Correcting for Measurement Error in Segmented Cox Model

Measurement error in the covariate of main interest (e.g. the exposure variable, or the risk factor) is common in epidemiologic and health studies. It can effect the relative risk estimator or other types of coefficients derived from the fitted regression model. In order to perform a measurement error analysis, one needs information about the error structure. Two sources of validation data are an internal subset of the main data, and external or independent study. For the both sources, the true covariate is measured (that is, without error), or alternatively, its surrogate, which is error-prone covariate, is measured several times (repeated measures). This paper compares the precision in estimation via the different validation sources in the Cox model with a changepoint in the main covariate, using the bias correction methods RC and RR. The theoretical properties under each validation source is presented. In a simulation study it is found that the best validation source in terms of smaller mean square error and narrower confidence interval is the internal validation with measure of the true covariate in a common disease case, and the external validation with repeated measures of the surrogate for a rare disease case. In addition, it is found that addressing the correlation between the true covariate and its surrogate, and the value of the changepoint, is needed, especially in the rare disease case

Audit fees in auditor switching

The auditor work is examining that a company's financial statements faithfully reflect its financial situation. His wage, the audit fees, are not fixed among all companies, but can be affected by the financial and structural characteristics of the company, as well as the characteristics of the firm he belongs to. Another factor that may affect his wage in an auditor switching, which can be resulted from changes in the company that may influence the fees. This paper examines the effect nature of the auditor switching on his wage, and the factors of the company characteristics and the economy data which determine the wage at switching. A product of the research are tools for predicting and evaluating the auditor wage at switching. These tools are important for the auditor himself, but also for the company manager to correctly determine the wage due to the possibility that the quality of the audit work depends on its fees. Two main results are obtained. First, the direction of the wage change in the switching year depends on the economic stability of the economy. Second, the switching effect on the direction and the change size in wage depends on the change size in the company characteristics before and after switching - a large change versus a stable one. We get that forecasting the change size in wage for companies with a larger change is their characteristics is paralleled to forecasting a wage increasing. And vice versa, forecasting the change size in wage for companies with a stable change in their characteristics is paralleled to forecasting a wage decreasing. But, whereas the former can be achieved based on the company characteristics and macroeconomics factors, the predictably of these characteristics and factors is negligible for the letter.Comment: 47 page

Modeling and replicating statistical topology, and evidence for CMB non-homogeneity

Under the banner of `Big Data', the detection and classification of structure in extremely large, high dimensional, data sets, is, one of the central statistical challenges of our times. Among the most intriguing approaches to this challenge is `TDA', or `Topological Data Analysis', one of the primary aims of which is providing non-metric, but topologically informative, pre-analyses of data sets which make later, more quantitative analyses feasible. While TDA rests on strong mathematical foundations from Topology, in applications it has faced challenges due to an inability to handle issues of statistical reliability and robustness and, most importantly, in an inability to make scientific claims with verifiable levels of statistical confidence. We propose a methodology for the parametric representation, estimation, and replication of persistence diagrams, the main diagnostic tool of TDA. The power of the methodology lies in the fact that even if only one persistence diagram is available for analysis -- the typical case for big data applications -- replications can be generated to allow for conventional statistical hypothesis testing. The methodology is conceptually simple and computationally practical, and provides a broadly effective statistical procedure for persistence diagram TDA analysis. We demonstrate the basic ideas on a toy example, and the power of the approach in a novel and revealing analysis of CMB non-homogeneity