Upon challenge, lymphocytes multiply and diversify to combat the infection, however, the mechanisms that drive this process are not well understood. A theoretical model has been proposed to explain how a diverse selection of cell fates is achieved, the Cyton model [Hawkins et al, 2007, PNAS]. In that model the censorship caused by competing drives for lymphocytes to undergo certain fates results in complex correlations and impacts the observed distribution of times to cellular events. In [Duffy et al, 2012, Science] the competition hypothesis is tested for consistency with data collected using a novel experimental procedure. Through the implementation and development of a collection of multivariate nonparametric statistical techniques, we create a set of tools that can aid the study of competition hypotheses in biological systems. As a worked example these tools are used to study data collected for the experiments in [Duffy et al, 2012, Science] to challenge some of the underlying assumptions of their parametric analysis. As an additional illustration further unpublished data collected during the experiments is used to study the time at which B cells divide, die and differentiate when they have already undergone class switching, allowing us to address the question of a cell type dependent change.