Identifying typical trajectories in longitudinal data: new approaches – IDOL

Cohort studies are studies in which the same variables are measured repeatedly over time. Each sequence of measures, known as the variable-trajectory, reflects the evolution of a phenomenon. In recent years we have seen the development of new tools to analyse these trajectories. The most widely used are partitioning techniques (Proc Traj or KmL for instance). They consist in grouping individuals whose trajectories are similar, thus defining "typical trajectories" that reflect the "mean" behaviour of the individuals in a given sub-group. However these techniques have a certain number of limitations. Collaboration between methodologists and physicians in our different teams has enabled priority lines of action for the development of methods to overcome these limitations, and thus considerably enhance the use made of the cohorts that have already been subjected to the more classic analyses. Thus our project has a threefold objective: i) to create new methods for partitioning longitudinal data, ii) to demonstrate their efficacy on existing cohorts, and iii) to make the newly-developed tools available to the scientific community in the form of computing libraries. The cohorts selected to implement these methodological developments are all prominent studies, and concern important societal issues: standardised care plan and Alzheimer's disease, long-term outcome of severely premature infants, access to and compliance with retroviral treatments in Senegal, hormone profiles of women without fertility problems, social and behavioural outcomes of children in Quebec. The analysis of these programmes has identified five methodological issues to be addressed by the present research programme:

- KmL3D: To date, partitioning techniques consider the temporal evolution of a single variable-trajectory. However it is possible to envisage complex interactions between trajectories. KmL3D will enable work on the concurrent evolution of several variable-trajectories by partitioning them simultaneously.

- KmLCov will partition the data integrating the effects of covariables (time-dependant or other) on the trajectories. Their effects may be specific for each class of trajectory.

- KmLShape: In certain circumstances, the exact moment of the appearance of a phenomenon is less important than the type of evolution that it exhibits. The ability to partition trajectories according to their shape or profile and to group individuals whose trajectories are close despite atime discrepancy is the objective of KmLShape.

- KmLVar: It may also be relevant to classify individuals according to whether their variable-trajectory is stable or fluctuates. Indeed, the degree of instability of a marker may provide more information than the evolution of its value. The aim of KmLVar is to enable the modelling and the identification of groups or trajectories with the same variance.

- Finally, partitioning techniques enable new approaches for imputing missing data in trajectories, based on both the known values for an individual and the mean trajectory of the group. The validation of the Copy Mean method is thus also an objective of this project.

In this way our project combines methodological research and application to real data, in response to research questionings from clinicians and epidemiologists. Each team will be in a position to propose original analyses of cohorts using the new tools developed within the programme. Ultimately, these new statistical techniques will be programmed and made available to the scientific community on a dedicated website, thus ensuring wide diffusion.