gms | German Medical Science

Introduction: Linear mixed models are commonly used to analyze longitudinal data in controlled clinical trials. In many situations this approach alone is adequate to draw conclusions about the effectiveness of clinical interventions.

However, patient response to medical interventions often varies. Depending on specific covariates responses might be different from patient to patient [1]. If these covariates are not known a priori or cannot be measured, linear mixed models might be unable to describe the possible trajectories of different patients to the medical intervention adequately.

Methods: Growth Mixture Models (GMM), which belong to the class of Finite Mixture Models, are used to analyze longitudinal data. By identifying clusters with different behavior they allow to estimate a mixed model separately for each cluster—without having to consider all the covariates explicitly in the model [2].

By now there is a large amount of literature that shows application examples and offers recommendations on how to use GMMs for the analysis of controlled clinical studies [1], [3], [4]. We used data from a real world, placebo controlled clinical trial where patients rated their health-related quality of life to investigate the usefulness of these recommendations.

Results: During the study several known problems of GMMs arose: Some models did not converge or yielded implausible parameter estimates (e.g., negative variances). Moreover, determining the best model (i.e., choosing the right number of clusters) was difficult. Apart from these often-discussed intricacies [2], [5] it became apparent that the programming language R, which was used to implement GMM algorithms for this study, currently does not offer some of the tools recommended by literature.

Despite these obstacles, the tested GMMs captured additional information. Indeed, by virtue of the initial clustering we identified typical trends in the placebo and treatment group, respectively. Two different clusters emerged when patients in the placebo group were analyzed separately. Both clusters showed a downward trend, but baseline values and the intensity of the downward trend were completely different.

The application of a GMM in the treatment group revealed the existence of three different clusters. None of them showed significant deterioration. These findings were generally confirmed when a GMM was applied to the entire data set. In this case, however, it was unclear whether a model with two or three classes was most appropriate to describe the output of the clinical study. Such different patterns within each treatment group are often more difficult to observe when only a linear mixed model is used to describe the data.

Discussion: GMMs can be a helpful complement to linear mixed models when analyzing longitudinal clinical data – in particular, when patients react differently to the treatment and not all relevant covariates are measured. Therefore, our study ads further evidence that GMMs can be helpful when practitioner want to understand the possible responses of patients to a medical intervention. On the other hand, the practitioner faces several difficulties that make it hard for him to use the models right now.

This research was conducted as part of the master's thesis of AH for which he was employed by Pfizer Pharma GmbH. NK and SB are employees of Pfizer Pharma GmbH.

The authors declare that an ethics committee vote is not required.