Oscillabolastic model, a new model for oscillatory dynamics, applied to the analysis of Hes1 gene expression and Ehrlich ascites tumor growth.

This paper introduces a new dynamical model, called the oscillabolastic model, to analyze the dynamical behavior of biomedical data when one observes oscillatory behavior. The proposed oscillabolastic model is sufficiently flexible to represent various types of oscillatory behavior. The oscillabolastic model is applied to two sets of data. The first data set deals with the oscillabolastic modeling of Ehrlich ascites tumor cells and the second one is the oscillabolastic modeling of the mean signal intensity of Hes1 gene expression in response to serum stimulation. A generalized oscillabolastic model is also suggested to accommodate cases in which predictor variables other than time are also involved.

A New Robust Method for Nonlinear Regression.

BACKGROUND: When outliers are present, the least squares method of nonlinear regression performs poorly. The main purpose of this paper is to provide a robust alternative technique to the Ordinary Least Squares nonlinear regression method. This new robust nonlinear regression method can provide accurate parameter estimates when outliers and/or influential observations are present. METHOD: Real and simulated data for drug concentration and tumor size-metastasis are used to assess the performance of this new estimator. Monte Carlo simulations are performed to evaluate the robustness of our new method in comparison with the Ordinary Least Squares method. RESULTS: In simulated data with outliers, this new estimator of regression parameters seems to outperform the Ordinary Least Squares with respect to bias, mean squared errors, and mean estimated parameters. Two algorithms have been proposed. Additionally and for the sake of computational ease and illustration, a Mathematica program has been provided in the Appendix. CONCLUSION: The accuracy of our robust technique is superior to that of the Ordinary Least Squares. The robustness and simplicity of computations make this new technique more appropriate and useful tool for the analysis of nonlinear regressions.

Robust Logistic and Probit Methods for Binary and Multinomial Regression.

In this paper we introduce new robust estimators for the logistic and probit regressions for binary, multinomial, nominal and ordinal data and apply these models to estimate the parameters when outliers or inluential observations are present. Maximum likelihood estimates don't behave well when outliers or inluential observations are present. One remedy is to remove inluential observations from the data and then apply the maximum likelihood technique on the deleted data. Another approach is to employ a robust technique that can handle outliers and inluential observations without removing any observations from the data sets. The robustness of the method is tested using real and simulated data sets.