Analysis of multilevel grouped survival data with time-varying regression coefficients.

Correlated or multilevel grouped survival data are common in medical and dental research. Two common approaches to analyze such data are the marginal and the random-effects approaches. Models and methods in the literature generally assume that the treatment effect is constant over time. A researcher may be interested in studying whether the treatment effects in a clinical trial vary over time, say fade out gradually. This is of particular clinical value when studying the long-term effect of a treatment. This paper proposed to extend the random effects grouped proportional hazards models by incorporating the possibly time-varying covariate effects into the model in terms of a state-space formulation. The proposed model is very flexible and the estimation can be performed using the MCMC approach with non-informative priors in the Bayesian framework. The method is applied to a data set from a prospective clinical trial investigating the effectiveness of silver diamine fluoride (SDF) and sodium fluoride (NaF) varnish in arresting active dentin caries in the Chinese preschool children. It is shown that the treatment groups with caries removal prior to the topical fluoride applications are most effective in shortening the arrest times in the first 6-month interval, but their effects fade out rapidly since then. The effects of treatment groups without caries removal prior to topical fluoride application drop at a very slow rate and can be considered as more or less constant over time. The applications of SDF solution is found to be more effective than the applications of NaF vanish.