  Clustered multistate process data are commonly encountered in multicenter
observational studies and clinical trials. A clinically important estimand with
such data is the marginal probability of being in a particular transient state
as a function of time. However, there is currently no method for nonparametric
marginal regression analysis of these probabilities with clustered multistate
process data. To address this problem, we propose a weighted functional
generalized estimating equations approach which does not impose Markov
assumptions or assumptions regarding the structure of the within-cluster
dependence, and allows for informative cluster size (ICS). The asymptotic
properties of the proposed estimators for the functional regression
coefficients are rigorously established and a nonparametric hypothesis testing
procedure for covariate effects is proposed. Simulation studies show that the
proposed method performs well even with a small number of clusters, and that
ignoring the within-cluster dependence and the ICS leads to invalid inferences.
The proposed method is used to analyze data from a multicenter clinical trial
on recurrent or metastatic squamous-cell carcinoma of the head and neck with a
stratified randomization design.
