A Bootstrap Approach for Validating Groups Identified by Latent Class Growth Models

Background: The use of longitudinal mixture models such as group-based trajectory modeling has seen a sharp increase during the last decades in the pharmacoepidemiology and public health literature. However, these methods have been criticized especially because of the data-driven modelling process which involves statistical decision-making.

Objectives: To validate the number of groups identified from latent class methods and to quantify the uncertainty in the number of groups.

Methods: We propose an approach that uses bootstrap to sample with replacement observations from the original data. For each bootstrap sample, the number of groups is selected using the Bayesian Information Criterion. The method allows investigating the statistical validity and the uncertainty of the groups identified in the original data by checking if the same solution is also found across the bootstrap samples. We evaluated the performance of our proposed approach using a simulation study. Scenarios with different sample sizes, number and shapes of groups were simulated. Datasets were generated using a multivariate normal model and 100 replications for each scenario were generated. For each replication, we applied our proposed approach taking 100 bootstrap samples and examined whether the bootstrap-estimated variability in the number of groups reflected the replication-wise variability. We also compared the replication-wise variability to the Bayesian posterior probability of group numbers. We evaluated the ability of three commonly used adequacy criteria to identify uncertainty in the number of groups (average posterior probability, odds of correct classification and relative entropy). Finally, we illustrated the proposed approach using data from the Quebec Integrated Chronic Disease Surveillance System to identify longitudinal medication patterns during 2015 and 2018 in people aged 75 to 80 years with diabetes.

Results: The bootstrap approach reproduced the true variability very well. The Bayesian posterior probability also performed well in most of the scenarios. However, in the scenario with intersecting groups and a sample size of 100, the posterior probability strongly underestimated the true variability. Common adequacy criteria were unable to detect the uncertainty in the number of groups.

Conclusions: We suggest the use of our bootstrap approach combined to other model adequacy criteria to better assess the quality of the classification in longitudinal mixture model.