Bivariate Mixture Modelling of Age at Onset Data in Twins
Model-fitting approaches to estimating the environmental and genetic components of variation rely on accurate diagnosis of twin type. This is almost never achieved in practice. Although the effects of these misclassification rates has not been studied in detail, it is believed to be a source of bias in the estimates of variance.
Classification of twin type can be achieved accurately, by genetic screening. This is not always feasible as it is an expensive process. The other method of classification is through the less than accurate questionnaires. The use of mixture models with twins data in the presence of misclassified labels was investigated by Neale in 2003 as a method of reducing the bias in the estimates of variance components.
Distributions such as the Exponential and the Weibull have been used extensively for modelling data that consists of times until failure. Under some circumstances, the simple Exponential or Weibull may not be appropriate. We develop Bayesian multivariate mixture models that incorporate classification error which we then apply to twin datasets including age of appendectomy data from the Australian Twins study (1990). This data includes bivariate survival data for $3808$ twin pairs. Results from a mixture of bivariate Weibull functions, which we fit to the data will be presented.