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

TL;DR

This paper develops methods for applying pseudo-value regression to clustered time-to-event data with informative cluster sizes, ensuring valid inference in complex multistate models.

Contribution

It introduces strategies for adjusting for informative cluster size in pseudo-value regression, supported by theoretical analysis and simulation studies.

Findings

Identifies correct adjustment strategies for ICS in pseudo-value regression.

Extends methodology to account for intra-cluster group size informativeness.

Demonstrates practical applications in medical studies.

Abstract

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.