E-value: a superior alternative to P-value and its adjustments in DNA methylation studies.

DNA methylation plays a crucial role in transcriptional regulation. Reduced representation bisulfite sequencing (RRBS) is a technique of increasing use for analyzing genome-wide methylation profiles. Many computational tools such as Metilene, MethylKit, BiSeq and DMRfinder have been developed to use RRBS data for the detection of the differentially methylated regions (DMRs) potentially involved in epigenetic regulations of gene expression. For DMR detection tools, as for countless other medical applications, P-values and their adjustments are among the most standard reporting statistics used to assess the statistical significance of biological findings. However, P-values are coming under increasing criticism relating to their questionable accuracy and relatively high levels of false positive or negative indications. Here, we propose a method to calculate E-values, as likelihood ratios falling into the null hypothesis over the entire parameter space, for DMR detection in RRBS data. We also provide the R package 'metevalue' as a user-friendly interface to implement E-value calculations into various DMR detection tools. To evaluate the performance of E-values, we generated various RRBS benchmarking datasets using our simulator 'RRBSsim' with eight samples in each experimental group. Our comprehensive benchmarking analyses showed that using E-values not only significantly improved accuracy, area under ROC curve and power, over that of P-values or adjusted P-values, but also reduced false discovery rates and type I errors. In applications using real RRBS data of CRL rats and a clinical trial on low-salt diet, the use of E-values detected biologically more relevant DMRs and also improved the negative association between DNA methylation and gene expression.

G-optimal designs for hierarchical linear models: an equivalence theorem and a nature-inspired meta-heuristic algorithm.

Hierarchical linear models are widely used in many research disciplines and estimation issues for such models are generally well addressed. Design issues are relatively much less discussed for hierarchical linear models but there is an increasing interest as these models grow in popularity. This paper discusses the G-optimality for predicting individual parameters in such models and establishes an equivalence theorem for confirming the G-optimality of an approximate design. Because the criterion is non-differentiable and requires solving multiple nested optimization problems, it is much harder to find and study G-optimal designs analytically. We propose a nature-inspired meta-heuristic algorithm called competitive swarm optimizer (CSO) to generate G-optimal designs for linear mixed models with different means and covariance structures. We further demonstrate that CSO is flexible and generally effective for finding the widely used locally D-optimal designs for nonlinear models with multiple interacting factors and some of the random effects are correlated. Our numerical results for a few examples suggest that G and D-optimal designs may be equivalent and we establish that D and G-optimal designs for hierarchical linear models are equivalent when the models have only a random intercept only. The challenging mathematical question of whether their equivalence applies more generally to other hierarchical models remains elusive.

Optimal designs for discrete-time survival models with random effects.

This paper considers the optimal design for the frailty model with discrete-time survival endpoints in longitudinal studies. We introduce the random effects into the discrete hazard models to account for the heterogeneity between experimental subjects, which causes the observations of the same subject at the sequential time points being correlated. We propose a general design method to collect the survival endpoints as inexpensively and efficiently as possible. A cost-based generalized D ([Formula: see text])-optimal design criterion is proposed to derive the optimal designs for estimating the fixed effects with cost constraint. Different computation strategies based on grid search or particle swarm optimization (PSO) algorithm are provided to obtain generalized D ([Formula: see text])-optimal designs. The equivalence theorem for the cost-based D ([Formula: see text])-optimal design criterion is given to verify the optimality of the designs. Our numerical results indicate that the presence of the random effects has a great influence on the optimal designs. Some useful suggestions are also put forward for future designing longitudinal studies.

Meta-analysis and sensitivity analysis for multi-arm trials with selection bias.

Multi-arm trials meta-analysis is a methodology used in combining evidence based on a synthesis of different types of comparisons from all possible similar studies and to draw inferences about the effectiveness of multiple compared-treatments. Studies with statistically significant results are potentially more likely to be submitted and selected than studies with non-significant results; this leads to false-positive results. In meta-analysis, combining only the identified selected studies uncritically may lead to an incorrect, usually over-optimistic conclusion. This problem is known asbiselection bias. In this paper, we first define a random-effect meta-analysis model for multi-arm trials by allowing for heterogeneity among studies. This general model is based on a normal approximation for empirical log-odds ratio. We then address the problem of publication bias by using a sensitivity analysis and by defining a selection model to the available data of a meta-analysis. This method allows for different amounts of selection bias and helps to investigate how sensitive the main interest parameter is when compared with the estimates of the standard model. Throughout the paper, we use binary data from Antiplatelet therapy in maintaining vascular patency of patients to illustrate the methods.