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Compositional data are common in many fields, both as outcomes and predictor variables. The inventory of models for the case when both the outcome and predictor variables are compositional is limited, and the existing models are often difficult to interpret in the compositional space, due to their use of complex log‐ratio transformations. We develop a transformation‐free linear regression model where the expected value of the compositional outcome is expressed as a single Markov transition from the compositional predictor. Our approach is based on estimating equations thereby not requiring complete specification of data likelihood and is robust to different data‐generating mechanisms. Our model is simple to interpret, allows for 0s and 1s in both the compositional outcome and covariates, and subsumes several interesting subcases of interest. We also develop permutation tests for linear independence and equality of effect sizes of two components of the predictor. Finally, we show that despite its simplicity, our model accurately captures the relationship between compositional data using two datasets from education and medical research. [ABSTRACT FROM AUTHOR]

This paper presents a model‐based method for clustering multivariate binary observations that incorporates constraints consistent with the scientific context. The approach is motivated by the precision medicine problem of identifying autoimmune disease patient subsets or classes who may require different treatments. We start with a family of restricted latent class models or RLCMs. However, in the motivating example and many others like it, the unknown number of classes and the definition of classes using binary states are among the targets of inference. We use a Bayesian approach to RLCMs in order to use informative prior assumptions on the number and definitions of latent classes to be consistent with scientific knowledge so that the posterior distribution tends to concentrate on smaller numbers of clusters and sparser binary patterns. The paper derives a posterior sampling algorithm based on Markov chain Monte Carlo with split‐merge updates to efficiently explore the space of clustering allocations. Through simulations under the assumed model and realistic deviations from it, we demonstrate greater interpretability of results and superior finite‐sample clustering performance for our method compared to common alternatives. The methods are illustrated with an analysis of protein data to detect clusters representing autoantibody classes among scleroderma patients. [ABSTRACT FROM AUTHOR]

Dynamic prediction of causal effects under different treatment regimens is an essential problem in precision medicine. It is challenging because the actual mechanisms of treatment assignment and effects are unknown in observational studies. We propose a multivariate generalized linear mixed-effects model and a Bayesian g-computation algorithm to calculate the posterior distribution of subgroup-specific intervention benefits of dynamic treatment regimes. Unmeasured time-invariant factors are included as subject-specific random effects in the assumed joint distribution of outcomes, time-varying confounders, and treatment assignments. We identify a sequential ignorability assumption conditional on treatment assignment heterogeneity, that is, analogous to balancing the latent treatment preference due to unmeasured time-invariant factors. We present a simulation study to assess the proposed method's performance. The method is applied to observational clinical data to investigate the efficacy of continuously using mycophenolate in different subgroups of scleroderma patients., (© The Author(s) 2024. Published by Oxford University Press on behalf of The International Biometric Society.)