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Informative cluster size (ICS) arises in situations with clustered data wherea latent relationship exists between the number of participants in a clusterand the outcome measures. Although this phenomenon has been sporadicallyreported in statistical literature for nearly two decades now, furtherexploration is needed in certain statistical methodologies to avoid potentiallymisleading inferences. For inference about population quantities withoutcovariates, inverse cluster size reweightings are often employed to adjust forICS. Further, to study the effect of covariates on disease progressiondescribed by a multistate model, the pseudo-value regression technique hasgained popularity in time-to-event data analysis. We seek to answer thequestion: "How to apply pseudo-value regression to clustered time-to-event datawhen cluster size is informative?" ICS adjustment by the reweighting method canbe performed in two steps; estimation of marginal functions of the multistatemodel and fitting the estimating equations based on pseudo-value responses,leading to four possible strategies. We present theoretical arguments andthorough simulation experiments to ascertain the correct strategy for adjustingfor ICS. A further extension of our methodology is implemented to includeinformativeness induced by the intra-cluster group size. We demonstrate themethods in two real-world applications: (i) to determine predictors of toothsurvival in a periodontal study, and (ii) to identify indicators of ambulatoryrecovery in spinal cord injury patients who participated in locomotor-trainingrehabilitation.

Adjusting for informative cluster size in pseudo-value based regression approaches with clustered time to event data