Nonparametric analysis of nonhomogeneous multistate processes with clustered observations

Area of Science:

• Biostatistics
• Clinical Trials Methodology
• Survival Analysis

Background:

• Clinical trials frequently involve complex event history data with multiple events.
• Standard multistate models assume independent observations, which is often violated in practice, particularly in multicenter studies.
• Violating independence assumptions can lead to improper analysis and invalid inferences.

Purpose of the Study:

• To develop nonparametric estimation and two-sample testing methods for population-averaged transition and state occupation probabilities.
• To address challenges posed by cluster-correlated, right-censored, and/or left-truncated observations in general multistate models.
• To provide robust statistical tools for analyzing complex event data without assuming within-cluster independence.

Main Methods:

• Utilized empirical process theory for uniform consistency and weak convergence to Gaussian processes.
• Developed closed-form variance estimators and proposed methodology for simultaneous confidence bands.
• Established asymptotic properties of nonparametric tests and provided theoretical validation for nonparametric cluster bootstrap.

Main Results:

• The proposed estimators are uniformly consistent and converge weakly to tight Gaussian processes.
• Closed-form variance estimators and simultaneous confidence bands were derived.
• Nonparametric cluster bootstrap methods are theoretically valid and practically implementable.
• Simulation studies demonstrated good performance and highlighted the risks of ignoring within-cluster dependence.

Conclusions:

• The developed methods provide valid and robust statistical inference for complex event history data in the presence of cluster dependence.
• Ignoring within-cluster dependence in multistate models can lead to erroneous conclusions.
• The methods are applicable to both Markov and non-Markov processes and demonstrated utility in a multicenter randomized controlled trial.