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The number of clusters (k=5) was chosen objectively by maximizing a combined score of: Silhouette coefficient on a discovery split: measures how well-separated the clusters are internally Adjusted Rand Index (ARI) on a held-out validation split: measures whether an independent reclustering of new data produces the same structure This two-stage validation approach guards against over-fitting the cluster count to a single sample

In addition, it leads to a much greater weight loss at 3 months (WMD: 2.91 kg) and at 6 months (WMD: 2.84 kg)

Hardened lumps or tenderness at repeated injection sites signal the need for more frequent rotation between your approved body zones

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