Testing for spatial correlation in nonstationary binary data, with application to aberrant crypt foci in colon carcinogenesis

Modeling clinical outcome using multiple correlated functional biomarkers: A Bayesian approach

In some biomedical studies, biomarkers are measured repeatedly along some spatial structure or over time and are subject to measurement error. In these studies, it is often of interest to evaluate associations between a clinical endpoint and these biomarkers (also known as functional biomarkers). There are potentially two levels of correlation in such data, namely, between repeated measurements of a biomarker from the same subject and between multiple biomarkers from the same subject; none of the existing methods accounts for correlation between multiple functional biomarkers. We propose a Bayesian approach to model a clinical outcome of interest (e.g. risk for colorectal cancer) in the presence of multiple functional biomarkers while accounting for potential correlation. Our simulations show that the proposed approach achieves good performance in finite samples under various settings. In the presence of substantial or moderate correlation, the proposed approach outperforms an existing approach that does not account for correlation. The proposed approach is applied to a study of biomarkers of risk for colorectal neoplasms and our results show that the risk for colorectal cancer is associated with two functional biomarkers, APC and TGF-α, in particular, with their values in the region between the proliferating and differentiating zones of colorectal crypts.

Semiparametric estimation for joint modeling of colorectal cancer risk and functional biomarkers measured with errors

This research is motivated by a pilot colorectal adenoma study, where the outcome of interest is the presence of colorectal adenoma representing risk for colorectal cancer, and the predictors of interest are protein biomarkers that are repeatedly measured with errors along the length of a microscopic structure in the human colon, the colon crypt. Biomarkers of this type are referred to as functional biomarkers. The investigators are interested in identifying features of functional biomarkers that are associated with risk for colorectal cancer. In this paper, we investigate a joint modeling approach, where the binary clinical outcome is modeled using a logistic regression model with the unobserved true functional biomarkers as the predictors. Most existing methods are developed either for linear models or for functional biomarkers measured without errors and cannot be directly applied to our data. The applicable methods include a two-step method and a maximum likelihood method, which have some limitations. We propose a robust semiparametric method to overcome the limitations of the existing methods. We study the properties of the proposed method, and show in simulations that it compares favorably with other methods and also offers significant savings in CPU time. We analyze the pilot colorectal adenoma data and show that expression levels of AFC, a tumor suppressor gene, in the transitional area from the proliferation zone to the differentiation zone of colon crypts are likely to be associated with risk for colorectal cancer. Given the relatively small sample size in the pilot study, our results need to be validated in the future full-scale studies.

Relative contributions of organ shape and receptor arrangement to the design of cricket's cercal system

Understanding the relative contributions of the shape of a sensory organ and the arrangement of receptors to the overall performance of the organ has long been a challenge for sensory biologists. We tackled this issue using the wind-sensing system of crickets, the cerci, two conical abdominal appendages covered with arrays of filiform hairs. Scanning electron microscopy coupled with 3D reconstruction methods were used for mapping of all cercal filiform hairs. The hairs are arranged according to their diameter in a way that avoids collisions with neighbours during hair deflection: long hairs are regularly spaced, whereas short hairs are both randomly and densely distributed. Particle image velocimetry showed that the variation in diameter of the cercus along its length modifies the pattern of fluid velocities. Hairs are subject to higher air flow amplitudes at the base than at the apex of the cercus. The relative importance of interactions between receptors and the air flow around the organ may explain the performance of the cricket's cercal system: it is characterised by a high density of statistically non-interacting short hairs located at the base of the cercus where sensitivity to air currents is the highest.

Aberrant crypt foci and semiparametric modeling of correlated binary data

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.

Ontogeny of air-motion sensing in cricket

Juvenile crickets suffer high rates of mortality by natural predators that they can detect using extremely sensitive air-sensing filiform hairs located on their cerci. Although a huge amount of knowledge has accumulated on the physiology, the neurobiology and the biomechanics of this sensory system in adults, the morphological and functional aspects of air sensing have not been as well studied in earlier life history stages. Using scanning electronic microscopy, we performed a survey of all cercal filiform hairs in seven instars of the wood cricket (Nemobius sylvestris). Statistical analyses allowed us to quantify profound changes in the number, the length and the distribution of cercal hairs during development. Of particular importance,we found a fivefold increase in hair number and the development of a bimodal length-frequency distribution of cercal hairs from the second instar onwards. Based on theoretical estimations of filiform hair population coding, we found that the cercal system is functional for a wide range of frequencies of biologically relevant oscillatory flows, even from the first instar. As the cricket develops, the overall sensitivity of the cercal system increases as a result of the appearance of new hairs, but the value of the best tuned frequency remains fixed between 150 and 180 Hz after the second instar. These frequencies nicely match those emitted by natural flying predators, suggesting that the development of the cercal array of hairs may have evolved in response to such signals.

Spatial Correlation of Gene Expression Measures in Tissue Microarray Core Analysis

Tissue microarrays (TMAs) make possible the screening of hundreds of different tumour samples for the expression of a specific protein. Automatic features extraction procedures lead to a series of covariates corresponding to the averaged stained scores. In this article, we model the random geometry of TMA cores using voronoi tesselations. This formalism enables the computation of indices of spatial correlation of stained scores using both classical and novel approaches. The potential of these spatial statistics to correctly discriminate between diseased and non-diseased cases is evaluated through the analysis of a TMA containing samples of breast carcinoma data. The results indicate a significant improvement in the breast cancer prognosis.