  Recent literature has found conditional transition rates to be a useful tool
for avoiding Markov assumptions in multistate models. While the estimation of
univariate conditional transition rates has been extensively studied, the
intertemporal dependencies captured in the bivariate conditional transition
rates still require a consistent estimator. We provide an estimator that is
suitable for censored data and emphasize the connection to the rich theory of
the estimation of bivariate survival functions. Bivariate conditional
transition rates are necessary for various applications in the survival context
but especially in the calculation of moments in life insurance mathematics.
