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  "Title": "Multistate Model Bias-Corrected Robust Variance",
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  "Description": "Computes robust and bias-corrected sandwich variance\nestimators for multi-state Cox models with clustered\ntime-to-event data. Also provides Wald tests for heterogeneity,\ngeneralized least-squares linear trends, and order-restricted\ntrends among transition-specific coefficients. The methodology\nextends the marginal Cox model bias-correction framework of\nWang et al. (2023) <doi:10.1002/bimj.202200113> to the\nmulti-state setting.",
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    {
      "page": "MMBCV",
      "title": "MMBCV: Bias-corrected cluster-robust sandwich variance for multistate Cox models",
      "topics": [
        "MMBCV"
      ]
    },
    {
      "page": "msdat3",
      "title": "Clustered multistate simulated dataset (counting-process format)",
      "topics": [
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      "filename": "mmbcv-intro.html",
      "title": "mmbcv: Bias-corrected sandwich variance for clustered multistate Cox models",
      "engine": "knitr::rmarkdown",
      "headings": [
        "Overview",
        "Cluster-robust and bias-corrected variance estimators",
        "Technical details",
        "Notation",
        "[\\widehat{\\mathrm{Var}}_{\\mathrm{robust}}(\\hat\\beta)",
        "A common sandwich form",
        "[\\widehat{\\mathrm{Var}}(\\hat\\beta)",
        "Martingale-residual (MR) correction",
        "[\\widehat{\\mathrm{Var}}_{\\mathrm{MR}}(\\hat\\beta)",
        "Multiplicative corrections: KC, FG, and MD",
        "[\\widehat{\\mathrm{Var}}_{\\mathrm{KC}}(\\hat\\beta)",
        "[C^{FG}_i",
        "[\\widehat{\\mathrm{Var}}_{\\mathrm{FG}}(\\hat\\beta)",
        "[\\widehat{\\mathrm{Var}}_{\\mathrm{MD}}(\\hat\\beta)",
        "Additive correction: MBN",
        "[\\widehat{\\mathrm{Var}}_{\\mathrm{MBN}}(\\hat\\beta)",
        "Hybrid MR estimators",
        "[\\widehat{\\mathrm{Var}}_{\\mathrm{KCMR}}(\\hat\\beta)",
        "[\\widehat{\\mathrm{Var}}_{\\mathrm{FGMR}}(\\hat\\beta)",
        "[\\widehat{\\mathrm{Var}}_{\\mathrm{MDMR}}(\\hat\\beta)",
        "[\\widehat{\\mathrm{Var}}_{\\mathrm{MBNMR}}(\\hat\\beta)",
        "Main function and arguments",
        "Worked example",
        "Example data",
        "Fitting a multistate Cox model with survival",
        "Computing variance estimators",
        "Interpreting the output",
        "Efron ties",
        "Tests for correlated coefficient patterns",
        "Common inputs and output",
        "[\\widehat",
        "Omnibus heterogeneity test",
        "[D\\widehat",
        "Generalized least-squares linear-trend test",
        "[\\widehat",
        "\\begin",
        "(A^\\top\\widehat V^{-1}A)^{-1}A^\\top\\widehat V^{-1}\\widehat{\\boldsymbol\\beta},\\qquad\\widehat{\\mathrm{Var}}(\\widehat{\\boldsymbol\\theta})",
        "Order-restricted test",
        "[\\widetilde",
        "[T=\\widehat",
        "[\\overline\\chi^2",
        "Worked examples",
        "Applying the tests to an MMBCV() analysis",
        "Standalone example with seven coefficients",
        "Selecting a subset and specifying unequal positions",
        "Practical remarks",
        "Choosing a variance estimator",
        "Choosing among the coefficient-pattern tests",
        "Reporting",
        "References"
      ],
      "created": "2026-03-31 17:18:22",
      "modified": "2026-07-22 06:46:10",
      "commits": 2
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