build based on 0e9edd0

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-15T13:53:14","documenter_version":"1.8.0"}}
+{"documenter":{"julia_version":"1.11.1","generation_timestamp":"2024-11-15T14:59:03","documenter_version":"1.8.0"}}

dev/Likelihood/index.html

@@ -71,4 +71,4 @@
 \\
 S(t|\lambda,k)=& 1-I(k,\lambda t)\\
 \ln S(t|\alpha,\kappa)=&\ln(1-I(\exp(\kappa)), \exp(\ln(t)-\alpha))\\
-\end{aligned}$</span></p><p>Where we define <span>$I(k,s)$</span> as the upper incomplete gamma function ratio given by</p><p class="math-container">\[I(k,s) = \frac{\int_o^s t^{k-1}\exp(-t)dt}{\Gamma(k)}\]</p><p>(see <a href="https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc"><code>gamma_inc</code></a> function from <a href="https://github.com/JuliaMath/SpecialFunctions.jl"><code>SpecialFunctions.jl</code></a>)</p><h3 id="Log-logistic-distribution"><a class="docs-heading-anchor" href="#Log-logistic-distribution">Log-logistic distribution</a><a id="Log-logistic-distribution-1"></a><a class="docs-heading-anchor-permalink" href="#Log-logistic-distribution" title="Permalink"></a></h3><p>(not yet implemented)</p><h2 id="Semi-parametric-partial-likelihoods"><a class="docs-heading-anchor" href="#Semi-parametric-partial-likelihoods">Semi-parametric partial likelihoods</a><a id="Semi-parametric-partial-likelihoods-1"></a><a class="docs-heading-anchor-permalink" href="#Semi-parametric-partial-likelihoods" title="Permalink"></a></h2><p>In the Cox model, the partial-likelihoods are used in place of the likelihood function. These models are are modeled directly in terms of hazard ratios, allowing that the baseline hazard can be an arbitrary distribution. The Cox models implemented here are semi-parametric because they include a combination of parametric (hazard ratios) and non-parametric (baseline hazard) components. Cox&#39;s original likelihood is used here, and, in place of tied survival times, two different options are implemented for addressing ties. See the <code>survival</code><sup class="footnote-reference"><a id="citeref-surv" href="#footnote-surv">[surv]</a></sup> package vignette for original citations and methods for baseline hazard and partial-likelihood calculations.</p><h3 id="Efron&#39;s-partial-likelihood"><a class="docs-heading-anchor" href="#Efron&#39;s-partial-likelihood">Efron&#39;s partial likelihood</a><a id="Efron&#39;s-partial-likelihood-1"></a><a class="docs-heading-anchor-permalink" href="#Efron&#39;s-partial-likelihood" title="Permalink"></a></h3><p>This is the default in coxph (documentation in progress)</p><ul><li>Baseline hazard calculations are made using an analogue of the Fleming-Harrington estimator.</li></ul><h3 id="Breslow&#39;s-partial-likelihood"><a class="docs-heading-anchor" href="#Breslow&#39;s-partial-likelihood">Breslow&#39;s partial likelihood</a><a id="Breslow&#39;s-partial-likelihood-1"></a><a class="docs-heading-anchor-permalink" href="#Breslow&#39;s-partial-likelihood" title="Permalink"></a></h3><p>Documentation in progress</p><ul><li>Baseline hazard calculations are made using an analogue of the Nelson-Aalen estimator. </li></ul><h2 id="Time-varying-covariates"><a class="docs-heading-anchor" href="#Time-varying-covariates">Time-varying covariates</a><a id="Time-varying-covariates-1"></a><a class="docs-heading-anchor-permalink" href="#Time-varying-covariates" title="Permalink"></a></h2><p>Documentation in progress</p><h2 id="Numerical-algorithms"><a class="docs-heading-anchor" href="#Numerical-algorithms">Numerical algorithms</a><a id="Numerical-algorithms-1"></a><a class="docs-heading-anchor-permalink" href="#Numerical-algorithms" title="Permalink"></a></h2><p>Fitting algorithms include direct calculation, hard-coded Newton-Raphson algorithms, and optimization algorithms from the <code>Optim.jl</code> module:</p><h3 id="Non-parametric-analysis"><a class="docs-heading-anchor" href="#Non-parametric-analysis">Non-parametric analysis</a><a id="Non-parametric-analysis-1"></a><a class="docs-heading-anchor-permalink" href="#Non-parametric-analysis" title="Permalink"></a></h3><ul><li>Kaplan-Meier: direct calculation</li><li>Aalen-Johansen: direct calculation</li></ul><h3 id="Semi-parametric-analysis"><a class="docs-heading-anchor" href="#Semi-parametric-analysis">Semi-parametric analysis</a><a id="Semi-parametric-analysis-1"></a><a class="docs-heading-anchor-permalink" href="#Semi-parametric-analysis" title="Permalink"></a></h3><ul><li>Cox model, Efron&#39;s partial likelihood: Newton-Raphson with analytic gradient and Hessian, utilizing step-halving if the infinite norm of the gradient increases in a step.  </li><li>Cox model, Breslow&#39;s partial likelihood: Newton-Raphson with analytic gradient and Hessian, utilizing step-halving if the infinite norm of the gradient increases in a step. </li></ul><h3 id="Parametric-analysis"><a class="docs-heading-anchor" href="#Parametric-analysis">Parametric analysis</a><a id="Parametric-analysis-1"></a><a class="docs-heading-anchor-permalink" href="#Parametric-analysis" title="Permalink"></a></h3><ul><li>AFT model (Weibull, Exponential, Log-normal): <a href="https://julianlsolvers.github.io/Optim.jl/stable/#algo/lbfgs/"><code>BFGS</code></a> algorithm from <a href="https://github.com/JuliaNLSolvers/Optim.jl/"><code>Optim.jl</code></a>, supplemented with analytic gradient and Hessian using a Hager-Zhang line-search algorithm and static scaling of the P matrix</li><li>AFT model (Gamma, Generalized gamma): <a href="https://julianlsolvers.github.io/Optim.jl/stable/#algo/lbfgs/"><code>BFGS</code></a> algorithm from <a href="https://github.com/JuliaNLSolvers/Optim.jl/"><code>Optim.jl</code></a> utilizing forward differencing to calculate gradient and approximate Hessian using a quadratic backtracking line-search algorithm with an initial quadratic approximation for scaling the P matrix</li></ul><hr/><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-kf"><a class="tag is-link" href="#citeref-kf">kf</a>Kalbfleisch, J. D., &amp; Prentice, R. L. (2011). The statistical analysis of failure time data, 2nd ed. John Wiley &amp; Sons.</li><li class="footnote" id="footnote-surv"><a class="tag is-link" href="#citeref-surv">surv</a><a href="https://cran.r-project.org/web/packages/survival/vignettes/validate.pdf">https://cran.r-project.org/web/packages/survival/vignettes/validate.pdf</a></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Help</a><a class="docs-footer-nextpage" href="../nonparametric/">Non-parametric survival analysis »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Friday 15 November 2024 13:53">Friday 15 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+\end{aligned}$</span></p><p>Where we define <span>$I(k,s)$</span> as the upper incomplete gamma function ratio given by</p><p class="math-container">\[I(k,s) = \frac{\int_o^s t^{k-1}\exp(-t)dt}{\Gamma(k)}\]</p><p>(see <a href="https://specialfunctions.juliamath.org/stable/functions_list/#SpecialFunctions.gamma_inc"><code>gamma_inc</code></a> function from <a href="https://github.com/JuliaMath/SpecialFunctions.jl"><code>SpecialFunctions.jl</code></a>)</p><h3 id="Log-logistic-distribution"><a class="docs-heading-anchor" href="#Log-logistic-distribution">Log-logistic distribution</a><a id="Log-logistic-distribution-1"></a><a class="docs-heading-anchor-permalink" href="#Log-logistic-distribution" title="Permalink"></a></h3><p>(not yet implemented)</p><h2 id="Semi-parametric-partial-likelihoods"><a class="docs-heading-anchor" href="#Semi-parametric-partial-likelihoods">Semi-parametric partial likelihoods</a><a id="Semi-parametric-partial-likelihoods-1"></a><a class="docs-heading-anchor-permalink" href="#Semi-parametric-partial-likelihoods" title="Permalink"></a></h2><p>In the Cox model, the partial-likelihoods are used in place of the likelihood function. These models are are modeled directly in terms of hazard ratios, allowing that the baseline hazard can be an arbitrary distribution. The Cox models implemented here are semi-parametric because they include a combination of parametric (hazard ratios) and non-parametric (baseline hazard) components. Cox&#39;s original likelihood is used here, and, in place of tied survival times, two different options are implemented for addressing ties. See the <code>survival</code><sup class="footnote-reference"><a id="citeref-surv" href="#footnote-surv">[surv]</a></sup> package vignette for original citations and methods for baseline hazard and partial-likelihood calculations.</p><h3 id="Efron&#39;s-partial-likelihood"><a class="docs-heading-anchor" href="#Efron&#39;s-partial-likelihood">Efron&#39;s partial likelihood</a><a id="Efron&#39;s-partial-likelihood-1"></a><a class="docs-heading-anchor-permalink" href="#Efron&#39;s-partial-likelihood" title="Permalink"></a></h3><p>This is the default in coxph (documentation in progress)</p><ul><li>Baseline hazard calculations are made using an analogue of the Fleming-Harrington estimator.</li></ul><h3 id="Breslow&#39;s-partial-likelihood"><a class="docs-heading-anchor" href="#Breslow&#39;s-partial-likelihood">Breslow&#39;s partial likelihood</a><a id="Breslow&#39;s-partial-likelihood-1"></a><a class="docs-heading-anchor-permalink" href="#Breslow&#39;s-partial-likelihood" title="Permalink"></a></h3><p>Documentation in progress</p><ul><li>Baseline hazard calculations are made using an analogue of the Nelson-Aalen estimator. </li></ul><h2 id="Time-varying-covariates"><a class="docs-heading-anchor" href="#Time-varying-covariates">Time-varying covariates</a><a id="Time-varying-covariates-1"></a><a class="docs-heading-anchor-permalink" href="#Time-varying-covariates" title="Permalink"></a></h2><p>Documentation in progress</p><h2 id="Numerical-algorithms"><a class="docs-heading-anchor" href="#Numerical-algorithms">Numerical algorithms</a><a id="Numerical-algorithms-1"></a><a class="docs-heading-anchor-permalink" href="#Numerical-algorithms" title="Permalink"></a></h2><p>Fitting algorithms include direct calculation, hard-coded Newton-Raphson algorithms, and optimization algorithms from the <code>Optim.jl</code> module:</p><h3 id="Non-parametric-analysis"><a class="docs-heading-anchor" href="#Non-parametric-analysis">Non-parametric analysis</a><a id="Non-parametric-analysis-1"></a><a class="docs-heading-anchor-permalink" href="#Non-parametric-analysis" title="Permalink"></a></h3><ul><li>Kaplan-Meier: direct calculation</li><li>Aalen-Johansen: direct calculation</li></ul><h3 id="Semi-parametric-analysis"><a class="docs-heading-anchor" href="#Semi-parametric-analysis">Semi-parametric analysis</a><a id="Semi-parametric-analysis-1"></a><a class="docs-heading-anchor-permalink" href="#Semi-parametric-analysis" title="Permalink"></a></h3><ul><li>Cox model, Efron&#39;s partial likelihood: Newton-Raphson with analytic gradient and Hessian, utilizing step-halving if the infinite norm of the gradient increases in a step.  </li><li>Cox model, Breslow&#39;s partial likelihood: Newton-Raphson with analytic gradient and Hessian, utilizing step-halving if the infinite norm of the gradient increases in a step. </li></ul><h3 id="Parametric-analysis"><a class="docs-heading-anchor" href="#Parametric-analysis">Parametric analysis</a><a id="Parametric-analysis-1"></a><a class="docs-heading-anchor-permalink" href="#Parametric-analysis" title="Permalink"></a></h3><ul><li>AFT model (Weibull, Exponential, Log-normal): <a href="https://julianlsolvers.github.io/Optim.jl/stable/#algo/lbfgs/"><code>BFGS</code></a> algorithm from <a href="https://github.com/JuliaNLSolvers/Optim.jl/"><code>Optim.jl</code></a>, supplemented with analytic gradient and Hessian using a Hager-Zhang line-search algorithm and static scaling of the P matrix</li><li>AFT model (Gamma, Generalized gamma): <a href="https://julianlsolvers.github.io/Optim.jl/stable/#algo/lbfgs/"><code>BFGS</code></a> algorithm from <a href="https://github.com/JuliaNLSolvers/Optim.jl/"><code>Optim.jl</code></a> utilizing forward differencing to calculate gradient and approximate Hessian using a quadratic backtracking line-search algorithm with an initial quadratic approximation for scaling the P matrix</li></ul><hr/><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-kf"><a class="tag is-link" href="#citeref-kf">kf</a>Kalbfleisch, J. D., &amp; Prentice, R. L. (2011). The statistical analysis of failure time data, 2nd ed. John Wiley &amp; Sons.</li><li class="footnote" id="footnote-surv"><a class="tag is-link" href="#citeref-surv">surv</a><a href="https://cran.r-project.org/web/packages/survival/vignettes/validate.pdf">https://cran.r-project.org/web/packages/survival/vignettes/validate.pdf</a></li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Help</a><a class="docs-footer-nextpage" href="../nonparametric/">Non-parametric survival analysis »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Friday 15 November 2024 14:59">Friday 15 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>

dev/coxmodel/index.html

@@ -294,4 +294,4 @@
 ─────┼────────────────────────────────────────────
    1 │  0.872755   0.954257   0.895928   0.912742
    2 │ -0.443074  -0.439597  -0.475232  -0.485941
-   3 │  1.32749    1.32809    1.28391    1.32294</code></pre><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-cfw"><a class="tag is-link" href="#citeref-cfw">cfw</a>Cheng SC, Fine JP, Wei LJ. Prediction of Cumulative Incidence Function under the Proportional Hazards Model. Biometrics. 1998;54:219–228.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../nonparametric/">« Non-parametric survival analysis</a><a class="docs-footer-nextpage" href="../parametric/">Parametric survival analysis with AFT models »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Friday 15 November 2024 13:53">Friday 15 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+   3 │  1.32749    1.32809    1.28391    1.32294</code></pre><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-cfw"><a class="tag is-link" href="#citeref-cfw">cfw</a>Cheng SC, Fine JP, Wei LJ. Prediction of Cumulative Incidence Function under the Proportional Hazards Model. Biometrics. 1998;54:219–228.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../nonparametric/">« Non-parametric survival analysis</a><a class="docs-footer-nextpage" href="../parametric/">Parametric survival analysis with AFT models »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Friday 15 November 2024 14:59">Friday 15 November 2024</span>. Using Julia version 1.11.1.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>