severe implications for study design in the form of up to fivefold increases in sampling effort. We also show the utility of simulations for identifying scenarios where GLMM-fitting methods can perform poorly.These results illustrate the inadequacy of standard analytical power analysis methods and the flexibility of simulation-based power analysis for GLMMs. The wider use of these methods should contribute to improving the quality of study design in EE.
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Project description:Upon a drastic change in environmental illumination, zebrafish larvae display a rapid locomotor response. This response can be simultaneously tracked from larvae arranged in multi-well plates. The resulting data have provided new insights into neuro-behaviour. The features of these data, however, present a challenge to traditional statistical tests. For example, many larvae display little or no movement. Thus, the larval responses have many zero values and are imbalanced. These responses are also measured repeatedly from the same well, which results in correlated observations. These analytical issues were addressed in this study by the generalized linear mixed model (GLMM). This approach deals with binary responses and characterizes the correlation of observations in the same group. It was used to analyze a previously reported dataset. Before applying the GLMM, the activity values were transformed to binary responses (movement vs. no movement) to reduce data imbalance. Moreover, the GLMM estimated the variations among the effects of different well locations, which would eliminate the location effects when two biological groups or conditions were compared. By addressing the data-imbalance and location-correlation issues, the GLMM effectively quantified true biological effects on zebrafish locomotor response.
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Project description:BackgroundTechnological advances involving RNA-Seq and Bioinformatics allow quantifying the transcriptional levels of genes in cells, tissues, and cell lines, permitting the identification of Differentially Expressed Genes (DEGs). DESeq2 and edgeR are well-established computational tools used for this purpose and they are based upon generalized linear models (GLMs) that consider only fixed effects in modeling. However, the inclusion of random effects reduces the risk of missing potential DEGs that may be essential in the context of the biological phenomenon under investigation. The generalized linear mixed models (GLMM) can be used to include both effects.MethodsWe present DEGRE (Differentially Expressed Genes with Random Effects), a user-friendly tool capable of inferring DEGs where fixed and random effects on individuals are considered in the experimental design of RNA-Seq research. DEGRE preprocesses the raw matrices before fitting GLMMs on the genes and the derived regression coefficients are analyzed using the Wald statistical test. DEGRE offers the Benjamini-Hochberg or Bonferroni techniques for P-value adjustment.ResultsThe datasets used for DEGRE assessment were simulated with known identification of DEGs. These have fixed effects, and the random effects were estimated and inserted to measure the impact of experimental designs with high biological variability. For DEGs' inference, preprocessing effectively prepares the data and retains overdispersed genes. The biological coefficient of variation is inferred from the counting matrices to assess variability before and after the preprocessing. The DEGRE is computationally validated through its performance by the simulation of counting matrices, which have biological variability related to fixed and random effects. DEGRE also provides improved assessment measures for detecting DEGs in cases with higher biological variability. We show that the preprocessing established here effectively removes technical variation from those matrices. This tool also detects new potential candidate DEGs in the transcriptome data of patients with bipolar disorder, presenting a promising tool to detect more relevant genes.ConclusionsDEGRE provides data preprocessing and applies GLMMs for DEGs' inference. The preprocessing allows efficient remotion of genes that could impact the inference. Also, the computational and biological validation of DEGRE has shown to be promising in identifying possible DEGs in experiments derived from complex experimental designs. This tool may help handle random effects on individuals in the inference of DEGs and presents a potential for discovering new interesting DEGs for further biological investigation.
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Project description:Niche theory predicts that species occurrence and abundance show non-linear, unimodal relationships with respect to environmental gradients. Unimodal models, such as the Gaussian (logistic) model, are however more difficult to fit to data than linear ones, particularly in a multi-species context in ordination, with trait modulated response and when species phylogeny and species traits must be taken into account. Adding squared terms to a linear model is a possibility but gives uninterpretable parameters. This paper explains why and when generalized linear mixed models, even without squared terms, can effectively analyse unimodal data and also presents a graphical tool and statistical test to test for unimodal response while fitting just the generalized linear mixed model. The R-code for this is supplied in Supplemental Information 1.
| S-EPMC3709111 | biostudies-literature