On the conditional probability for assessing time dependence of association in shared frailty models with bivariate current status data

- A variant of an association measure is presented for bivariate current status data.
- Maximum likelihood estimation and standard errors are developed for this measure.
- The proposed estimator and standard errors show good finite sample performance.
- The measure can vary with time even in the absence of any time-dependent effects.
- The measure lacks interpretability in suggesting appropriate frailty models.

Shared frailty models are frequently used for inducing dependence between survival times. In this paper, we consider bivariate current status data that are reasonable to model by shared frailty models. A time-dependent association measure that has a conditional probability interpretation is revisited for its potential application to such data. We propose a method of estimation and derive asymptotic standard errors for this measure. Its small sample performance and its performance in assessing the temporal variation in the strength of association in realistic scenarios is investigated by means of experiments. We show that the measure based on the conditional probability can vary with time even in the absence of any time-dependent effects. Furthermore, we give evidence that it lacks interpretability in suggesting appropriate frailty models. We provide an illustration with multivariate current status data arising from a community-based study of cardiovascular diseases in Taiwan. We compare the observed patterns of association with the ones obtained by employing a fairly new time-varying association measure that is relevant for shared frailty models, owing to its connection to the cross-ratio function, and which serves as a diagnostic tool for suggesting classes of frailty distributions with constant, increasing or decreasing association over time.