It is a common practice to analyze complex longitudinal data using nonlinear mixed-effects (NLME) models with normality assumption. The NLME models with normal distributions provide the most popular framework for modeling continuous longitudinal outcomes, assuming individuals are from a homogeneous population and relying on random-effects to accommodate inter-individual variation. However, the following two issues may standout: (i) normality assumption for model errors may cause lack of robustness and subsequently lead to invalid inference and unreasonable estimates, particularly, if the data exhibit skewness and (ii) a homogeneous population assumption may be unrealistically obscuring important features of between-subject and within-subject variations, which may result in unreliable modeling results. There has been relatively few studies concerning longitudinal data with both heterogeneity and skewness features. In the last two decades, the skew distributions have shown beneficial in dealing with asymmetric data in various applications. In this article, our objective is to address the simultaneous impact of both features arisen from longitudinal data by developing a flexible finite mixture of NLME models with skew distributions under Bayesian framework that allows estimates of both model parameters and class membership probabilities for longitudinal data. Simulation studies are conducted to assess the performance of the proposed models and methods, and a real example from an AIDS clinical trial illustrates the methodology by modeling the viral dynamics to compare potential models with different distribution specifications; the analysis results are reported.
Longitudinal and time-to-event data are often observed together. Finite mixture models are currently used to analyze nonlinear heterogeneous longitudinal data, which, by releasing the homogeneity restriction of nonlinear mixed-effects (NLME) models, can cluster individuals into one of the pre-specified classes with class membership probabilities. This clustering may have clinical significance, and be associated with clinically important time-to-event data. This article develops a joint modeling approach to a finite mixture of NLME models for longitudinal data and proportional hazard Cox model for time-to-event data, linked by individual latent class indicators, under a Bayesian framework. The proposed joint models and method are applied to a real AIDS clinical trial data set, followed by simulation studies to assess the performance of the proposed joint model and a naive two-step model, in which finite mixture model and Cox model are fitted separately.
We recommend using the 60% UCL of SD, maximum SD, 80th-percentile SD, and 75th-percentile SD to calculate sample size when 1 or 2 samples, 3 samples, 4-5 samples, and more than 5 samples of data are available, respectively. Using the sample SD or average SD to calculate sample size should be avoided.
Object oriented data analysis (OODA) aims at statistically analyzing populations of complicated objects. This paper is motivated by a study of cell images in cell culture biology, which highlights a common critical issue: choice of data objects. Instead of conventionally treating either the individual cells or the wells (a container in which the cells are grown) as data objects, a new type of data object is proposed, that is the union of a well with its corresponding set of cells. This paper contains two parts. The first part is the image data analysis, which suggests empirically that the cell-well unions can be a better choice of data objects than the cells or the wells alone. The second part discusses the benefit of choosing cell-well unions as data objects using an illustrative example and simulations. This research suggests that OODA is not simply a frame work for understanding the structure of the data analysis. It leads to useful interdisciplinary discussion that gives better results through more appropriate choice of data objects, especially for complex data analyses.
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