Robustness assessment of regressions using cluster analysis typologies: a bootstrap procedure with application in state sequence analysis

Background: In standard Sequence Analysis, similar trajectories are clustered together to create a typology of trajectories, which is then often used to evaluate the association between sequence patterns and covariates inside regression models. The sampling uncertainty, which affects both the derivation of the typology and the associated regressions, is typically ignored in this analysis, an oversight that may lead to wrong statistical conclusions. We propose utilising sampling variation to derive new estimates that further inform on the association of interest.

Methods: We introduce a novel procedure to assess the robustness of regression results obtained from the standard analysis. Bootstrap samples are drawn from the data, and for each bootstrap, a new typology replicating the original one is constructed, followed by the estimation of the corresponding regression models. The bootstrap estimates are then combined using a multilevel modelling framework that mimics a meta-analysis. The fitted values from this multilevel model allow to account for the sampling uncertainty in the inferential analysis. We illustrate the methodology by applying it to the study of healthcare utilisation trajectories in a Swiss cohort of diabetic patients.

Results: The procedure provides robust estimates for an association of interest, along with 95% prediction intervals, representing the range of expected values if the clustering and associated regressions were performed on a new sample from the same underlying distribution. It also identifies central and borderline trajectories within each cluster. Regarding the illustrative application, while there was evidence of an association between regular lipid testing and subsequent healthcare utilisation patterns in the original analysis, this is not supported in the robustness assessment.

Conclusions: Investigating the relationship between trajectory patterns and covariates is of interest in many situations. However, it is a challenging task with potential pitfalls. Our Robustness Assessment of Regression using Cluster Analysis Typologies (RARCAT) may assist in ensuring the robustness of such association studies. The method is applicable wherever clustering is combined with regression analysis, so its relevance goes beyond State Sequence Analysis.