Marginal analysis of bivariate mixed responses with measurement error and misclassification

Bivariate responses with mixed continuous and binary variables arise commonly in applications such as clinical trials and genetic studies. Statistical methods based on jointly modeling continuous and binary variables have been available. However, such methods ignore the effects of response mismeasurement, a ubiquitous feature in applications. It has been well studied that in many settings, ignorance of mismeasurement in variables usually results in biased estimation. In this paper, we consider the setting with a bivariate outcome vector which contains a continuous component and a binary component both subject to mismeasurement. We propose estimating equation approaches to handle measurement error in the continuous response and misclassification in the binary response simultaneously. The proposed estimators are consistent and robust to certain model misspecification, provided regularity conditions. Extensive simulation studies confirm that the proposed methods successfully correct the biases resulting from the error-in-variables under various settings. The proposed methods are applied to analyze the outbred Carworth Farms White mice data arising from a genome-wide association study.

Time-Dependent System Reliability Analysis for Bivariate Responses

Time-dependent system reliability is computed as the probability that the responses of a system do not exceed prescribed failure thresholds over a time duration of interest. In this work, an efficient time-dependent reliability analysis method is proposed for systems with bivariate responses which are general functions of random variables and stochastic processes. Analytical expressions are derived first for the single and joint upcrossing rates based on the first-order reliability method (FORM). Time-dependent system failure probability is then estimated with the computed single and joint upcrossing rates. The method can efficiently and accurately estimate different types of upcrossing rates for the systems with bivariate responses when FORM is applicable. In addition, the developed method is applicable to general problems with random variables, stationary, and nonstationary stochastic processes. As the general system reliability can be approximated with the results from reliability analyses for individual responses and bivariate responses, the proposed method can be extended to reliability analysis of general systems with more than two responses. Three examples, including a parallel system, a series system, and a hydrokinetic turbine blade application, are used to demonstrate the effectiveness of the proposed method.

Time-Dependent Reliability Analysis for Bivariate Responses

Time-dependent system reliability is measured by the probability that the responses of a system do not exceed prescribed failure thresholds over a period of time. In this work, an efficient time-dependent reliability analysis method is developed for bivariate responses that are general functions of random variables and stochastic processes. The proposed method is based on single and joint upcrossing rates, which are calculated by the First Order Reliability Method (FORM). The method can efficiently produce accurate upcrossing rates for the systems with two responses. The upcrossing rates can then be used for system reliability predictions with two responses. As the general system reliability may be approximated with the results from reliability analyses for individual responses and bivariate responses, the proposed method can be extended to reliability analysis for general systems with more than two responses. Two examples, including a parallel system and a series system, are presented.