A multiple imputation approach for clustered interval-censored survival data

Multivariate interval-censored failure time data arise commonly in many studies of epidemiology and biomedicine. Analysis of these type of data is more challenging than the right-censored data. We propose a simple multiple imputation strategy to recover the order of occurrences based on the interval-censored event times using a conditional predictive distribution function derived from a parametric gamma random effects model. By imputing the interval-censored failure times, the estimation of the regression and dependence parameters in the context of a gamma frailty proportional hazards model using the well-developed EM algorithm is made possible. A robust estimator for the covariance matrix is suggested to adjust for the possible misspecification of the parametric baseline hazard function. The finite sample properties of the proposed method are investigated via simulation. The performance of the proposed method is highly satisfactory, whereas the computation burden is minimal. The proposed method is also applied to the diabetic retinopathy study (DRS) data for illustration purpose and the estimates are compared with those based on other existing methods for bivariate grouped survival data.