2. Dalla Lana School of Public Health, University of Toronto, Toronto, Ontario M5T 3M7, Canada.
3. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada.
Background: Paired failure time data often arise in medical studies involving familial information. When each member of a pair is subject to interval-truncation, there is lack of literature on methodologies for analyzing such data. The aim of this paper is to develop an approach for examining the association between paired failure times under the presence of interval-truncation.
Methods: A conditional frailty model is described and an expectation-maximization algorithm is developed for estimation of the model parameters. Simulation studies are conducted to examine the performance of the proposed algorithm, and an application of the methods is illustrated using data from a familial study on pairs of siblings diagnosed with schizophrenia.
Results: The results from the simulation studies show that all model parameters can be estimated with negligible bias, even under finite sample size. In the motivating dataset, our proposed model and method of estimation reveal a strong presence of dependence among times to diagnosis of schizophrenia within pairs of siblings.
Discussion: The proposed conditional frailty model is easy to implement since the expectation step of the algorithm is relatively straightforward. The maximization step also provides closed form expressions for the parameter estimates of the hazard function.
Keywords: Frailty model, interval-truncation, bivariate failure time data, monte carlo EM algorithm