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Linear mixed models are commonly used in analyzing stepped-wedge cluster randomized trials. A key consideration for analyzing a stepped-wedge cluster randomized trial is accounting for the potentially complex correlation structure, which can be achieved by specifying random-effects. The simplest random effects structure is random intercept but more complex structures such as random cluster-by-period, discrete-time decay, and more recently, the random intervention structure, have been proposed. Specifying appropriate random effects in practice can be challenging: assuming more complex correlation structures may be reasonable but they are vulnerable to computational challenges. To circumvent these challenges, robust variance estimators may be applied to linear mixed models to provide consistent estimators of standard errors of fixed effect parameters in the presence of random-effects misspecification. However, there has been no empirical investigation of robust variance estimators for stepped-wedge cluster randomized trials. In this article, we review six robust variance estimators (both standard and small-sample bias-corrected robust variance estimators) that are available for linear mixed models in R, and then describe a comprehensive simulation study to examine the performance of these robust variance estimators for stepped-wedge cluster randomized trials with a continuous outcome under different data generators. For each data generator, we investigate whether the use of a robust variance estimator with either the random intercept model or the random cluster-by-period model is sufficient to provide valid statistical inference for fixed effect parameters, when these working models are subject to random-effect misspecification. Our results indicate that the random intercept and random cluster-by-period models with robust variance estimators performed adequately. The CR3 robust variance estimator (approximate jackknife) estimator, coupled with the number of clusters minus two degrees of freedom correction, consistently gave the best coverage results, but could be slightly conservative when the number of clusters was below 16. We summarize the implications of our results for the linear mixed model analysis of stepped-wedge cluster randomized trials and offer some practical recommendations on the choice of the analytic model. [ABSTRACT FROM AUTHOR]

We propose the "Marshall–Olkin Bivariate Weibull Model with Modified Singularity MOBW- μ ", which focuses on bivariate distributions essential for reliability and survival analyses. Distributions such as the Marshall–Olkin bivariate exponential (MOBE) and the Marshall–Olkin bivariate Weibull (MOBW) are discussed. The MOBW- μ model is introduced, which incorporates a lag parameter μ in the singular part, and probabilistic properties such as the joint survival function, marginal density functions, and the bivariate hazard rate function are explored. In addition, aspects such as the correlation structure and survival copulation are addressed and we show that the correlation of the MOBW- μ is always lower than that of its copula, regardless of the parameters. The latter result implies that the MOBW- μ does not have the Lancaster's phenomenon that explains that any nonlinear transformation of variables decreases the correlation in absolute value. The article concludes by presenting a robust theoretical framework applicable to various disciplines. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the reaction-diffusion equation subject to Dirichlet and Neumann boundary conditions where the input function on the boundary is randomly fluctuated. First we study the fundamental case when this function is a white noise. Explicit form of the correlation function is derived for the reaction-diffusion equation in a half-plane. In this case we obtain the Karhunen–Loève expansion (KL) of the solution which is a partially homogeneous random field, i.e., it is homogeneous along the horizontal direction, and is inhomogeneous in the vertical direction. Then, based on this representation, we extend this result to the general case when the function prescribed on the boundary is an arbitrary homogeneous random field. [ABSTRACT FROM AUTHOR]

The study proposes a two-step hybrid methodology for sparse generalized estimation equations modeling of the drivers of shareholder value creation. Through the methodology, the validity of the Gordon constant growth model is established and other non-dividend factors’ contribution to shareholder value creation is assessed. The two-step hybrid method involves picking out the right intra-subject correlation matrix and set of regressors using EAIC and QIC respectively (EAIC-QIC) and then obtaining the penalized GEE estimators of the selected model. Penalization is useful in removing redundant regressors from the final model. The performance of the proposed method was compared to that of exclusively using QIC method in selecting both the correlation matrix and set of regressors. The study results showed that, whereas EAIC preferred the parsimonious order one auto-aggressive {AR(1)} structure for the data, QIC preferred the unstructured matrix which estimates the highest number of correlation parameters. Using the AR(1) structure and Algorithm 2, the GEE model chosen had higher efficiency compared to when QIC is used to select both the correlation matrix and regressors. Based on the results, the study concludes that adopting hybrid methods enhances efficiency of GEE estimators. On firm value, the study concludes that besides the elements in the Gordon-Constant growth model, the financial health of a firm is a vital indicator of value creation ability by firms. [ABSTRACT FROM AUTHOR]

We propose the “Marshall–Olkin Bivariate Weibull Model with Modified Singularity MOBW-μ”, which focuses on bivariate distributions essential for reliability and survival analyses. Distributions such as the Marshall–Olkin bivariate exponential (MOBE) and the Marshall–Olkin bivariate Weibull (MOBW) are discussed. The MOBW-μ model is introduced, which incorporates a lag parameter μ in the singular part, and probabilistic properties such as the joint survival function, marginal density functions, and the bivariate hazard rate function are explored. In addition, aspects such as the correlation structure and survival copulation are addressed and we show that the correlation of the MOBW-μ is always lower than that of its copula, regardless of the parameters. The latter result implies that the MOBW-μ does not have the Lancaster’s phenomenon that explains that any nonlinear transformation of variables decreases the correlation in absolute value. The article concludes by presenting a robust theoretical framework applicable to various disciplines.