Multiple imputation to estimate the association between eyes in disease progression with interval-censored data

In many ophthalmologic studies, progression of diseases such as diabetic retinopathy, age-related maculopathy, cataract, and glaucoma is only noted when each eye is examined at intervals that commonly vary between subjects. Such data are often analysed using continuous time survival methods with observed progression assumed to occur at the end of the interval. Tied times of progression can lead to substantial bias in estimation of the association between progression in right and left eyes. We describe a multiple imputation strategy to create multiple data sets without ties, based on drawing interval-censored progression times from a parametric gamma frailty model that accounts for continuous and discrete covariates. We illustrate the method with data from 478 patients with insulin-dependent diabetes mellitus who were followed for progression of diabetic retinopathy in the Sorbinil Retinopathy Trial. Resolution of tied failure times allows for valid estimation of the hazard of progression in one eye given the progression status of the other eye. A simulation study suggests that the method performs well. Results highlight the advantage of multiple imputation that data imputed under one model can be analysed under several alternative models.