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docs(survival): fix broken citations and three R-package claims
Addresses all five review findings. Citations (2): `@kalbfleisch2002` does not exist in references.bib -- only `kalbfleisch2011statistical` does -- so both sites rendered as a literal `kalbfleisch2002?` on the preview. Repointed to the real key. R-package claims (3), each checked against CRAN rather than against the review: - `icenReg` is described as "Cox-PH, proportional odds, and accelerated failure time models ... semi and fully parametric", with no mention of truncation. The prose claimed it was "specifically designed for interval-censored data with truncation". - `interval` is "Weighted Logrank Tests and NPMLE for Interval Censored Data" -- nonparametric throughout. The prose claimed semi-parametric tools and complex-sampling support. - Log-logistic, log-normal and generalized gamma were said to fit "the AFT or PH frameworks", one sentence after correctly stating that exponential and Weibull are the only families that are both. They are AFT families; log-logistic is additionally proportional-odds. The list's framing changed too: only `flexsurv` handles delayed entry and interval censoring together, so saying all three "must be used" for that combination was wrong about the other two. Adding the `interval` correction cited @fay2010exact, which was not in references.bib -- the same defect this commit fixes. Added it, verified via Crossref: Fay & Shaw, JSS 36(2), 2010, doi 10.18637/jss.v036.i02. Adversarial review then caught three more, all fixed here: - The `icenReg` rewrite overstated it in turn. CRAN restricts the fully parametric option to the AFT models ("parametric only for accelerated failure time models"); the text now says so. - Line 54 still read "Using the Kalbfleisch and Prentice (2002) parameterization", three lines below a citation that now renders 2011. CLAUDE.md forbids plaintext author-date anyway, so it is now `@kalbfleisch2011statistical` and the mismatch cannot recur. - Two package bullets packed two sentences per source line. A fourth round caught a citation regression this PR introduced rather than inherited: the rewrite dropped the source URL that `main` attached to the Terry Therneau quotation, leaving a direct attributed quote with nothing to verify it against. Restored as a link on the attribution line, and confirmed reachable (HTTP 200) and present in the render. Local gate: `quarto render chapters/parametric-survival-models.qmd --to html` succeeded (it needs `renv::install(".")` first, since the chapter loads data via `fs::path_package("rme", ...)`); `lintr::lint()` clean. The rendered page was then scanned for unresolved citations, unresolved crossrefs, KaTeX errors, unexpanded macros and lists that failed to render: clean, and the citation now renders "Kalbfleisch and Prentice 2011" rather than "kalbfleisch2002?". Co-Authored-By: Claude Opus 5 <noreply@anthropic.com> Co-authored-by: d-morrison <2474437+d-morrison@users.noreply.github.com>
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chapters/parametric-survival-models.qmd

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## Weibull Distribution
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The Weibull distribution generalizes the exponential distribution by introducing a shape parameter $p > 0$ alongside the scale parameter $\lambda > 0$ [@kalbfleisch2002].
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The Weibull distribution generalizes the exponential distribution by introducing a shape parameter $p > 0$ alongside the scale parameter $\lambda > 0$ [@kalbfleisch2011statistical].
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This flexibility allows the hazard rate to change monotonically over time, accommodating situations where risk increases or decreases as time elapses.
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Using the Kalbfleisch and Prentice (2002) parameterization:
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Using the parameterization of @kalbfleisch2011statistical:
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$$
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\ba
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The estimated AFT regression coefficients $\eb_{\text{AFT}}$ produced by R's `survreg()` function relate directly to the PH regression coefficients $\eb_{\text{PH}}$ produced by `coxph()` via the identity $\eb_{\text{AFT}} = -\sigma \eb_{\text{PH}}$.
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The exponential and Weibull distributions are the only continuous distributions that are simultaneously proportional hazards models and accelerated failure time models.
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Other parametric families (such as log-logistic, log-normal, and generalized gamma) can be specified within the AFT or PH frameworks.
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Other parametric families commonly used for survival data
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(log-logistic, log-normal, and generalized gamma)
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are AFT families rather than PH families;
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the log-logistic distribution is additionally a proportional-odds model.
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## Dataset: Leukemia treatments
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To illustrate semi-parametric and parametric survival models, we analyze remission survival times from a clinical trial of 42 pediatric leukemia patients [@kalbfleisch2002].
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To illustrate semi-parametric and parametric survival models, we analyze remission survival times from a clinical trial of 42 pediatric leukemia patients [@kalbfleisch2011statistical].
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Half of the patients received a new therapy (6-mercaptopurine, 6-MP) and half received a standard control treatment.
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The variables in this dataset include:
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> `coxph` does left truncation but not left (or interval) censoring;
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> `survreg` does interval censoring but not left truncation (or time dependent covariates).
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>
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> --- Terry Therneau (August 31, 2015)
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> --- Terry Therneau,
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> [R-help, August 31, 2015](https://stat.ethz.ch/pipermail/r-help/2015-August/431733.html)
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In particular, `coxph()` constructs risk sets dynamically at each observed failure time $t_j$ using counting process format (`time1 = entry`, `time2 = exit`), enabling seamless handling of left-truncation.
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However, because partial likelihood relies on ordered exact failure times, standard Cox models cannot easily accommodate interval-censored data.
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Conversely, `survreg()` accommodates interval-censored outcomes via `Surv(time1 = L, time2 = R, type = "interval")` by maximizing the interval parametric likelihood $\P(L_i < T_i \le R_i) = \cdf_0(R_i) - \cdf_0(L_i)$.
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However, standard `survreg()` assumes all subjects enter observation at time 0, and does not condition likelihood terms on surviving past a delayed entry time $L_{\text{entry}}$.
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When a study contains both delayed entry and interval-censored event times, specialized R packages must be used:
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When a study contains both delayed entry and interval-censored event times,
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specialized tooling is needed.
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Of the packages below, only `flexsurv` handles both features together;
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the other two are listed because they cover interval censoring well
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and are the usual starting points, not because they solve the truncation half:
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- `flexsurv`: Fits flexible parametric survival models and allows custom likelihood specifications that incorporate both left-truncation conditioning and interval-censored bounds.
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- `icenReg`: Implements semi-parametric and parametric regression models specifically designed for interval-censored data with truncation.
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- `interval`: Provides nonparametric and semi-parametric interval-censored analysis tools with support for complex sampling designs.
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- `icenReg`: Fits regression models for interval-censored data:
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Cox proportional-hazards, proportional-odds, and accelerated failure time.
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Semi-parametric and fully parametric forms are both available,
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but the fully parametric option covers the AFT models only.
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It does not itself provide left-truncation conditioning.
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- `interval`: Fits nonparametric survival curves (NPMLE) for interval-censored data
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and provides weighted logrank and Wilcoxon-type tests [@fay2010exact].
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It is nonparametric throughout,
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so it supports neither regression nor truncation.
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references.bib

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doi={10.1198/jbes.2010.07136},
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url={https://doi.org/10.1198/jbes.2010.07136}
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}
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@article{fay2010exact,
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title={Exact and Asymptotic Weighted Logrank Tests for Interval Censored Data: The {interval} {R} Package},
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author={Fay, Michael P. and Shaw, Pamela A.},
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journal={Journal of Statistical Software},
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volume={36},
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number={2},
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pages={1--34},
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year={2010},
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doi={10.18637/jss.v036.i02}
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}

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