{
  "abstract": "Two-slope mixed-effects models with subject-specific changepoints are widely used to describe biphasic longitudinal trajectories. Treatment-arm summaries are often reported using a single \"typical subject\" curve obtained by plugging mean parameter values into the subject-specific model. This can be misleading when changepoint timing varies across individuals, because averaging subject-specific curves is not the same as evaluating one curve at average parameter values. A related issue is that individual trajectories may bend gradually rather than change slope through a literal kink, with transition sharpness varying between subjects. We propose population-average estimands for two-slope mixed models with random changepoints and smooth subject-level transitions. These estimands target the treatment-arm mean trajectory and instantaneous slope by averaging over fitted heterogeneity in changepoint timing and transition sharpness. We use a baseline-anchored normal-convolution soft hinge, which preserves the broken stick interpretation, includes the abrupt changepoint model as a limiting case, and allows analytic evaluation of the changepoint-marginalized kernels under a truncated normal changepoint distribution for fixed transition sharpness. Averaging over the fitted transition sharpness distribution is then performed by deterministic one-dimensional quadrature. In an application to HIV-1 RNA data from ACTG Protocol 315, with censoring and heavy-tailed residuals, the marginal summaries reveal a more gradual population-level transition than conventional plug-in summaries. The marginal slope remains more negative for longer, and the marginal mean continues to decline after the plug-in curve has begun to flatten. These results illustrate the main reporting implication: in random changepoint models, representative subject curves should not be treated as population-average trajectories or slopes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34165",
  "author_total": 3,
  "authors": [
    {
      "name": "Divan A. Burger"
    },
    {
      "name": "Sean van der Merwe"
    },
    {
      "name": "Emmanuel Lesaffre"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bzfd80hb55kxq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34165",
  "fulltext_url": null,
  "id": "bzfd80hb55kxq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34165",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Bayesian Inference"
    ]
  ],
  "openalex": "W7223813318",
  "pdf_url": "https://arxiv.org/pdf/2610.34165",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bzfd80hb55kxq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:49Z",
      "native_id": "2610.34165",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34165"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Population-average trajectories and slopes in smooth random changepoint mixed models",
  "title_text": "Population-average trajectories and slopes in smooth random changepoint mixed models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:49Z",
  "url": "https://research.draconitic.com/paper/bzfd80hb55kxq",
  "venue": "arXiv",
  "versions": []
}