Nonparametric analysis of nonhomogeneous multistate processes with clustered observations

Abstract

Frequently, clinical trials and observational studies involve complex event history data with multiple events. When the observations are independent, the analysis of such studies can be based on standard methods for multistate models. However, the independence assumption is often violated, such as in multicenter studies, which makes standard methods improper. This work addresses the issue of nonparametric estimation and two‐sample testing for the population‐averaged transition and state occupation probabilities under general multistate models with cluster‐correlated, right‐censored, and/or left‐truncated observations. The proposed methods do not impose assumptions regarding the within‐cluster dependence, allow for informative cluster size, and are applicable to both Markov and non‐Markov processes. Using empirical process theory, the estimators are shown to be uniformly consistent and to converge weakly to tight Gaussian processes. Closed‐form variance estimators are derived, rigorous methodology for the calculation of simultaneous confidence bands is proposed, and the asymptotic properties of the nonparametric tests are established. Furthermore, I provide theoretical arguments for the validity of the nonparametric cluster bootstrap, which can be readily implemented in practice regardless of how complex the underlying multistate model is. Simulation studies show that the performance of the proposed methods is good, and that methods that ignore the within‐cluster dependence can lead to invalid inferences. Finally, the methods are illustrated using data from a multicenter randomized controlled trial.

Semiparametric Marginal Regression for Clustered Competing Risks Data with Missing Cause of Failure

“…One may consider nonparametric or semiparametric models for the marginal probability π l (W ij , γ 0 ), or machine learning methods to predict the missing causes of failure. Moreover, extending the methodology for more general clustered and incomplete multi-state data (Liquet et al, 2012;Lan et al, 2017;Bakoyannis, 2020) is of interest from both practical and theoretical standpoints. Williamson, J. M., H.-Y.…”

“…By conditions C1, C4, and C5, and lemmas 1 and 2 in the supporting information of Bakoyannis (2020), the class of functions…”

“…Clustered competing risks data are commonly encountered in multicenter studies (Zhou et al, 2012;Diao and Zeng, 2013). An important feature of such data is that the outcomes of individuals from the same cluster are typically dependent and, thus, the standard assumption of independence is violated (Balan and Putter, 2019;Bakoyannis, 2020). Therefore, standard methods for competing risks data are not applicable in the presence of clustering.…”

Individual factors predict substance use treatment course patterns among patients in community-based substance use disorder treatment

“…First, we estimated the cumulative incidence of premature termination (i.e., cumulative probability of premature termination over time) using a moment-based nonparametric estimator that takes into account the potential association across different treatment episodes of the same individual [ 33 ]. We created cumulative incidence plots to display the probability of premature termination after admission across depression and substance use subgroups over time.…”

“…Two-sample nonparametric comparisons of the cumulative incidences were conducted using a Kolmogorov-Smirnov-type test [ 34 ]. To take the within-individual dependence into account, significance level was calculated using 1000 cluster bootstrap replications [ 33 ]. For the pairwise comparison of the cumulative incidences across the SUD groups (primary AUD vs primary OUD vs primary Other), we applied the Bonferroni correction.…”