The beta distribution is a versatile function that accommodates a broad range of probability distribution shapes. Beta regression based on the beta distribution can be used to model a response variable y that takes values in open unit interval (0, 1). Zero/one inflated beta (ZOIB) regression models can be applied when y takes values from closed unit interval [0, 1]. The ZOIB model is based a piecewise distribution that accounts for the probability mass at 0 and 1, in addition to the probability density within (0, 1). This paper introduces an R packagezoib that provides Bayesian inferences for a class of ZOIB models. The statistical methodology underlying the zoib package is discussed, the functions covered by the package are outlined, and the usage of the package is illustrated with three examples of different data and model types. The package is comprehensive and versatile in that it can model data with or without inflation at 0 or 1, accommodate clustered and correlated data via latent variables, perform penalized regression as needed, and allow for model comparison via the computation of the DIC criterion.
Species sensitivity distribution (SSD) is the most common method used to derive water quality criteria, but there are still issues to be resolved. Here, issues associated with application of SSD methods, including species selection, plotting position, and cutoff point setting, are addressed. A preliminary improvement to the SSD approach based on post-stratified sampling theory is proposed. In the improved method, selection of species is based on biota of a specific basin, and the whole species in the specific ecosystem are considered. After selecting species to be included and calculating the cumulative probability, a new method to set the critical threshold for protection of ecosystem-level structure and function is proposed. The alternative method was applied in a case study in which a water quality criterion (WQC) was derived for ammonia in the Songhua River (SHR), China.
The 2‐in‐1 adaptive design allows seamless expansion of an ongoing Phase II trial into a Phase III trial to expedite a drug development program. Since its publication, it has generated a lot of interest. So far, most of the related research focused on type I error control. Similar to most adaptive designs, 2‐in‐1 design could also pose a great challenge on estimation of treatment effect due to the data‐driven adaptation. In addition, the use of intermediate endpoint for interim adaptive decision‐making is a less well‐studied field. In this paper, we investigate the bias and variances in estimation for 2‐in‐1 design and some of its extensions, and propose some bias‐adjusted estimators for 2‐in‐1 design. The properties of the proposed estimators are further studied theoretically and/or numerically, so as to provide guidance on how to interpret the estimated treatment effect of 2‐in‐1 design.
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