Correcting for binomial measurement error in predictors in regression with application to analysis of DNA methylation rates by bisulfite sequencing.

Motivated by a genetic application, this paper addresses the problem of fitting regression models when the predictor is a proportion measured with error. While the problem of dealing with additive measurement error in fitting regression models has been extensively studied, the problem where the additive error is of a binomial nature has not been addressed. The measurement errors here are heteroscedastic for two reasons; dependence on the underlying true value and changing sampling effort over observations. While some of the previously developed methods for treating additive measurement error with heteroscedasticity can be used in this setting, other methods need modification. A new version of simulation extrapolation is developed, and we also explore a variation on the standard regression calibration method that uses a beta-binomial model based on the fact that the true value is a proportion. Although most of the methods introduced here can be used for fitting non-linear models, this paper will focus primarily on their use in fitting a linear model. While previous work has focused mainly on estimation of the coefficients, we will, with motivation from our example, also examine estimation of the variance around the regression line. In addressing these problems, we also discuss the appropriate manner in which to bootstrap for both inferences and bias assessment. The various methods are compared via simulation, and the results are illustrated using our motivating data, for which the goal is to relate the methylation rate of a blood sample to the age of the individual providing the sample. Copyright © 2016 John Wiley & Sons, Ltd.

In silico modeling of Itk activation kinetics in thymocytes suggests competing positive and negative IP4 mediated feedbacks increase robustness.

The inositol-phosphate messenger inositol(1,3,4,5)tetrakisphosphate (IP4) is essential for thymocyte positive selection by regulating plasma-membrane association of the protein tyrosine kinase Itk downstream of the T cell receptor (TCR). IP4 can act as a soluble analog of the phosphoinositide 3-kinase (PI3K) membrane lipid product phosphatidylinositol(3,4,5)trisphosphate (PIP3). PIP3 recruits signaling proteins such as Itk to cellular membranes by binding to PH and other domains. In thymocytes, low-dose IP4 binding to the Itk PH domain surprisingly promoted and high-dose IP4 inhibited PIP3 binding of Itk PH domains. However, the mechanisms that underlie the regulation of membrane recruitment of Itk by IP4 and PIP3 remain unclear. The distinct Itk PH domain ability to oligomerize is consistent with a cooperative-allosteric mode of IP4 action. However, other possibilities cannot be ruled out due to difficulties in quantitatively measuring the interactions between Itk, IP4 and PIP3, and in generating non-oligomerizing Itk PH domain mutants. This has hindered a full mechanistic understanding of how IP4 controls Itk function. By combining experimentally measured kinetics of PLCγ1 phosphorylation by Itk with in silico modeling of multiple Itk signaling circuits and a maximum entropy (MaxEnt) based computational approach, we show that those in silico models which are most robust against variations of protein and lipid expression levels and kinetic rates at the single cell level share a cooperative-allosteric mode of Itk regulation by IP4 involving oligomeric Itk PH domains at the plasma membrane. This identifies MaxEnt as an excellent tool for quantifying robustness for complex TCR signaling circuits and provides testable predictions to further elucidate a controversial mechanism of PIP3 signaling.