Regression Analysis of Multivariate Interval-Censored Failure Time Data with Application to Tumorigenicity Experiments Xingwei Tong *; 1 , Man-Hua Chen 2 , and Jianguo Sun 2 1 School of Mathematical Sciences, Beijing Normal University, Beijing, P.R. China 100875 2 Department of Statistics, University of Missouri, 146 Middlebush Hall, Columbia, MO 65211, USA Received 30 July 2007, revised 3 December 2007, accepted 14 December 2007 Summary This paper discusses multivariate interval-censored failure time data that occur when there exist several correlated survival times of interest and only interval-censored data are available for each survival time. Such data occur in many fields. One is tumorigenicity experiments, which usually concern different types of tumors, tumors occurring in different locations of animals, or together. For regression analysis of such data, we develop a marginal inference approach using the additive hazards model and apply it to a set of bivariate interval-censored data arising from a tumorigenicity experiment. Simulation studies are conducted for the evaluation of the presented approach and suggest that the approach performs well for practical situations. Key words: Additive hazards model; Interval-censoring; Marginal approach; Medical follow- up studies. 1 Introduction This paper discusses regression analysis of multivariate interval-censored failure time data that occur if more than one survival variable is of interest and only interval-censored data are available for these variables (Goggins and Finkelstein (2000) and Kim and Xue (2002)). By interval-censored data (Fin- kelstein (1986), Sun (2005)), we mean that the survival times of interest are observed only to belong to some intervals instead of being known exactly or right-censored (Kalbfleisch and Prentice (2002)). Such data occur in many fields and one is tumorigenicity experiments. In these experiments, one may be concerned with different types of tumors, tumors in different body locations of animals, or differ- ent types of tumors in different locations. Although the time to tumor occurrence is usually the vari- able of interest, one usually only observes the tumor presence or absence when animals die or are sacrificed. Thus the survival time of interest is either left- or right-censored. Another field in which interval-censored failure time data frequently occur is medical follow-up studies and in these cases, each study subject is examined or observed periodically. In consequence, the survival events of interest are usually observed only to occur between examination times with the exact occurrence times being unknown. A typical example of correlated or multivariate failure time data is given by a study on eyes in which times to certain infection or event for both left and right eyes may be of interest, or a twin study in which one is interested in the joint analysis of times to certain event for both twins. Lin (1994) gave several examples of correlated right-censored failure time data. For multivariate interval-censored data, among others, Goggins and Finkelstein (2000) gave a set of bivariate interval-censored data arising from an AIDS clinical trial on HIV-infected indivi- duals. * Corresponding author: e-mail: xweitong@bnu.edu.cn 364 Biometrical Journal 50 (2008) 3, 364–374 DOI: 10.1002/bimj.200710418 # 2008 WILEY-VCH Verlag GmbH &Co. KGaA, Weinheim