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  <div class="section" id="module-maui.utils">





  
  

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<span id="maui-utilities"></span><h1>Maui Utilities<a class="headerlink" href="#module-maui.utils" title="Permalink to this headline">¶</a></h1>





  
  

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<p>The maui.utils model contains utility functions for multi-omics analysis





  
  

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using maui.</p>





  
  

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<dl class="function">





  
  

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<dt id="maui.utils.compute_harrells_c">





  
  

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<code class="descclassname">maui.utils.</code><code class="descname">compute_harrells_c</code><span class="sig-paren">(</span><em>z, survival, duration_column='duration', observed_column='observed', cox_penalties=[0.1, 1, 10, 100, 1000, 10000], cv_folds=5</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/maui/utils.html#compute_harrells_c"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#maui.utils.compute_harrells_c" title="Permalink to this definition">¶</a></dt>





  
  

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<dd><p>Compute’s Harrell’s c-Index for a Cox Proportional Hazards regression modeling





  
  

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survival by the latent factors in z.</p>





  
  

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<p>z:                  pd.DataFrame (n_samples, n_latent factors)





  
  

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survival:           pd.DataFrame of survival information and relevant covariates</p>





  
  

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<blockquote>





  
  

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<div>(such as sex, age at diagnosis, or tumor stage)</div></blockquote>





  
  

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<dl class="docutils">





  
  

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<dt>duration_column:    the name of the column in <code class="docutils literal notranslate"><span class="pre">survival</span></code> containing the</dt>





  
  

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<dd>duration (time between diagnosis and death or last followup)</dd>





  
  

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<dt>observed_column:    the name of the column in <code class="docutils literal notranslate"><span class="pre">survival</span></code> containing</dt>





  
  

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<dd>indicating whether time of death is known</dd>





  
  

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<dt>cox_penalties:      penalty coefficient in Cox PH solver (see <code class="docutils literal notranslate"><span class="pre">lifelines.CoxPHFitter</span></code>)</dt>





  
  

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<dd>to try. Returns the best c given by the different penalties





  
  

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(by cross-validation)</dd>





  
  

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</dl>





  
  

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<p>cv_folds:           number of cross-validation folds to compute C</p>





  
  

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<dl class="docutils">





  
  

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<dt>cs: array, Harrell’s c-Index, an auc-like metric for survival prediction accuracy.</dt>





  
  

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<dd>one value per cv_fold</dd>





  
  

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</dl>





  
  

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</dd></dl>





  
  

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<dl class="function">





  
  

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<dt id="maui.utils.compute_roc">





  
  

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<code class="descclassname">maui.utils.</code><code class="descname">compute_roc</code><span class="sig-paren">(</span><em>z</em>, <em>y</em>, <em>classifier=LinearSVC(C=0.001</em>, <em>class_weight=None</em>, <em>dual=True</em>, <em>fit_intercept=True</em>, <em>intercept_scaling=1</em>, <em>loss='squared_hinge'</em>, <em>max_iter=1000</em>, <em>multi_class='ovr'</em>, <em>penalty='l2'</em>, <em>random_state=None</em>, <em>tol=0.0001</em>, <em>verbose=0)</em>, <em>cv_folds=10</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/maui/utils.html#compute_roc"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#maui.utils.compute_roc" title="Permalink to this definition">¶</a></dt>





  
  

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<dd><p>Compute the ROC (false positive rate, true positive rate) using cross-validation.</p>





  
  

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<p>z:          DataFrame (n_samples, n_latent_factors) of latent factor values





  
  

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y:          Series (n_samples,) of ground-truth labels to try to predict





  
  

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classifier: Classifier object to use, default <code class="docutils literal notranslate"><span class="pre">LinearSVC(C=.001)</span></code></p>





  
  

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<dl class="docutils">





  
  

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<dt>roc_curves: dict, one key per class as well as “mean”, each value is a dataframe</dt>





  
  

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<dd>containing the tpr (true positive rate) and fpr (falce positive rate)





  
  

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defining that class (or the mean) ROC.</dd>





  
  

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</dl>





  
  

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</dd></dl>





  
  

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<dl class="function">





  
  

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<dt id="maui.utils.correlate_factors_and_features">





  
  

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<code class="descclassname">maui.utils.</code><code class="descname">correlate_factors_and_features</code><span class="sig-paren">(</span><em>z</em>, <em>concatenated_data</em>, <em>pval_threshold=0.001</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/maui/utils.html#correlate_factors_and_features"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#maui.utils.correlate_factors_and_features" title="Permalink to this definition">¶</a></dt>





  
  

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<dd><p>Compute pearson correlation of latent factors with input features.</p>





  
  

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<p>z:                  (n_samples, n_factors) DataFrame of latent factor values, output of maui model





  
  

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concatenated_data:  (n_samples, n_features) DataFrame of concatenated multi-omics data</p>





  
  

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<dl class="docutils">





  
  

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<dt>feature_s:  DataFrame (n_features, n_latent_factors)</dt>





  
  

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<dd>Latent factors representation of the data X.</dd>





  
  

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</dl>





  
  

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</dd></dl>





  
  

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<dl class="function">





  
  

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<dt id="maui.utils.estimate_kaplan_meier">





  
  

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<code class="descclassname">maui.utils.</code><code class="descname">estimate_kaplan_meier</code><span class="sig-paren">(</span><em>y</em>, <em>survival</em>, <em>duration_column='duration'</em>, <em>observed_column='observed'</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/maui/utils.html#estimate_kaplan_meier"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#maui.utils.estimate_kaplan_meier" title="Permalink to this definition">¶</a></dt>





  
  

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<dd><p>Estimate survival curves for groups defined in y based on survival data in <code class="docutils literal notranslate"><span class="pre">survival</span></code></p>





  
  

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<dl class="docutils">





  
  

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<dt>y:                  pd.Series, groups (clusters, subtypes). the index is</dt>





  
  

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<dd>the sample names</dd>





  
  

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<dt>survival:           pd.DataFrame with the same index as y, with columns for</dt>





  
  

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<dd>the duration (survival time for each patient) and whether





  
  

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or not the death was observed. If the death was not





  
  

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observed (sensored), the duration is the time of the last





  
  

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followup.</dd>





  
  

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</dl>





  
  

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<p>duration_column:        the name of the column in  <code class="docutils literal notranslate"><span class="pre">survival</span></code> with the duration





  
  

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observed_column:    the name of the column in <code class="docutils literal notranslate"><span class="pre">survival</span></code> with True/False values</p>





  
  

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<blockquote>





  
  

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<div>for whether death was observed or not</div></blockquote>





  
  

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<dl class="docutils">





  
  

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<dt>km_estimates:       pd.DataFrame, index is the timeline, columns are survival</dt>





  
  

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<dd>functions (estimated by Kaplan-Meier) for each class, as





  
  

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defined in <code class="docutils literal notranslate"><span class="pre">y</span></code>.</dd>





  
  

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</dl>





  
  

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</dd></dl>





  
  

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<dl class="function">





  
  

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<dt id="maui.utils.filter_factors_by_r2">





  
  

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<code class="descclassname">maui.utils.</code><code class="descname">filter_factors_by_r2</code><span class="sig-paren">(</span><em>z</em>, <em>x</em>, <em>threshold=0.02</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/maui/utils.html#filter_factors_by_r2"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#maui.utils.filter_factors_by_r2" title="Permalink to this definition">¶</a></dt>





  
  

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<dd><p>Filter latent factors by the R^2 of a linear model predicting features x





  
  

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from latent factors z.</p>





  
  

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<p>z:  (n_samples, n_factors) DataFrame of latent factor values, output of a maui model





  
  

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x:  (n_samples, n_features) DataFrame of concatenated multi-omics data</p>





  
  

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<dl class="docutils">





  
  

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<dt>z_filtered: (n_samples, n_factors) DataFrame of latent factor values,</dt>





  
  

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<dd>with only those columns from the input <cite>z</cite> which have an R^2





  
  

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above the threshold when using that column as an input





  
  

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to a linear model predicting <cite>x</cite>.</dd>





  
  

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</dl>





  
  

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</dd></dl>





  
  

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<dl class="function">





  
  

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<dt id="maui.utils.map_factors_to_feaures_using_linear_models">





  
  

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<code class="descclassname">maui.utils.</code><code class="descname">map_factors_to_feaures_using_linear_models</code><span class="sig-paren">(</span><em>z</em>, <em>x</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/maui/utils.html#map_factors_to_feaures_using_linear_models"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#maui.utils.map_factors_to_feaures_using_linear_models" title="Permalink to this definition">¶</a></dt>





  
  

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<dd><p>Get feature &lt;-&gt; latent factors mapping from linear models.





  
  

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Runs one univariate (multi-output) linear model per latent factor in <cite>z</cite>,





  
  

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predicting the values of the features <cite>x</cite>, in order to get weights





  
  

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between inputs and outputs.</p>





  
  

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<p>z:  (n_samples, n_factors) DataFrame of latent factor values, output of a maui model





  
  

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x:  (n_samples, n_features) DataFrame of concatenated multi-omics data</p>





  
  

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<dl class="docutils">





  
  

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<dt>W:  (n_features, n_latent_factors) DataFrame</dt>





  
  

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<dd>w_{ij} is the coefficient associated with feature <cite>i</cite> in a linear model





  
  

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predicting it from latent factor <cite>j</cite>.</dd>





  
  

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</dl>





  
  

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</dd></dl>





  
  

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<dl class="function">





  
  

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<dt id="maui.utils.merge_factors">





  
  

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<code class="descclassname">maui.utils.</code><code class="descname">merge_factors</code><span class="sig-paren">(</span><em>z</em>, <em>l=None</em>, <em>threshold=0.17</em>, <em>merge_fn=&lt;function mean&gt;</em>, <em>metric='correlation'</em>, <em>linkage='single'</em>, <em>plot_dendro=True</em>, <em>plot_dendro_ax=None</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/maui/utils.html#merge_factors"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#maui.utils.merge_factors" title="Permalink to this definition">¶</a></dt>





  
  

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<dd><p>Merge latent factors in <cite>z</cite> which form clusters, as defined by hierarchical





  
  

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clustering where a cluster is formed by cutting at a pre-set threshold, i.e.





  
  

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merge factors if their distance to one-another is below <cite>threshold</cite>.</p>





  
  

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<p>z:              (n_samples, n_factors) DataFrame of latent factor values, output of a maui model





  
  

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metric:         Distance metric to merge factors by, one which is supported by</p>





  
  

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<blockquote>





  
  

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<div><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.spatial.distance.pdist()</span></code></div></blockquote>





  
  

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<dl class="docutils">





  
  

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<dt>linkage:        The kind of linkage to form hierarchical clustering, one which is</dt>





  
  

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<dd>supported by <code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.cluster.hierarchy.linkage()</span></code></dd>





  
  

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<dt>l:              As an alternative to supplying <cite>metric</cite> and <cite>linkage</cite>, supply a</dt>





  
  

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<dd>linkage matrix of your own choice, such as one computed by





  
  

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<code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.cluster.hierarchy.linkage()</span></code></dd>





  
  

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<dt>threshold:      The distance threshold. latent factors with similarity below the</dt>





  
  

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<dd>threshold will be merged to form single latent facator</dd>





  
  

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<dt>merge_fn:       A function which will be used to merge latent factors. The default</dt>





  
  

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<dd>is <code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.mean()</span></code>, i.e. the newly formed (merged) latent factor





  
  

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will be the mean of the merged ones. Supply any function here which





  
  

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has the same interface, i.e. takes a matrix and an axis.</dd>





  
  

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<dt>plot_dendro:    Boolean. If True, the function will plot a dendrogram showing</dt>





  
  

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<dd>which latent factors are merged and the threshold.</dd>





  
  

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</dl>





  
  

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</dd></dl>





  
  

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<dl class="function">





  
  

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<dt id="maui.utils.multivariate_logrank_test">





  
  

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<code class="descclassname">maui.utils.</code><code class="descname">multivariate_logrank_test</code><span class="sig-paren">(</span><em>y</em>, <em>survival</em>, <em>duration_column='duration'</em>, <em>observed_column='observed'</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/maui/utils.html#multivariate_logrank_test"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#maui.utils.multivariate_logrank_test" title="Permalink to this definition">¶</a></dt>





  
  

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<dd><p>Compute the multivariate log-rank test for differential survival





  
  

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among the groups defined by <code class="docutils literal notranslate"><span class="pre">y</span></code> in the survival data in <code class="docutils literal notranslate"><span class="pre">survival</span></code>,





  
  

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under the null-hypothesis that all groups have the same survival function





  
  

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(i.e. test whether at least one group has different survival rates)</p>





  
  

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<dl class="docutils">





  
  

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<dt>y:                  pd.Series, groups (clusters, subtypes). the index is</dt>





  
  

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<dd>the sample names</dd>





  
  

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<dt>survival:           pd.DataFrame with the same index as y, with columns for</dt>





  
  

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<dd>the duration (survival time for each patient) and whether





  
  

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or not the death was observed. If the death was not





  
  

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observed (sensored), the duration is the time of the last





  
  

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followup.</dd>





  
  

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</dl>





  
  

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<p>duration_column:        the name of the column in  <code class="docutils literal notranslate"><span class="pre">survival</span></code> with the duration





  
  

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observed_column:    the name of the column in <code class="docutils literal notranslate"><span class="pre">survival</span></code> with True/False values</p>





  
  

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<blockquote>





  
  

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<div>for whether death was observed or not</div></blockquote>





  
  

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<p>test_statistic:     the test statistic (chi-square)





  
  

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p_value:            the associated p_value</p>





  
  

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</dd></dl>





  
  

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<dl class="function">





  
  

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<dt id="maui.utils.scale">





  
  

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<code class="descclassname">maui.utils.</code><code class="descname">scale</code><span class="sig-paren">(</span><em>df</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/maui/utils.html#scale"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#maui.utils.scale" title="Permalink to this definition">¶</a></dt>





  
  

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<dd><p>Scale and center data</p>





  
  

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<p>df:     pd.DataFrame (n_features, n_samples) non-scaled data</p>





  
  

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<p>scaled: pd.DataFrame (n_features, n_samples) scaled data</p>





  
  

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</dd></dl>





  
  

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<dl class="function">





  
  

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<dt id="maui.utils.select_clinical_factors">





  
  

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<code class="descclassname">maui.utils.</code><code class="descname">select_clinical_factors</code><span class="sig-paren">(</span><em>z</em>, <em>survival</em>, <em>duration_column='duration'</em>, <em>observed_column='observed'</em>, <em>alpha=0.05</em>, <em>cox_penalizer=0</em><span class="sig-paren">)</span><a class="reference internal" href="_modules/maui/utils.html#select_clinical_factors"><span class="viewcode-link">[source]</span></a><a class="headerlink" href="#maui.utils.select_clinical_factors" title="Permalink to this definition">¶</a></dt>





  
  

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<dd><p>Select latent factors which are predictive of survival. This is





  
  

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accomplished by fitting a Cox Proportional Hazards (CPH) model to each





  
  

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latent factor, while controlling for known covariates, and only keeping





  
  

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those latent factors whose coefficient in the CPH is nonzero (adjusted





  
  

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p-value &lt; alpha).</p>





  
  

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<dl class="docutils">





  
  

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<dt>survival:           pd.DataFrame of survival information and relevant covariates</dt>





  
  

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<dd>(such as sex, age at diagnosis, or tumor stage)</dd>





  
  

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<dt>duration_column:    the name of the column in <code class="docutils literal notranslate"><span class="pre">survival</span></code> containing the</dt>





  
  

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<dd>duration (time between diagnosis and death or last followup)</dd>





  
  

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<dt>observed_column:    the name of the column in <code class="docutils literal notranslate"><span class="pre">survival</span></code> containing</dt>





  
  

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<dd>indicating whether time of death is known</dd>





  
  

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<dt>alpha:              threshold for p-value of CPH coefficients to call a latent</dt>





  
  

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<dd>factor clinically relevant (p &lt; alpha)</dd>





  
  

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<p>cox_penalizer:      penalty coefficient in Cox PH solver (see <code class="docutils literal notranslate"><span class="pre">lifelines.CoxPHFitter</span></code>)</p>





  
  

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<dt>z_clinical: pd.DataFrame, subset of the latent factors which have been</dt>





  
  

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