  Informative cluster size (ICS) arises in situations with clustered data where
a latent relationship exists between the number of participants in a cluster
and the outcome measures. Although this phenomenon has been sporadically
reported in statistical literature for nearly two decades now, further
exploration is needed in certain statistical methodologies to avoid potentially
misleading inferences. For inference about population quantities without
covariates, inverse cluster size reweightings are often employed to adjust for
ICS. Further, to study the effect of covariates on disease progression
described by a multistate model, the pseudo-value regression technique has
gained popularity in time-to-event data analysis. We seek to answer the
question: "How to apply pseudo-value regression to clustered time-to-event data
when cluster size is informative?" ICS adjustment by the reweighting method can
be performed in two steps; estimation of marginal functions of the multistate
model and fitting the estimating equations based on pseudo-value responses,
leading to four possible strategies. We present theoretical arguments and
thorough simulation experiments to ascertain the correct strategy for adjusting
for ICS. A further extension of our methodology is implemented to include
informativeness induced by the intra-cluster group size. We demonstrate the
methods in two real-world applications: (i) to determine predictors of tooth
survival in a periodontal study, and (ii) to identify indicators of ambulatory
recovery in spinal cord injury patients who participated in locomotor-training
rehabilitation.
