Reader Comments

Post a new comment on this article

Growth mixture models: an interesting way to look at data but not always trustworthy

Posted by wojohnso on 16 Apr 2014 at 18:57 GMT

This paper presented data in an interesting way. Growth mixture models were applied to serial BMI data in a sub-sample (n=645) of participants in the Whitehall II study who subsequently developed diabetes. The authors claim to have identified three “distinct trajectories” of pre-disease BMI. The problem is that only one of these trajectories or classes comprised a reasonable number of participants (“stable overweight” n=604), with the other two accounting for just 6% of the sample (“progressive weight gainers” n=15; “persistently obese” n=26). The posterior probabilities of participants belonging to the classes to which they were assigned were poor for these two classes and the trajectories were imprecisely estimated (wide confidence intervals). Further, the trajectory for the smallest class (progressive weight gainers) appeared to suffer from tail problems (i.e., inflections when none exist), which is a common problem encountered when modelling trajectories with polynomials (as was done in this paper). Growth mixture models are known to identify classes even if none exist, and that is what I believe has happened here. The two trajectories that I do trust belonged to the “stable overweight” class and the group of participants who didn’t develop diabetes (n=6,060) who were not included in the growth mixture model. A more powerful analytical approach might have been to apply the growth mixture model in the full sample and then investigate the percentage in each class who had developed diabetes. This could have been done for all the other cardio-metabolic measures (blood pressure, cholesterol, glucose, etc), instead of analysing them using mixed effects models (i.e., one mean trajectory) and imposing the extracted BMI classes as an explanatory variable. While the trajectories for the other cardio-metabolic outcomes have led to some nice interpretation of the BMI classes, they also suffer from small sample sizes in two of the BMI classes, wide confidence intervals, and tail problems. Because the “stable overweight” BMI trajectory was slightly higher than the BMI trajectory for people who didn’t develop diabetes, I do not understand how these results “suggest that strategies focusing on small weight reductions for the entire population” may be the most beneficial. Surely, the results suggest the opposite – that we should try and lower BMI in higher risk individuals (i.e., those who developed diabetes) so that it is more similar to that in lower risk individuals (i.e., those who didn’t develop diabetes).

No competing interests declared.

RE: Growth mixture models: an interesting way to look at data but not always trustworthy

Kristine_Faerch replied to wojohnso on 20 Apr 2014 at 06:38 GMT

We appreciate this relevant comment addressing some of the challenges related to the use of latent class trajectory analysis.
It is well known that latent class trajectory analysis often results in rather small groups, which we also found in this particular study. However, as opposed to latent trajectory models often used in the literature, we applied a mixed-effects model including a random effect for time. This allows for individual variation around the mean trajectory (of the individual’s latent class) and reduces the risk of modelling random noise. The classes found were significantly different from each other despite the wide confidence intervals and the small number of participants in two of them. Therefore, we believe these groups reflect meaningful and different trajectories of BMI development. The posterior probabilities of group membership showed 75-78% for the two smallest groups and 96% for the large group, which are acceptable and comparable to those found in most other studies.
It is correct that “tail problems” can occur when fitting trajectories with cubic polynomials. The alternative is to fit models without cubic terms, which will give less flexible models with even more imprecise trajectory shapes. We have only included a cubic term when significant in the model, but we do agree that some of the trajectories seem to be affected by the polynomial function, especially in the beginning (left side) of the trajectory.
Your suggestion about applying the latent class trajectory analysis in the full sample instead of in those who do develop diabetes is interesting, but not possible if the aim is to study obesity development prior to diabetes diagnosis. The time scale used in our study is based on the diagnosis of diabetes (for those who developed diabetes) and on the last examination (for those who did not develop diabetes). This means that for the diabetes-free population, time 0 is merely a random time point in a person’s life, and for that reason the trajectory should only be fitted with a linear model. If latent classes of BMI trajectories were to be studied in the entire population, the only meaningful time scale would be age. However, this would change the focus of the paper and as such it was outside the scope of the current study.
Our suggestion about focusing on small weight reductions for the entire population relates to the fact that on average the majority of those who developed diabetes were only slightly overweight at time of diagnosis. Unfortunately, it is often not known who will and will not develop diabetes in the population, and the “high-risk” individuals may be quite difficult to identify because most likely they do not have symptoms of their future diabetes. Accordingly, it is difficult to focus on small weight changes in only these individuals, although we agree it would be most cost-effective.
Lastly, it should be mentioned that the latent class trajectory analysis is data driven and mainly hypothesis generating, and therefore the results need to be confirmed in other study populations before any firm conclusions can be drawn. However, we do believe that latent class trajectory analysis is potentially a powerful method for uncovering heterogeneity in disease development which would otherwise have been overlooked.

Dorte Vistisen and Kristine Færch
Steno Diabetes Center, Gentofte

No competing interests declared.