Longitudinal clustering provides a detailed yet comprehensible description of time profiles among subjects. With several approaches that are commonly used for this purpose, it remains unclear under which conditions a method is preferred over another method. We investigated the performance of five methods using Monte Carlo simulations on synthetic datasets, representing various scenarios involving polynomial time profiles. The performance was evaluated on two aspects: The agreement of the group assignment to the simulated reference, as measured by the split-join distance, and the trend estimation error, as measured by a weighted minimum of the mean squared error (WMMSE). Growth mixture modeling (GMM) was found to achieve the best overall performance, followed closely by a two-step approach using growth curve modeling and k-means (GCKM). Considering the model similarities between GMM and GCKM, the latter is preferred for large datasets for its computational efficiency. Longitudinal k-means (KML) and group-based trajectory modeling were found to have practically identical solutions in the case that the group trajectory model of the latter method is correctly specified. Both methods performed less than GMM and GCKM in most settings.

Background Sleep apnea patients on CPAP therapy exhibit differences in how they adhere to the therapy. Previous studies have demonstrated the benefit of describing adherence in terms of discernible longitudinal patterns. However, these analyses have been done on a limited number of patients, and did not properly represent the temporal characteristics and heterogeneity of adherence. Methods We illustrate the potential of identifying patterns of adherence with a latent-class heteroskedastic hurdle trajectory approach using generalized additive modeling. The model represents the adherence trajectories on three aspects over time: the daily hurdle of using the therapy, the daily time spent on therapy, and the day-to-day variability. The combination of these three characteristics has not been studied before. Results Applying the proposed model to a dataset of 10,000 patients in their first three months of therapy resulted in nine adherence groups, among which 49% of patients exhibited a change in adherence over time. The identified group trajectories revealed a non-linear association between the change in the daily hurdle of using the therapy, and the average time on therapy. The largest difference between groups was observed in the patient motivation score. The adherence patterns were also associated with different levels of high residual AHI, and day-to-day variability in leakage. Conclusion The inclusion of the hurdle model and the heteroskedastic model into the mixture model enabled the discovery of additional adherence patterns, and a more descriptive representation of patient behavior over time. Therapy adherence was mostly affected by a lack of attempts over time, suggesting that encouraging these patients to attempt therapy on a daily basis, irrespective of the number of hours used, could drive adherence. We believe the methodology is applicable to other domains of therapy or medication adherence.