View source for SMHS Usage Rfundamentals HTML Output Example

==[[SMHS_Usage_Rfundamentals| R Fundamentals]] - Example R-generated HTML Output==

The HTML file below is an example of an [[SMHS_Usage_Rfundamentals|R-output automatically exported from RStudio using knitr (see details here)]].

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 <div id="header">
 <h1 class="title">R HTML Export Demo using the SOCR PD Data</h1>
 <h4 class="author"><em>SOCR Team</em></h4>
 <h4 class="date"><em>April 12, 2016</em></h4>
 </div>
 
 
 <div id="data-import-from-socr-data-server" class="section level2">
 <h2>Data Import from SOCR Data server</h2>
 <pre class="r"><code>library(rvest)</code></pre>
 <pre><code>## Warning: package 'rvest' was built under R version 3.2.2</code></pre>
 <pre><code>## Loading required package: xml2</code></pre>
 <pre><code>## Warning: package 'xml2' was built under R version 3.2.2</code></pre>
 <pre class="r"><code>wiki &lt;- read_html(&quot;http://wiki.socr.umich.edu/index.php/SOCR_Data_PD_BiomedBigMetadata&quot;)
 html_nodes(wiki, &quot;#content&quot;)</code></pre>
 <pre><code>## {xml_nodeset (1)}
 ## [1] &lt;div id=&quot;content&quot; class=&quot;mw-body-primary&quot; role=&quot;main&quot;&gt;\n\t&lt;a id=&quot;top ...</code></pre>
 <pre class="r"><code>pd &lt;- html_table(html_nodes(wiki,&quot;table&quot;)[[1]])</code></pre>
 </div>
 <div id="data-preparation-factorization-of-patient-diagnosis" class="section level2">
 <h2>Data Preparation (factorization of patient diagnosis)</h2>
 <pre class="r"><code>## Convert Dx to a dichotomous variable
 ## pd$Dx &lt;- gsub(&quot;PD&quot;, 0, pd$Dx)
 ## pd$Dx &lt;- gsub(&quot;HC&quot;, 1, pd$Dx)
 ## pd$Dx &lt;- gsub(&quot;SWEDD&quot;, 2, pd$Dx)
 pd$Dx &lt;- as.factor(pd$Dx)</code></pre>
 </div>
 <div id="multivariate-linear-regression-analysis-predict-binary-dx" class="section level2">
 <h2>Multivariate Linear Regression Analysis (predict binary DX)</h2>
 <pre class="r"><code>## Full Model
 m1 &lt;- glm(Dx ~ L_caudate_Volume + R_caudate_Volume + L_putamen_Volume + R_putamen_Volume + L_hippocampus_Volume + R_hippocampus_Volume + cerebellum_Volume + L_lingual_gyrus_Volume + R_lingual_gyrus_Volume + L_fusiform_gyrus_Volume + R_fusiform_gyrus_Volume + Sex + Weight + Age + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + chr12_rs34637584_GT + chr17_rs11868035_GT, data=pd, family=&quot;binomial&quot;)
 summary(m1)</code></pre>
 <pre><code>## 
 ## Call:
 ## glm(formula = Dx ~ L_caudate_Volume + R_caudate_Volume + L_putamen_Volume + 
 ##     R_putamen_Volume + L_hippocampus_Volume + R_hippocampus_Volume + 
 ##     cerebellum_Volume + L_lingual_gyrus_Volume + R_lingual_gyrus_Volume + 
 ##     L_fusiform_gyrus_Volume + R_fusiform_gyrus_Volume + Sex + 
 ##     Weight + Age + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + 
 ##     chr12_rs34637584_GT + chr17_rs11868035_GT, family = &quot;binomial&quot;, 
 ##     data = pd)
 ## 
 ## Deviance Residuals: 
 ##     Min       1Q   Median       3Q      Max  
 ## -2.3126  -0.9250   0.5125   0.8234   1.9586  
 ## 
 ## Coefficients:
 ##                           Estimate Std. Error z value Pr(&gt;|z|)    
 ## (Intercept)             -3.610e+01  1.950e+01  -1.852 0.064086 .  
 ## L_caudate_Volume        -2.210e-03  2.666e-03  -0.829 0.407062    
 ## R_caudate_Volume        -2.253e-03  2.226e-03  -1.012 0.311614    
 ## L_putamen_Volume         3.911e-03  1.985e-03   1.970 0.048863 *  
 ## R_putamen_Volume        -4.274e-03  1.305e-03  -3.274 0.001058 ** 
 ## L_hippocampus_Volume     2.417e-03  1.333e-03   1.813 0.069879 .  
 ## R_hippocampus_Volume    -1.219e-03  1.160e-03  -1.051 0.293196    
 ## cerebellum_Volume        5.974e-04  6.215e-04   0.961 0.336450    
 ## L_lingual_gyrus_Volume   4.474e-04  6.471e-04   0.691 0.489338    
 ## R_lingual_gyrus_Volume   3.031e-04  6.885e-04   0.440 0.659740    
 ## L_fusiform_gyrus_Volume  1.896e-03  6.581e-04   2.882 0.003957 ** 
 ## R_fusiform_gyrus_Volume  8.328e-04  7.843e-04   1.062 0.288270    
 ## Sex                      1.668e-01  1.478e-01   1.129 0.259059    
 ## Weight                  -2.691e-02  7.195e-03  -3.740 0.000184 ***
 ## Age                     -1.520e-02  7.348e-03  -2.069 0.038568 *  
 ## UPDRS_part_I             4.891e-02  1.006e-01   0.486 0.626761    
 ## UPDRS_part_II            4.854e-02  1.487e-02   3.265 0.001095 ** 
 ## UPDRS_part_III           9.177e-02  1.032e-02   8.894  &lt; 2e-16 ***
 ## chr12_rs34637584_GT      1.136e+00  1.527e-01   7.438 1.02e-13 ***
 ## chr17_rs11868035_GT     -7.815e-01  1.481e-01  -5.277 1.31e-07 ***
 ## ---
 ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 ## 
 ## (Dispersion parameter for binomial family taken to be 1)
 ## 
 ##     Null deviance: 1467.0  on 1127  degrees of freedom
 ## Residual deviance: 1204.2  on 1108  degrees of freedom
 ## AIC: 1244.2
 ## 
 ## Number of Fisher Scoring iterations: 4</code></pre>
 <pre class="r"><code>par(mfrow=c(2,4))  # default layout() call may not be  sufficiently large  to contain the entire plot, so we extent it
 plot(m1)</code></pre>
 
 </div>
 <div id="variable-selection" class="section level2">
 <h2>Variable Selection</h2>
 <pre class="r"><code>library(leaps)</code></pre>
 <pre><code>## Warning: package 'leaps' was built under R version 3.2.2</code></pre>
 <pre class="r"><code>library(MASS)
 reg1 &lt;- regsubsets(Dx ~ L_caudate_Volume + R_caudate_Volume + L_putamen_Volume + R_putamen_Volume + L_hippocampus_Volume + R_hippocampus_Volume + cerebellum_Volume + L_lingual_gyrus_Volume + R_lingual_gyrus_Volume + L_fusiform_gyrus_Volume + R_fusiform_gyrus_Volume + Sex + Weight + Age + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + chr12_rs34637584_GT + chr17_rs11868035_GT, data=pd)
 summary(reg1)</code></pre>
 <pre><code>## Subset selection object
 ## Call: regsubsets.formula(Dx ~ L_caudate_Volume + R_caudate_Volume + 
 ##     L_putamen_Volume + R_putamen_Volume + L_hippocampus_Volume + 
 ##     R_hippocampus_Volume + cerebellum_Volume + L_lingual_gyrus_Volume + 
 ##     R_lingual_gyrus_Volume + L_fusiform_gyrus_Volume + R_fusiform_gyrus_Volume + 
 ##     Sex + Weight + Age + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + 
 ##     chr12_rs34637584_GT + chr17_rs11868035_GT, data = pd)
 ## 19 Variables  (and intercept)
 ##                         Forced in Forced out
 ## L_caudate_Volume            FALSE      FALSE
 ## R_caudate_Volume            FALSE      FALSE
 ## L_putamen_Volume            FALSE      FALSE
 ## R_putamen_Volume            FALSE      FALSE
 ## L_hippocampus_Volume        FALSE      FALSE
 ## R_hippocampus_Volume        FALSE      FALSE
 ## cerebellum_Volume           FALSE      FALSE
 ## L_lingual_gyrus_Volume      FALSE      FALSE
 ## R_lingual_gyrus_Volume      FALSE      FALSE
 ## L_fusiform_gyrus_Volume     FALSE      FALSE
 ## R_fusiform_gyrus_Volume     FALSE      FALSE
 ## Sex                         FALSE      FALSE
 ## Weight                      FALSE      FALSE
 ## Age                         FALSE      FALSE
 ## UPDRS_part_I                FALSE      FALSE
 ## UPDRS_part_II               FALSE      FALSE
 ## UPDRS_part_III              FALSE      FALSE
 ## chr12_rs34637584_GT         FALSE      FALSE
 ## chr17_rs11868035_GT         FALSE      FALSE
 ## 1 subsets of each size up to 8
 ## Selection Algorithm: exhaustive
 ##          L_caudate_Volume R_caudate_Volume L_putamen_Volume
 ## 1  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 2  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 3  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 4  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 5  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 6  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 7  ( 1 ) &quot; &quot;              &quot;*&quot;              &quot; &quot;             
 ## 8  ( 1 ) &quot; &quot;              &quot;*&quot;              &quot; &quot;             
 ##          R_putamen_Volume L_hippocampus_Volume R_hippocampus_Volume
 ## 1  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 2  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 3  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 4  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 5  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 6  ( 1 ) &quot;*&quot;              &quot; &quot;                  &quot; &quot;                 
 ## 7  ( 1 ) &quot;*&quot;              &quot; &quot;                  &quot; &quot;                 
 ## 8  ( 1 ) &quot;*&quot;              &quot; &quot;                  &quot; &quot;                 
 ##          cerebellum_Volume L_lingual_gyrus_Volume R_lingual_gyrus_Volume
 ## 1  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 2  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 3  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 4  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 5  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 6  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 7  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 8  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ##          L_fusiform_gyrus_Volume R_fusiform_gyrus_Volume Sex Weight Age
 ## 1  ( 1 ) &quot; &quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot; &quot;
 ## 2  ( 1 ) &quot; &quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot; &quot;
 ## 3  ( 1 ) &quot; &quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot; &quot;
 ## 4  ( 1 ) &quot; &quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot;*&quot;
 ## 5  ( 1 ) &quot;*&quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot;*&quot;
 ## 6  ( 1 ) &quot;*&quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot;*&quot;
 ## 7  ( 1 ) &quot;*&quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot;*&quot;
 ## 8  ( 1 ) &quot;*&quot;                     &quot; &quot;                     &quot; &quot; &quot;*&quot;    &quot;*&quot;
 ##          UPDRS_part_I UPDRS_part_II UPDRS_part_III chr12_rs34637584_GT
 ## 1  ( 1 ) &quot; &quot;          &quot; &quot;           &quot; &quot;            &quot;*&quot;                
 ## 2  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot; &quot;            &quot;*&quot;                
 ## 3  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 4  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 5  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 6  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 7  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 8  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ##          chr17_rs11868035_GT
 ## 1  ( 1 ) &quot; &quot;                
 ## 2  ( 1 ) &quot; &quot;                
 ## 3  ( 1 ) &quot; &quot;                
 ## 4  ( 1 ) &quot; &quot;                
 ## 5  ( 1 ) &quot; &quot;                
 ## 6  ( 1 ) &quot; &quot;                
 ## 7  ( 1 ) &quot; &quot;                
 ## 8  ( 1 ) &quot; &quot;</code></pre>
 </div>
 <div id="forward-selection" class="section level2">
 <h2>Forward Selection</h2>
 <pre class="r"><code>reg2 &lt;- regsubsets(Dx ~ L_caudate_Volume + R_caudate_Volume + L_putamen_Volume + R_putamen_Volume + L_hippocampus_Volume + R_hippocampus_Volume + cerebellum_Volume + L_lingual_gyrus_Volume + R_lingual_gyrus_Volume + L_fusiform_gyrus_Volume + R_fusiform_gyrus_Volume + Sex + Weight + Age + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + chr12_rs34637584_GT + chr17_rs11868035_GT, data=pd, method=&quot;forward&quot;)
 summary(reg2)</code></pre>
 <pre><code>## Subset selection object
 ## Call: regsubsets.formula(Dx ~ L_caudate_Volume + R_caudate_Volume + 
 ##     L_putamen_Volume + R_putamen_Volume + L_hippocampus_Volume + 
 ##     R_hippocampus_Volume + cerebellum_Volume + L_lingual_gyrus_Volume + 
 ##     R_lingual_gyrus_Volume + L_fusiform_gyrus_Volume + R_fusiform_gyrus_Volume + 
 ##     Sex + Weight + Age + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + 
 ##     chr12_rs34637584_GT + chr17_rs11868035_GT, data = pd, method = &quot;forward&quot;)
 ## 19 Variables  (and intercept)
 ##                         Forced in Forced out
 ## L_caudate_Volume            FALSE      FALSE
 ## R_caudate_Volume            FALSE      FALSE
 ## L_putamen_Volume            FALSE      FALSE
 ## R_putamen_Volume            FALSE      FALSE
 ## L_hippocampus_Volume        FALSE      FALSE
 ## R_hippocampus_Volume        FALSE      FALSE
 ## cerebellum_Volume           FALSE      FALSE
 ## L_lingual_gyrus_Volume      FALSE      FALSE
 ## R_lingual_gyrus_Volume      FALSE      FALSE
 ## L_fusiform_gyrus_Volume     FALSE      FALSE
 ## R_fusiform_gyrus_Volume     FALSE      FALSE
 ## Sex                         FALSE      FALSE
 ## Weight                      FALSE      FALSE
 ## Age                         FALSE      FALSE
 ## UPDRS_part_I                FALSE      FALSE
 ## UPDRS_part_II               FALSE      FALSE
 ## UPDRS_part_III              FALSE      FALSE
 ## chr12_rs34637584_GT         FALSE      FALSE
 ## chr17_rs11868035_GT         FALSE      FALSE
 ## 1 subsets of each size up to 8
 ## Selection Algorithm: forward
 ##          L_caudate_Volume R_caudate_Volume L_putamen_Volume
 ## 1  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 2  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 3  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 4  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 5  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 6  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 7  ( 1 ) &quot; &quot;              &quot;*&quot;              &quot; &quot;             
 ## 8  ( 1 ) &quot; &quot;              &quot;*&quot;              &quot; &quot;             
 ##          R_putamen_Volume L_hippocampus_Volume R_hippocampus_Volume
 ## 1  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 2  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 3  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 4  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 5  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 6  ( 1 ) &quot;*&quot;              &quot; &quot;                  &quot; &quot;                 
 ## 7  ( 1 ) &quot;*&quot;              &quot; &quot;                  &quot; &quot;                 
 ## 8  ( 1 ) &quot;*&quot;              &quot; &quot;                  &quot; &quot;                 
 ##          cerebellum_Volume L_lingual_gyrus_Volume R_lingual_gyrus_Volume
 ## 1  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 2  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 3  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 4  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 5  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 6  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 7  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 8  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ##          L_fusiform_gyrus_Volume R_fusiform_gyrus_Volume Sex Weight Age
 ## 1  ( 1 ) &quot; &quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot; &quot;
 ## 2  ( 1 ) &quot; &quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot; &quot;
 ## 3  ( 1 ) &quot; &quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot; &quot;
 ## 4  ( 1 ) &quot; &quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot;*&quot;
 ## 5  ( 1 ) &quot;*&quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot;*&quot;
 ## 6  ( 1 ) &quot;*&quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot;*&quot;
 ## 7  ( 1 ) &quot;*&quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot;*&quot;
 ## 8  ( 1 ) &quot;*&quot;                     &quot; &quot;                     &quot; &quot; &quot;*&quot;    &quot;*&quot;
 ##          UPDRS_part_I UPDRS_part_II UPDRS_part_III chr12_rs34637584_GT
 ## 1  ( 1 ) &quot; &quot;          &quot; &quot;           &quot; &quot;            &quot;*&quot;                
 ## 2  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot; &quot;            &quot;*&quot;                
 ## 3  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 4  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 5  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 6  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 7  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 8  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ##          chr17_rs11868035_GT
 ## 1  ( 1 ) &quot; &quot;                
 ## 2  ( 1 ) &quot; &quot;                
 ## 3  ( 1 ) &quot; &quot;                
 ## 4  ( 1 ) &quot; &quot;                
 ## 5  ( 1 ) &quot; &quot;                
 ## 6  ( 1 ) &quot; &quot;                
 ## 7  ( 1 ) &quot; &quot;                
 ## 8  ( 1 ) &quot; &quot;</code></pre>
 </div>
 <div id="backward-selection" class="section level2">
 <h2>Backward Selection</h2>
 <pre class="r"><code>reg3 &lt;- regsubsets(Dx ~ L_caudate_Volume + R_caudate_Volume + L_putamen_Volume + R_putamen_Volume + L_hippocampus_Volume + R_hippocampus_Volume + cerebellum_Volume + L_lingual_gyrus_Volume + R_lingual_gyrus_Volume + L_fusiform_gyrus_Volume + R_fusiform_gyrus_Volume + Sex + Weight + Age + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + chr12_rs34637584_GT + chr17_rs11868035_GT, data=pd, method=&quot;backward&quot;)
 summary(reg3)</code></pre>
 <pre><code>## Subset selection object
 ## Call: regsubsets.formula(Dx ~ L_caudate_Volume + R_caudate_Volume + 
 ##     L_putamen_Volume + R_putamen_Volume + L_hippocampus_Volume + 
 ##     R_hippocampus_Volume + cerebellum_Volume + L_lingual_gyrus_Volume + 
 ##     R_lingual_gyrus_Volume + L_fusiform_gyrus_Volume + R_fusiform_gyrus_Volume + 
 ##     Sex + Weight + Age + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + 
 ##     chr12_rs34637584_GT + chr17_rs11868035_GT, data = pd, method = &quot;backward&quot;)
 ## 19 Variables  (and intercept)
 ##                         Forced in Forced out
 ## L_caudate_Volume            FALSE      FALSE
 ## R_caudate_Volume            FALSE      FALSE
 ## L_putamen_Volume            FALSE      FALSE
 ## R_putamen_Volume            FALSE      FALSE
 ## L_hippocampus_Volume        FALSE      FALSE
 ## R_hippocampus_Volume        FALSE      FALSE
 ## cerebellum_Volume           FALSE      FALSE
 ## L_lingual_gyrus_Volume      FALSE      FALSE
 ## R_lingual_gyrus_Volume      FALSE      FALSE
 ## L_fusiform_gyrus_Volume     FALSE      FALSE
 ## R_fusiform_gyrus_Volume     FALSE      FALSE
 ## Sex                         FALSE      FALSE
 ## Weight                      FALSE      FALSE
 ## Age                         FALSE      FALSE
 ## UPDRS_part_I                FALSE      FALSE
 ## UPDRS_part_II               FALSE      FALSE
 ## UPDRS_part_III              FALSE      FALSE
 ## chr12_rs34637584_GT         FALSE      FALSE
 ## chr17_rs11868035_GT         FALSE      FALSE
 ## 1 subsets of each size up to 8
 ## Selection Algorithm: backward
 ##          L_caudate_Volume R_caudate_Volume L_putamen_Volume
 ## 1  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 2  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 3  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 4  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 5  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 6  ( 1 ) &quot; &quot;              &quot; &quot;              &quot; &quot;             
 ## 7  ( 1 ) &quot; &quot;              &quot;*&quot;              &quot; &quot;             
 ## 8  ( 1 ) &quot; &quot;              &quot;*&quot;              &quot; &quot;             
 ##          R_putamen_Volume L_hippocampus_Volume R_hippocampus_Volume
 ## 1  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 2  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 3  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 4  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 5  ( 1 ) &quot; &quot;              &quot; &quot;                  &quot; &quot;                 
 ## 6  ( 1 ) &quot;*&quot;              &quot; &quot;                  &quot; &quot;                 
 ## 7  ( 1 ) &quot;*&quot;              &quot; &quot;                  &quot; &quot;                 
 ## 8  ( 1 ) &quot;*&quot;              &quot; &quot;                  &quot; &quot;                 
 ##          cerebellum_Volume L_lingual_gyrus_Volume R_lingual_gyrus_Volume
 ## 1  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 2  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 3  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 4  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 5  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 6  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 7  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ## 8  ( 1 ) &quot; &quot;               &quot; &quot;                    &quot; &quot;                   
 ##          L_fusiform_gyrus_Volume R_fusiform_gyrus_Volume Sex Weight Age
 ## 1  ( 1 ) &quot; &quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot; &quot;
 ## 2  ( 1 ) &quot; &quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot; &quot;
 ## 3  ( 1 ) &quot; &quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot; &quot;
 ## 4  ( 1 ) &quot; &quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot;*&quot;
 ## 5  ( 1 ) &quot;*&quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot;*&quot;
 ## 6  ( 1 ) &quot;*&quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot;*&quot;
 ## 7  ( 1 ) &quot;*&quot;                     &quot; &quot;                     &quot; &quot; &quot; &quot;    &quot;*&quot;
 ## 8  ( 1 ) &quot;*&quot;                     &quot; &quot;                     &quot; &quot; &quot;*&quot;    &quot;*&quot;
 ##          UPDRS_part_I UPDRS_part_II UPDRS_part_III chr12_rs34637584_GT
 ## 1  ( 1 ) &quot; &quot;          &quot; &quot;           &quot; &quot;            &quot;*&quot;                
 ## 2  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot; &quot;            &quot;*&quot;                
 ## 3  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 4  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 5  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 6  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 7  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ## 8  ( 1 ) &quot;*&quot;          &quot; &quot;           &quot;*&quot;            &quot;*&quot;                
 ##          chr17_rs11868035_GT
 ## 1  ( 1 ) &quot; &quot;                
 ## 2  ( 1 ) &quot; &quot;                
 ## 3  ( 1 ) &quot; &quot;                
 ## 4  ( 1 ) &quot; &quot;                
 ## 5  ( 1 ) &quot; &quot;                
 ## 6  ( 1 ) &quot; &quot;                
 ## 7  ( 1 ) &quot; &quot;                
 ## 8  ( 1 ) &quot; &quot;</code></pre>
 </div>
 <div id="reduced-model" class="section level2">
 <h2>Reduced Model</h2>
 <pre class="r"><code>m2 &lt;- glm(Dx ~ R_caudate_Volume + R_fusiform_gyrus_Volume + Weight + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + chr12_rs34637584_GT + chr17_rs11868035_GT, data=pd, family=&quot;binomial&quot;)
 summary(m2)</code></pre>
 <pre><code>## 
 ## Call:
 ## glm(formula = Dx ~ R_caudate_Volume + R_fusiform_gyrus_Volume + 
 ##     Weight + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + 
 ##     chr12_rs34637584_GT + chr17_rs11868035_GT, family = &quot;binomial&quot;, 
 ##     data = pd)
 ## 
 ## Deviance Residuals: 
 ##     Min       1Q   Median       3Q      Max  
 ## -2.1034  -0.9941   0.5432   0.8438   1.9065  
 ## 
 ## Coefficients:
 ##                           Estimate Std. Error z value Pr(&gt;|z|)    
 ## (Intercept)             -4.6549832  7.7471401  -0.601 0.547930    
 ## R_caudate_Volume        -0.0024399  0.0021297  -1.146 0.251937    
 ## R_fusiform_gyrus_Volume  0.0008031  0.0007508   1.070 0.284794    
 ## Weight                  -0.0269228  0.0069556  -3.871 0.000109 ***
 ## UPDRS_part_I             0.0865148  0.0962768   0.899 0.368863    
 ## UPDRS_part_II            0.0471636  0.0143506   3.287 0.001014 ** 
 ## UPDRS_part_III           0.0860347  0.0099415   8.654  &lt; 2e-16 ***
 ## chr12_rs34637584_GT      1.1672942  0.1421042   8.214  &lt; 2e-16 ***
 ## chr17_rs11868035_GT     -0.7393041  0.1429901  -5.170 2.34e-07 ***
 ## ---
 ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 ## 
 ## (Dispersion parameter for binomial family taken to be 1)
 ## 
 ##     Null deviance: 1467.0  on 1127  degrees of freedom
 ## Residual deviance: 1238.5  on 1119  degrees of freedom
 ## AIC: 1256.5
 ## 
 ## Number of Fisher Scoring iterations: 4</code></pre>
 <pre class="r"><code>par(mfrow=c(2,2))
 plot(m2)</code></pre>
 </div>
 <div id="removing-bad-leverage-points" class="section level2">
 <h2>Removing Bad Leverage Points</h2>
 <pre class="r"><code>n &lt;- dim(pd)[1]
 case &lt;- c(1:n)
 cooks &lt;- cooks.distance(m2)
 cooks_outlier &lt;- case[cooks&gt;4/(length(pd$Dx)-2)]
 cooks_outlier</code></pre>
 <pre><code>##  [1]  653  654  655  656  673  674  675  676 1025 1026 1027 1028</code></pre>
 <pre class="r"><code>m2 &lt;- glm(Dx ~ R_caudate_Volume + R_fusiform_gyrus_Volume + Weight + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + chr12_rs34637584_GT + chr17_rs11868035_GT, data=pd[-cooks_outlier,], family=&quot;binomial&quot;)
 summary(m2)</code></pre>
 <pre><code>## 
 ## Call:
 ## glm(formula = Dx ~ R_caudate_Volume + R_fusiform_gyrus_Volume + 
 ##     Weight + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + 
 ##     chr12_rs34637584_GT + chr17_rs11868035_GT, family = &quot;binomial&quot;, 
 ##     data = pd[-cooks_outlier, ])
 ## 
 ## Deviance Residuals: 
 ##     Min       1Q   Median       3Q      Max  
 ## -2.1806  -0.9525   0.5194   0.8178   1.8609  
 ## 
 ## Coefficients:
 ##                           Estimate Std. Error z value Pr(&gt;|z|)    
 ## (Intercept)             -6.6561223  7.9427555  -0.838    0.402    
 ## R_caudate_Volume        -0.0026930  0.0021848  -1.233    0.218    
 ## R_fusiform_gyrus_Volume  0.0010330  0.0007694   1.343    0.179    
 ## Weight                  -0.0310176  0.0071300  -4.350 1.36e-05 ***
 ## UPDRS_part_I             0.1332157  0.0987274   1.349    0.177    
 ## UPDRS_part_II            0.0595924  0.0148204   4.021 5.80e-05 ***
 ## UPDRS_part_III           0.0947331  0.0103083   9.190  &lt; 2e-16 ***
 ## chr12_rs34637584_GT      1.2794104  0.1458133   8.774  &lt; 2e-16 ***
 ## chr17_rs11868035_GT     -0.7348668  0.1466157  -5.012 5.38e-07 ***
 ## ---
 ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 ## 
 ## (Dispersion parameter for binomial family taken to be 1)
 ## 
 ##     Null deviance: 1446.8  on 1115  degrees of freedom
 ## Residual deviance: 1190.5  on 1107  degrees of freedom
 ## AIC: 1208.5
 ## 
 ## Number of Fisher Scoring iterations: 4</code></pre>
 <pre class="r"><code>par(mfrow=c(2,2))
 plot(m2)</code></pre>
 
 </div>
 <div id="log-transformation" class="section level2">
 <h2>Log Transformation</h2>
 <pre class="r"><code>m3 &lt;- glm(Dx ~ log(R_caudate_Volume) + log(R_fusiform_gyrus_Volume) + log(Weight) + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + chr12_rs34637584_GT + chr17_rs11868035_GT, data=pd[-cooks_outlier,], family=&quot;binomial&quot;)
 summary(m3)</code></pre>
 <pre><code>## 
 ## Call:
 ## glm(formula = Dx ~ log(R_caudate_Volume) + log(R_fusiform_gyrus_Volume) + 
 ##     log(Weight) + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + 
 ##     chr12_rs34637584_GT + chr17_rs11868035_GT, family = &quot;binomial&quot;, 
 ##     data = pd[-cooks_outlier, ])
 ## 
 ## Deviance Residuals: 
 ##     Min       1Q   Median       3Q      Max  
 ## -2.1723  -0.9456   0.5177   0.8192   1.8614  
 ## 
 ## Coefficients:
 ##                               Estimate Std. Error z value Pr(&gt;|z|)    
 ## (Intercept)                  -63.35131   71.87608  -0.881    0.378    
 ## log(R_caudate_Volume)         -2.84111    2.19100  -1.297    0.195    
 ## log(R_fusiform_gyrus_Volume)  10.00512    7.69485   1.300    0.194    
 ## log(Weight)                   -2.44090    0.56224  -4.341 1.42e-05 ***
 ## UPDRS_part_I                   0.13423    0.09872   1.360    0.174    
 ## UPDRS_part_II                  0.06010    0.01482   4.054 5.02e-05 ***
 ## UPDRS_part_III                 0.09425    0.01029   9.160  &lt; 2e-16 ***
 ## chr12_rs34637584_GT            1.28158    0.14584   8.788  &lt; 2e-16 ***
 ## chr17_rs11868035_GT           -0.73351    0.14663  -5.003 5.66e-07 ***
 ## ---
 ## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
 ## 
 ## (Dispersion parameter for binomial family taken to be 1)
 ## 
 ##     Null deviance: 1446.8  on 1115  degrees of freedom
 ## Residual deviance: 1190.3  on 1107  degrees of freedom
 ## AIC: 1208.3
 ## 
 ## Number of Fisher Scoring iterations: 4</code></pre>
 <pre class="r"><code>par(mfrow=c(2,2))
 plot(m3)</code></pre>
 
 </div>
 <div id="multicollinearity-check" class="section level2">
 <h2>Multicollinearity Check</h2>
 <pre class="r"><code>library(car)
 vif(m2)</code></pre>
 <pre><code>##        R_caudate_Volume R_fusiform_gyrus_Volume                  Weight 
 ##                1.024786                1.053087                1.056551 
 ##            UPDRS_part_I           UPDRS_part_II          UPDRS_part_III 
 ##                1.019879                1.027360                1.046336 
 ##     chr12_rs34637584_GT     chr17_rs11868035_GT 
 ##                1.054836                1.060063</code></pre>
 <pre class="r"><code>## Here, each of the variance inflaction factors is less than 5, so the multicollinearity between these predictors does not affect the result significantly.</code></pre>
 </div>
 <div id="likelihood-ratio-test" class="section level2">
 <h2>Likelihood Ratio Test</h2>
 <pre class="r"><code>with(m2, null.deviance - deviance)</code></pre>
 <pre><code>## [1] 256.336</code></pre>
 <pre class="r"><code>with(m2, df.null - df.residual)</code></pre>
 <pre><code>## [1] 8</code></pre>
 <pre class="r"><code>with(m2, pchisq(null.deviance - deviance, df.null - df.residual, lower.tail = FALSE))</code></pre>
 <pre><code>## [1] 7.811597e-51</code></pre>
 <pre class="r"><code>## The chi-square of 403 with 8 degrees of freedom and an associated p-value of less than 0.001 indicates that the model as a whole fits significantly better than an empty model.</code></pre>
 </div>
 <div id="linear-discriminant-analysis" class="section level2">
 <h2>Linear Discriminant Analysis</h2>
 <pre class="r"><code>## Consider time = 0 only
 pdzero &lt;- pd[which(pd$Time==0),]
 ## Split dataset into 70% training and 30% testing set
 set.seed(666)
 train_index &lt;- sample(dim(pdzero)[1], trunc(dim(pdzero)[1]*0.7))
 train &lt;- pdzero[train_index,]
 test &lt;- pdzero[-train_index,]
 library(MASS)
 lda.fit &lt;- lda(Dx~L_caudate_Volume + R_caudate_Volume + L_putamen_Volume + R_putamen_Volume + L_hippocampus_Volume + R_hippocampus_Volume + cerebellum_Volume + L_lingual_gyrus_Volume + R_lingual_gyrus_Volume + L_fusiform_gyrus_Volume + R_fusiform_gyrus_Volume + Sex + Weight + Age + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + chr12_rs34637584_GT + chr17_rs11868035_GT, data=train)
 lda.predict &lt;- predict(lda.fit, test)
 table(lda.predict$class, test$Dx)</code></pre>
 <pre><code>##        
 ##         HC PD SWEDD
 ##   HC    17  3     8
 ##   PD     9 22     3
 ##   SWEDD  7 11     5</code></pre>
 </div>
 <div id="logistic-regression-analysis" class="section level2">
 <h2>Logistic Regression Analysis</h2>
 <pre class="r"><code>## Break up the three-level dependent variable into two binary variables
 pdzero$PD_YN &lt;- ifelse(pdzero$Dx==&quot;PD&quot;, 1, 0)
 pdzero$SWEDD_YN &lt;- ifelse(pdzero$Dx==&quot;SWEDD&quot;, 1, 0)
 ## Split the dataset into 70% training and 30% testing set
 set.seed(666)
 train_index &lt;- sample(dim(pdzero)[1], trunc(dim(pdzero)[1]*0.7))
 train &lt;- pdzero[train_index,]
 test &lt;- pdzero[-train_index,]
 ## PD_YN as outcome
 log1 &lt;- glm(PD_YN ~ L_caudate_Volume + R_caudate_Volume + L_putamen_Volume + R_putamen_Volume + L_hippocampus_Volume + R_hippocampus_Volume + cerebellum_Volume + L_lingual_gyrus_Volume + R_lingual_gyrus_Volume + L_fusiform_gyrus_Volume + R_fusiform_gyrus_Volume + Sex + Weight + Age + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + chr12_rs34637584_GT + chr17_rs11868035_GT, data=train, family=&quot;binomial&quot;)
 probPD &lt;- predict(log1, test, type=&quot;response&quot;)
 median(probPD) # 0.30</code></pre>
 <pre><code>## [1] 0.2983791</code></pre>
 <pre class="r"><code>resultPD &lt;- ifelse(probPD&gt;0.3, 1, 0)
 table(resultPD, test$PD_YN)</code></pre>
 <pre><code>##         
 ## resultPD  0  1
 ##        0 30 13
 ##        1 19 23</code></pre>
 <pre class="r"><code>## SWEDD as outcome
 log2 &lt;- glm(SWEDD_YN ~ L_caudate_Volume + R_caudate_Volume + L_putamen_Volume + R_putamen_Volume + L_hippocampus_Volume + R_hippocampus_Volume + cerebellum_Volume + L_lingual_gyrus_Volume + R_lingual_gyrus_Volume + L_fusiform_gyrus_Volume + R_fusiform_gyrus_Volume + Sex + Weight + Age + UPDRS_part_I + UPDRS_part_II + UPDRS_part_III + chr12_rs34637584_GT + chr17_rs11868035_GT, data=train, family=&quot;binomial&quot;)
 probSW &lt;- predict(log2, test, type=&quot;response&quot;)
 median(probSW) # 0.301</code></pre>
 <pre><code>## [1] 0.3013772</code></pre>
 <pre class="r"><code>resultSW &lt;- ifelse(probSW&gt;0.2, 1, 0)
 table(resultSW, test$SWEDD_YN)</code></pre>
 <pre><code>##         
 ## resultSW  0  1
 ##        0 19  2
 ##        1 50 14</code></pre>
 <pre class="r"><code>## Combine the results of two logistic model together
 finalpred &lt;- NULL
 for (i in 1:dim(test)[1]) {
   if (resultPD[i]==1 &amp; resultSW[i]==0) {
     finalpred[i] &lt;- &quot;PD&quot;
   }
   if (resultPD[i]==1 &amp; resultSW[i]==1) {
     finalpred[i] &lt;- ifelse(probPD[i]&gt;probSW[i], &quot;PD&quot;, &quot;SW&quot;)
   }
   if (resultPD[i]==0 &amp; resultSW[i]==1) {
     finalpred[i] &lt;- &quot;SW&quot;
   }
   if (resultPD[i]==0 &amp; resultSW[i]==0) {
     finalpred[i] &lt;- &quot;HC&quot;
   }
 }
 table(finalpred, test$Dx)</code></pre>
 <pre><code>##          
 ## finalpred HC PD SWEDD
 ##        HC  3  1     1
 ##        PD 15 21     3
 ##        SW 15 14    12</code></pre>
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