Aberrant crypt foci and semiparametric modeling of correlated binary data

Summary .   Motivated by the spatial modeling of aberrant crypt foci (ACF) in colon carcinogenesis, we consider binary data with probabilities modeled as the sum of a nonparametric mean plus a latent Gaussian spatial process that accounts for short-range dependencies. The mean is modeled in a general way using regression splines. The mean function can be viewed as a fixed effect and is estimated with a penalty for regularization. With the latent process viewed as another random effect, the model becomes a generalized linear mixed model. In our motivating data set and other applications, the sample size is too large to easily accommodate maximum likelihood or restricted maximum likelihood estimation (REML), so pairwise likelihood, a special case of composite likelihood, is used instead. We develop an asymptotic theory for models that are sufficiently general to be used in a wide variety of applications, including, but not limited to, the problem that motivated this work. The splines have penalty parameters that must converge to zero asymptotically: we derive theory for this along with a data-driven method for selecting the penalty parameter, a method that is shown in simulations to improve greatly upon standard devices, such as likelihood crossvalidation. Finally, we apply the methods to the data from our experiment ACF. We discover an unexpected location for peak formation of ACF.     

Bayesian hierarchical spatially correlated functional data analysis with application to colon carcinogenesis

Summary .   In this article, we present new methods to analyze data from an experiment using rodent models to investigate the role of p27, an important cell-cycle mediator, in early colon carcinogenesis. The responses modeled here are essentially functions nested within a two-stage hierarchy. Standard functional data analysis literature focuses on a single stage of hierarchy and conditionally independent functions with near white noise. However, in our experiment, there is substantial biological motivation for the existence of spatial correlation among the functions, which arise from the locations of biological structures called colonic crypts: this possible functional correlation is a phenomenon we term crypt signaling . Thus, as a point of general methodology, we require an analysis that allows for functions to be correlated at the deepest level of the hierarchy. Our approach is fully Bayesian and uses Markov chain Monte Carlo methods for inference and estimation. Analysis of this data set gives new insights into the structure of p27 expression in early colon carcinogenesis and suggests the existence of significant crypt signaling. Our methodology uses regression splines, and because of the hierarchical nature of the data, dimension reduction of the covariance matrix of the spline coefficients is important: we suggest simple methods for overcoming this problem.     

Testing the correlation for clustered categorical and censored discrete time-to-event data when covariates are measured without/with errors

In the analysis of clustered categorical data, it is of common interest to test for the correlation within clusters, and the heterogeneity across different clusters. We address this problem by proposing a class of score tests for the null hypothesis that the variance components are zero in random effects models, for clustered nominal and ordinal categorical responses. We extend the results to accommodate clustered censored discrete time-to-event data. We next consider such tests in the situation where covariates are measured with errors. We propose using the SIMEX method to construct the score tests for the null hypothesis that the variance components are zero. Key advantages of the proposed score tests are that they can be easily implemented by fitting standard polytomous regression models and discrete failure time models, and that they are robust in the sense that no assumptions need to be made regarding the distributions of the random effects and the unobserved covariates. The asymptotic properties of the proposed tests are studied. We illustrate these tests by analyzing two data sets and evaluate their performance with simulations.