Reliability of cluster results for different types of time adjustments in complex disease research

We aim to identify subtypes of diseases like Osteoarthritis (OA) and Parkinson´s Disease (PD) that present clinical heterogeneity. We do so by searching for homogeneous clusters in values of markers that reflect the severity of the disease. In the current paper we consider two important items for a cluster analysis. First, as time can contribute largely to the measured variability in the data, we search for the most appropriate way to adjust for it. Second, as we aim for reliable cluster analyses, cluster results should exhibit robustness to little change in the data. To investigate these issues, we transform the data by adding noise of different levels before cluster modeling and we rely on a χ²-based measure of association to compare cluster results for different types of time adjustment. The results of our experiments suggest to adjust data for a logarithmic age effect for OA and a square root effect of the disease duration for PD because these adjustments lead more reliable cluster results.