  We consider nonparametric inference for event time distributions based on
current status data. We show that in this scenario conventional mixture priors,
including the popular Dirichlet process mixture prior, lead to biologically
uninterpretable results as they unnaturally skew the probability mass for the
event times toward the extremes of the observed data. Simple assumptions on
dependent censoring can fix the problem. We then extend the discussion to
bivariate current status data with partial ordering of the two outcomes. In
addition to dependent censoring, we also exploit some minimal known structure
relating the two event times. We design a Markov chain Monte Carlo algorithm
for posterior simulation. Applied to a recurrent infection study, the method
provides novel insights into how symptoms-related hospital visits are affected
by covariates.
