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Abstract We propose a model-based clustering method for high-dimensional longitudinal data via regularization in this paper. This study was motivated by the Trial of Activity in Adolescent Girls (TAAG), which aimed to examine multilevel factors related to the change of physical activity by following up a cohort of 783 girls over 10 years from adolescence to early adulthood. Our goal is to identify the intrinsic grouping of subjects with similar patterns of physical activity trajectories and the most relevant predictors within each group. The previous analyses conducted clustering and variable selection in two steps, while our new method can perform the tasks simultaneously. Within each cluster, a linear mixed-effects model (LMM) is fitted with a doubly penalized likelihood to induce sparsity for parameter estimation and effect selection. The large-sample joint properties are established, allowing the dimensions of both fixed and random effects to increase at an exponential rate of the sample size, with a general class of penalty functions. Assuming subjects are drawn from a Gaussian mixture distribution, model effects and cluster labels are estimated via a coordinate descent algorithm nested inside the Expectation-Maximization (EM) algorithm. Bayesian Information Criterion (BIC) is used to determine the optimal number of clusters and the values of tuning parameters. Our numerical studies show that the new method has satisfactory performance and is able to accommodate complex data with multilevel and/or longitudinal effects. 

Allograft is the current gold standard for treating critical-sized bone defects. However, allograft healing is usually compromised partially due to poor host-mediated vascularization. In the efforts towards developing new methods to enhance allograft healing, a non-terminal technique for monitoring the vascularization is needed in pre-clinical mouse models. In this study, we developed a non-invasive instrument based on spatial frequency domain imaging (SFDI) for longitudinal monitoring of the mouse femoral graft healing. SFDI technique provided total hemoglobin concentration (THC) and oxygen saturation (StO₂) of the graft and the surrounding soft tissues. SFDI measurements were performed from 1 day before to 44 days after graft transplantation. Autograft, another type of bone graft with higher vascularization potential was also measured as a comparison to allograft. For both grafts, the overall temporal changes of the measured THC agreed with the physiological expectations of vascularization timeline during bone healing. A significantly greater increase in THC was observed in the autograft group compared to the allograft group, which agreed with the expectation that allografts have more compromised vascularization.