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:[email protected] 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.Development and application of statistical models for medical scientific researc

Pathway analysis for family data using nested random-effects models

Recently we proposed a novel two-step approach to test for pathway effects in disease progression. The goal of this approach is to study the joint effect of multiple single-nucleotide polymorphisms that belong to certain genes. By using random effects, our approach acknowledges the correlations within and between genes when testing for pathway effects. Gene-gene and gene-environment interactions can be included in the model. The method can be implemented with standard software, and the distribution of the test statistics under the null hypothesis can be approximated by using standard chi-square distributions. Hence no extensive permutations are needed for computations of the p-value. In this paper we adapt and apply the method to family data, and we study its performance for sequence data from Genetic Analysis Workshop 17. For the set of unrelated subjects, the performance of the new test was disappointing. We found a power of 6% for the binary outcome and of 18% for the quantitative trait Q1. For family data the new approach appears to perform well, especially for the quantitative outcome. We found a power of 39% for the binary outcome and a power of 89% for the quantitative trait Q1

Corrigendum to: Poisson-Tweedie mixed-effects model: a flexible approach for the analysis of longitudinal RNA-seq data (Aug, 10.1177/1471082X20936017, 2020)

Functional Genomics of Muscle, Nerve and Brain Disorder

Gene analysis for longitudinal family data using random-effects models

We have extended our recently developed 2-step approach for gene-based analysis to the family design and to the analysis of rare variants. The goal of this approach is to study the joint effect of multiple single-nucleotide polymorphisms that belong to a gene. First, the information in a gene is summarized by 2 variables, namely the empirical Bayes estimate capturing common variation and the number of rare variants. By using random effects for the common variants, our approach acknowledges the within-gene correlations. In the second step, the 2 summaries were included as covariates in linear mixed models. To test the null hypothesis of no association, a multivariate Wald test was applied. We analyzed the simulated data sets to assess the performance of the method. Then we applied the method to the real data set and identified a significant association between FRMD4B and diastolic blood pressure (p-value = 8.3 × 10(-12))

A bi-dimensional finite mixture model for longitudinal data subject to dropout

In longitudinal studies, subjects may be lost to follow-up, or miss some of the planned visits, leading to incomplete response sequences. When the probability of non-response, conditional on the available covariates and the observed responses, still depends on unobserved outcomes, the dropout mechanism is said to be non ignorable. A common objective is to build a reliable association structure to account for dependence between the longitudinal and the dropout processes. Starting from the existing literature, we introduce a random coefficient based dropout model where the association between outcomes is modeled through discrete latent effects. These effects are outcome-specific and account for heterogeneity in the univariate profiles. Dependence between profiles is introduced by using a bi-dimensional representation for the corresponding distribution. In this way, we define a flexible latent class structure which allows to efficiently describe both dependence within the two margins of interest and dependence between them. By using this representation we show that, unlike standard (unidimensional) finite mixture models, the non ignorable dropout model properly nests its ignorable counterpart. We detail the proposed modeling approach by analyzing data from a longitudinal study on the dynamics of cognitive functioning in the elderly. Further, the effects of assumptions about non ignorability of the dropout process on model parameter estimates are (locally) investigated using the index of (local) sensitivity to non-ignorability

Pathway testing for longitudinal metabolomics

We propose a top-down approach for pathway analysis of longitudinal metabolite data. We apply a score test based on a shared latent process mixed model which can identify pathways with differentially progressing metabolites. The strength of our approach is that it can handle unbalanced designs, deals with potential missing values in the longitudinal markers, and gives valid results even with small sample sizes. Contrary to bottom-up approaches, correlations between metabolites are explicitly modeled leveraging power gains. For large pathway sizes, a computationally efficient solution is proposed based on pseudo-likelihood methodology. We demonstrate the advantages of the proposed method in identification of differentially expressed pathways through simulation studies. Finally, longitudinal metabolite data from a mice experiment is analyzed to demonstrate our methodology.Functional Genomics of Muscle, Nerve and Brain Disorder

Plasma lipidomic analysis shows a disease progression signature in mdx mice

Duchenne muscular dystrophy (DMD) is a rare genetic disorder affecting paediatric patients. The disease course is characterized by loss of muscle mass, which is rapidly substituted by fibrotic and adipose tissue. Clinical and preclinical models have clarified the processes leading to muscle damage and myofiber degeneration. Analysis of the fat component is however emerging as more evidence shows how muscle fat fraction is associated with patient performance and prognosis. In this article we aimed to study whether alterations exist in the composition of lipids in plasma samples obtained from mouse models. Analysis of plasma samples was performed in 4 mouse models of DMD and wild-type mice by LC-MS. Longitudinal samplings of individual mice covering an observational period of 7 months were obtained to cover the different phases of the disease. We report clear elevation of glycerolipids and glycerophospholipids families in dystrophic mice compared to healthy mice. Triacylglycerols were the strongest contributors to the signatures in mice. Annotation of individual lipids confirmed the elevation of lipids belonging to these families as strongest discriminants between healthy and dystrophic mice. A few sphingolipids (such as ganglioside GM2, sphingomyelin and ceramide), sterol lipids (such as cholesteryl oleate and cholesteryl arachidonate) and a fatty acyl (stearic acid) were also found to be affected in dystrophic mice. Analysis of serum and plasma samples show how several lipids are affected in dystrophic mice affected by muscular dystrophy. This study sets the basis to further investigations to understand how the lipid signature relates to the disease biology and muscle performance.Development and application of statistical models for medical scientific researc

Long-term effect of α1-antitrypsin augmentation therapy on the decline of FEV1 in deficient patients: an analysis of the AIR database

Lung structure and function; COPD and smokingEstructura y función pulmonar; EPOC y tabaquismoEstructura i funció pulmonar; MPOC i tabaquismeBackground Patients with ZZ (Glu342Lys) α-1-antitrypsin deficiency (ZZ-AATD) who received augmentation therapy with α-1-antitrypsin (AAT) in randomised controlled trials over 2–3 years failed to show a significant reduction of the annual decline of forced expiratory volume in 1 s (FEV1). Methods To compare the trajectory of FEV1 change during 4 or more years in ZZ-AATD patients with emphysema receiving or not receiving intravenous augmentation therapy, a retrospective analysis of FEV1 values entered in the Alpha-1 International Registry (AIR) of ZZ-AATD patients from five different European countries (Germany, UK, Spain, Italy and the Netherlands) was performed. The post-bronchodilator FEV1 % predicted values for baseline and follow-up over time from patients were analysed using linear mixed effects models. Results Data of 374 patients were analysed: 246 untreated and 128 treated with intravenous AAT augmentation therapy. The mean±sd follow-up duration of the untreated group was 8.60±3.34 years and 8.59±2.62 years for the treated group. The mixed effects model analysis showed a mean FEV1 decline of −0.931% predicted per year (95% CI −1.144 to −0.718) in the untreated group and a decline of −1.016% predicted per year (95% CI −1.319 to −0.7145) in the treated group. The likelihood ratio test showed no difference between the two groups (p=0.71). Conclusion In our study population, we could not detect a significant difference in the annual decline of FEV1 by AAT augmentation treatment over a mean period of 8.6 years. Other approaches are needed to validate any benefit of augmentation therapy.This study was supported by Stichting AIR

A shared-parameter continuous-time hidden Markov and survival model for longitudinal data with informative dropout

A shared-parameter approach for jointly modeling longitudinal and survival data is proposed. With respect to available approaches, it allows for time-varying random effects that affect both the longitudinal and the survival processes. The distribution of these random effects is modeled according to a continuous-time hidden Markov chain so that transitions may occur at any time point. For maximum likelihood estimation, we propose an algorithm based on a discretization of time until censoring in an arbitrary number of time windows. The observed information matrix is used to obtain standard errors. We illustrate the approach by simulation, even with respect to the effect of the number of time windows on the precision of the estimates, and by an application to data about patients suffering from mildly dilated cardiomyopathy