SurvivalBIV : estimation of the bivariate distribution function for sequentially ordered events under univariate censoring

In many medical studies, patients can experience several events. The times between consecutive events (gap times) are often of interest and lead to problems that have received much attention recently. In this work we consider the estimation of the bivariate distribution function for censored gap times, using survivalBIV a software application for R. Some related problems such as the estimation of the marginal distribution of the second gap time is also discussed. It describes the capabilities of the program for estimating these quantities using four di erent approaches, all using the Kaplan-Meier estimator of survival. One of these estimators is based on Bayes' theorem and Kaplan-Meier survival function. Two estimators were recently proposed using the Kaplan-Meier estimator pertaining to the distribution of the total time to weight the bivariate data (de Uña- Álvarez and Meira-Machado 2008 and de Uña- Álvarez and Amorim 2011). The software can also be used to implement the estimator proposed in Lin, Sun, and Ying (1999), which is based on inverse probability of censoring weighted. The software is illustrated using data from a bladder cancer study.The authors acknowledge receiving financial support from the Portuguese Ministry of Science, Technology and Higher Education in the form of grants PTDC/MAT/104879/2008 and SFRH/BD/62284/2009. This research was financed by FEDER Funds through "Programa Operacional Factores de Competitividade - COMPETE" and by Portuguese Funds through FCT - "Fundacao para a Ciencia e a Tecnologia", within the Project Est-C/MAT/UI0013/2011. The authors are grateful to the reviewers for their helpful comments