build based on 04d6a68

dev/.documenter-siteinfo.json

@@ -1 +1 @@
-{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-12-14T02:30:56","documenter_version":"1.8.0"}}
+{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-12-15T02:34:38","documenter_version":"1.8.0"}}

dev/index.html

@@ -570,4 +570,4 @@
     end
     # submit job
     run(`qsub tmp.sh`)
-end</code></pre><h2 id="Proportional-Odds-Assumption"><a class="docs-heading-anchor" href="#Proportional-Odds-Assumption">Proportional Odds Assumption</a><a id="Proportional-Odds-Assumption-1"></a><a class="docs-heading-anchor-permalink" href="#Proportional-Odds-Assumption" title="Permalink"></a></h2><p>The ordered multinomial model used in this package is a cumulative logit model where one effect size is estimated for each covariate. Using the logit link yields the commonly used proportional odds model which assumes the proportional odds assumption holds for your data/model. The proportional odds assumption assumes that the effect of a covariate <span>$\boldsymbol{\beta}$</span> is constant across different groupings of the ordinal outcome i.e.</p><p>The SNP&#39;s effect (on the odds ratio) is the same for the odds ratio of mild vs {medium, severe} as it is for the odds ratio of {mild, medium} vs severe. </p><p>The consequences/neccesity of this assumption has been thoroughly discussed, as an example see <a href="https://www.fharrell.com/post/po/">this blog post</a>. In simualtions, we did not find violation of this to increase type I error. As stated in the post, when the assumption is violated (meaning there are different effect sizes for different groupings), the estimated effect size is like a weighted average of the different effect sizes. Formal tests for proportional odds are likely to reject the assumption for large n (see p. 306, Categorical Data Analysis 3rd edition by Agresti). Violation of this assumption means the effect size <span>$\boldsymbol{\beta}$</span> differs across outcome strata, but should not imply a significant finding is not significant.</p></article><nav class="docs-footer"><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="Saturday 14 December 2024 02:30">Saturday 14 December 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end</code></pre><h2 id="Proportional-Odds-Assumption"><a class="docs-heading-anchor" href="#Proportional-Odds-Assumption">Proportional Odds Assumption</a><a id="Proportional-Odds-Assumption-1"></a><a class="docs-heading-anchor-permalink" href="#Proportional-Odds-Assumption" title="Permalink"></a></h2><p>The ordered multinomial model used in this package is a cumulative logit model where one effect size is estimated for each covariate. Using the logit link yields the commonly used proportional odds model which assumes the proportional odds assumption holds for your data/model. The proportional odds assumption assumes that the effect of a covariate <span>$\boldsymbol{\beta}$</span> is constant across different groupings of the ordinal outcome i.e.</p><p>The SNP&#39;s effect (on the odds ratio) is the same for the odds ratio of mild vs {medium, severe} as it is for the odds ratio of {mild, medium} vs severe. </p><p>The consequences/neccesity of this assumption has been thoroughly discussed, as an example see <a href="https://www.fharrell.com/post/po/">this blog post</a>. In simualtions, we did not find violation of this to increase type I error. As stated in the post, when the assumption is violated (meaning there are different effect sizes for different groupings), the estimated effect size is like a weighted average of the different effect sizes. Formal tests for proportional odds are likely to reject the assumption for large n (see p. 306, Categorical Data Analysis 3rd edition by Agresti). Violation of this assumption means the effect size <span>$\boldsymbol{\beta}$</span> differs across outcome strata, but should not imply a significant finding is not significant.</p></article><nav class="docs-footer"><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="Sunday 15 December 2024 02:34">Sunday 15 December 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>