notebooks/PCR_MTBLS404.ipynb

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    "<div style=\"text-align: justify; padding:5px; background-color:rgb(252, 253, 255); border: 1px solid lightgrey; padding-left: 1em; padding-right: 1em;\">\n",
    "    <font color='red'>To begin: Click anywhere in this cell and press <kbd>Run</kbd> on the menu bar. This executes the current cell and then highlights the next cell. There are two types of cells. A <i>text cell</i> and a <i>code cell</i>. When you <kbd>Run</kbd> a text cell (<i>we are in a text cell now</i>), you advance to the next cell without executing any code. When you <kbd>Run</kbd> a code cell (<i>identified by <span style=\"font-family: courier; color:black; background-color:white;\">In[ ]:</span> to the left of the cell</i>) you advance to the next cell after executing all the Python code within that cell. Any visual results produced by the code (text/figures) are reported directly below that cell. Press <kbd>Run</kbd> again. Repeat this process until the end of the notebook. <b>NOTE:</b> All the cells in this notebook can be automatically executed sequentially by clicking <kbd>Kernel</kbd><font color='black'>→</font><kbd>Restart and Run All</kbd>. Should anything crash then restart the Jupyter Kernal by clicking <kbd>Kernel</kbd><font color='black'>→</font><kbd>Restart</kbd>, and start again from the top.\n",
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    "<div style=\"text-align: justify; padding:5px; background-color:rgb(252, 253, 255); border: 1px solid lightgrey; padding-left: 1em; padding-right: 1em;\">\n",
    "<img src=\"https://github.com/CIMCB/MetabComparisonBinaryML/blob/master/cimcb_logo.png?raw=true\" width=\"180px\" align=\"right\" style=\"padding: 20px\">\n",
    "    \n",
    "<h1> PCR_MTBLS404 </h1>\n",
    "\n",
    "<br>\n",
    "<br>\n",
    "<br>\n",
    "<p style=\"text-align: justify\"> The study used in this tutorial has been previously published by  <a href=\"https://doi.org/10.1021/acs.jproteome.5b00354\">Thévenot et al. (2015)</a>, and the deconvolved and annotated data file deposited at the Metabolights data repository. The data can be accessed directly via its study ID: <a href=\"https://www.ebi.ac.uk/metabolights/MTBLS404\">MTBLS404</a>. This workflow requires data to be formatted as a Microsoft Excel file, using the Tidy Data framework (i.e. each column is a variable, and row is an observation). As such, the Excel file contains a Data Sheet and Peak Sheet. The Data Sheet contains all the metabolite concentrations and metadata associated with each observation (requiring the inclusion of the columns: Idx, SampleID, and Class). The Peak Sheet contains all the metadata pertaining to each measured metabolite (requiring the inclusion of the columns: Idx, Name, and Label). Please inspect the Excel file <a href=\"https://github.com/CIMCB/MetabComparisonBinaryML/blob/master/dynamic/data/MTBLS404.xlsx?raw=true\">MTBLS404.xlsx</a> used in this workflow before proceeding.</p>\n",
    "\n",
    "<p style=\"text-align: justify\">This is a urine LC-MS dataset consisting of 120 named metabolites. This paper was an analysis of the variations of the human adult urinary metabolome with age, body mass index, and gender. For the purpose of this study, we compare males (Class=1; n=101) and females (Class=0; n=83) in a binary discriminant analysis.</p>\n",
    "    \n",
    "<br>\n",
    "\n",
    "</ol> \n",
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    "<div style=\"text-align: justify; padding:5px; background-color:rgb(252, 253, 255); border: 1px solid lightgrey; padding-left: 1em; padding-right: 1em;\">\n",
    "    \n",
    "<h1> PCR Workflow </h1> \n",
    "<br>\n",
    "<p style=\"text-align: justify\"> This Jupyter Notebook implements the complete workflow for creating, optimising, and evaluating a principal component regression (PCR) model. PCR is a two-stage algorithm combining principal component analysis (PCA) and multiple linear regression (MLR), where the first N principal component scores act as the independent variables of the MLR, and the binary classification the is the dependent variable. The value of N is chosen by the user. <b> PCA was implemented using <a href=\"https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html\">PCA</a>\n",
    "    and MLR using <a href=\"https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html\">Linear Regression</a> from scikit-learn.</b></p>\n",
    "<i style=\"text-align: justify\"> Please refer to the 'cimcb' package documentation for further details regarding this specific implementation: <a href=\"https://cimcb.github.io/cimcb\">https://cimcb.github.io/cimcb</a></i>\n",
    " \n",
    "<br>\n",
    "<br>\n",
    "<b style=\"text-align: justify\"> PCR uses the following Hyperparameter(s):</b>\n",
    "<ul style=\"list-style-type: square;\">\n",
    "    <li><code>n_components</code>: number of principal components projected into the MLR (default = 2)</li>\n",
    "</ul>\n",
    "<i style=\"text-align: justify\">The purpose of each hyperparameter is explained here:  <a href=\"https://link.springer.com/content/pdf/10.1007/978-3-642-04898-2_455.pdf\">Jolliffe (2011)</a></i>\n",
    " \n",
    "<br>\n",
    "<br>\n",
    "\n",
    "<b style=\"text-align: justify\"> The notebook workflow is broken into the following steps:</b>\n",
    "\n",
    "<ol>\n",
    "    <li><b><i>Import Packages</i></b>: First, the Python packages required for this workflow need to be imported (<a href=\"http://www.numpy.org/\"><code>numpy</code></a>, <a href=\"https://pandas.pydata.org/\"><code>pandas</code></a>, and <a href=\"https://cimcb.github.io/cimcb\"><code>cimcb</code></a>).\n",
    "</li>\n",
    "    <li><b><i>Load Data & Peak Sheet:</i></b> From the Excel spreadsheet, import the Data and Peak spreadsheets and create two respective <a href=\"https://pandas.pydata.org/\">Pandas</a> tables: <code>DataTable</code> and <code>PeakTable</code>.</li>\n",
    "    <li><b><i>Extract X & Y:</i></b> Next, we reduce the data in <code>DataTable</code> to include only those observations needed for the binary comparison and create a new table: <code>DataTable2</code>. We define one column of the data table to be the \"outcome\" variable <code>Outcomes</code>, and convert the class labels in this column to a binary outcome vector <code>Y</code>, where <code>1</code> is the positive outcome, and <code>0</code> the negative outcome (eg. case=1 & control=0). A new variable <code>peaklist</code> is created to hold the names (M1...Mn) of the metabolites to be used in the discriminant analysis. To create an independent dataset to evaluate, <a href=\"https://scikit-learn.org/stable/\">scikit-learn</a> module's <a href=\"https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html\"><code>train_test_split()</code></a> function is used. The data is split into 2/3rd training (<code>DataTrain</code> and <code>YTrain</code>), and 1/3rd test (<code>DataTest</code> and <code>YTest</code>). The metabolite data corresponding to <code>peaklist</code> is extracted from <code>DataTrain</code> and placed in a matrix <code>XTrain</code>. The <code>XTrain</code> matrix is log-transformed and auto-scaled, with missing values imputed using k-nearest neighbours (k=3). Then the metabolite data corresponding to <code>peaklist</code> is extracted from <code>DataTest</code> and placed in a matrix <code>XTest</code>. The <code>XTest</code> matrix is log-transformed and auto-scaled (using mu and sigma from <code>XTrain</code>), with missing values imputed using k-nearest neighbours (k=3).\n",
    "    <li><b><i>Hyperparameter Optimisation:</i></b> Here, we use the helper function <code>cb.cross_val.KFold()</code> to carry out 5-fold cross-validation of a set of PCR models configured with different numbers of principal components (1 to 30). This helper function is generally applicable, and the values being passed to it are: \n",
    "    <ul>\n",
    "    <li>The class of model to be created by the function, <code>cb.model.PCR</code>.</li>\n",
    "        <li>The metabolite matrix, <code>XTknn</code>, and binary outcome vector, <code>Y</code>.</li>\n",
    "        <li>A dictionary, <code>param_dict</code>, describing key:value pairs where the key is a parameter that is passed to the model, and the value is a list of values to be passed to that parameter.</li>\n",
    "        <li>The number of folds in the cross-validation, <code>folds</code>, and the number of Monte Carlo repetitions of the k-fold CV, <code>n_mc</code>.</li></ul>\n",
    "When <code>cv.run()</code> followed by <code>cv.plot(metric='r2q2')</code> are run the results are displayed as 2 plots of $R^2$ and $Q^2$ statistics: (a) the difference ($R^2 - Q^2$) vs. $Q^2$, and (b) absolute values of both $R^2$ and $Q^2$ against the number of components. These plots are used to aid in selecting the optimal number of components.</li>\n",
    "    <li><b><i>Build Model & Evaluate:</i></b> Here, we use the class <code>cb.model.PCR()</code> to building a PCR model using the optimal hyperparameter values determined in step 4. The model is trained on the training dataset, <code>XTrainKnn</code>, and tested on the independent test dataset, <code>XTestKnn</code>. Next, the trained model's <code>.evaluate()</code> method is used to visualise model performance for both the training and independent test dataset using: a <a href=\"https://www.data-to-viz.com/graph/violin.html\">violin plot</a> showing the distributions of negative and positive responses as violin and box-whisker plots; a <a href=\"https://books.google.com.au/books?id=7WBMrZ9umRYC\">probability density function</a> plot for each response type, and a <a href=\"https://doi.org/10.1007/s11306-012-0482-9\">ROC curve</a> that displays the curve for the training dataset (green) and test dataset (yellow).\n",
    "   <li><b><i>Bootstrap Evaluation:</i></b> Finally, to create an estimate of the robustness and a measure of generalised predictive ability of this model we perform  <a href=\"https://link.springer.com/article/10.1007%2FBF00058655\">bootstrap aggregation</a> (Bagging) using the helper function <code>cb.bootstrap.Per()</code> with 100 boostrapped models. This generates a population of 100 model predictions for both the training set (in-bag prediction - IB) and the holdout test set (out-of-bag - OOB) from the full dataset, with the metabolite matrix, <code>XBootKnn</code>, and binary outcome vector, <code>Y</code>. These predictions are visualised with a box-violin and probability density function plot for the aggregate model. The ROC curve displays the curve for the training dataset (green) and test dataset (yellow) from section 5 with 95% confidence intervals (light green band = IB & light yellow band = OOB).\n",
    "  <li><b><i>Export Results:</i></b> Exporting the model evaluation results as an Excel spreadsheet.</li>\n",
    "</ol> \n",
    "\n",
    "</div>"
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   "source": [
    "### 1. Import Packages"
   ]
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   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import cimcb as cb\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "print('All packages successfully loaded')"
   ]
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   "source": [
    "### 2. Load Data & Peak Sheet"
   ]
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    "home = 'data/' \n",
    "file = 'MTBLS404.xlsx'  \n",
    "\n",
    "DataTable,PeakTable = cb.utils.load_dataXL(home + file, DataSheet='Data', PeakSheet='Peak') "
   ]
  },
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   "source": [
    "### 3. Extract X & Y"
   ]
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    "# Extract PeakList\n",
    "PeakList = PeakTable['Name']  \n",
    "\n",
    "# Select Subset of Data\n",
    "DataTable2 = DataTable[(DataTable.Class == 1) | (DataTable.Class == 0)]\n",
    "\n",
    "# Create a Binary Y Vector \n",
    "Outcomes = DataTable2['Class']\n",
    "Y = Outcomes.values \n",
    "\n",
    "# Split Data into Train (2/3) and Test (1/3)\n",
    "DataTrain, DataTest, YTrain, YTest = train_test_split(DataTable2, Y, test_size=1/3, stratify=Y, random_state=40)\n",
    "\n",
    "# Extract Train Data \n",
    "XTrain = DataTrain[PeakList]                                    \n",
    "XTrainLog = np.log(XTrain)                                          \n",
    "XTrainScale, mu, sigma = cb.utils.scale(XTrainLog, method='auto', return_mu_sigma=True)              \n",
    "XTrainKnn = cb.utils.knnimpute(XTrainScale, k=3)    \n",
    "\n",
    "# Extract Test Data\n",
    "XTest = DataTest[PeakList]                                    \n",
    "XTestLog = np.log(XTest)                                          \n",
    "XTestScale = cb.utils.scale(XTestLog, method='auto', mu=mu, sigma=sigma)             \n",
    "XTestKnn = cb.utils.knnimpute(XTestScale, k=3)                                          "
   ]
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   "source": [
    "### 4. Hyperparameter Optimisation"
   ]
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   "source": [
    "# Parameter Dictionary\n",
    "param_dict = {'n_components': [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]} \n",
    "\n",
    "# Initialise\n",
    "cv = cb.cross_val.KFold(model=cb.model.PCR,                      \n",
    "                        X=XTrainKnn,                                 \n",
    "                        Y=YTrain,                               \n",
    "                        param_dict=param_dict,                   \n",
    "                        folds=5,\n",
    "                        n_mc=10)                                \n",
    "\n",
    "# Run and Plot\n",
    "cv.run()  \n",
    "cv.plot(metric='r2q2')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5. Build Model & Evaluate"
   ]
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   "source": [
    "# Build Mode1\n",
    "model = cb.model.PCR(n_components=17)\n",
    "YPredTrain = model.train(XTrainKnn, YTrain)\n",
    "YPredTest = model.test(XTestKnn)\n",
    "\n",
    "# Put YTrain and YPredTrain in a List\n",
    "EvalTrain = [YTrain, YPredTrain]\n",
    "\n",
    "# Put YTest and YPrestTest in a List\n",
    "EvalTest = [YTest, YPredTest]\n",
    "\n",
    "# Evaluate Model (include Test Dataset)\n",
    "model.evaluate(testset=EvalTest) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6. Bootstrap Evaluation"
   ]
  },
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   "cell_type": "code",
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   "source": [
    "# Extract X Data\n",
    "XBoot = DataTable2[PeakList]\n",
    "XBootLog = np.log(XBoot)\n",
    "XBootScale = cb.utils.scale(XBootLog, method='auto')\n",
    "XBootKnn = cb.utils.knnimpute(XBootScale, k=3)\n",
    "YPredBoot = model.train(XBootKnn, Y)\n",
    "\n",
    "# Build Boostrap Models\n",
    "bootmodel = cb.bootstrap.Per(model, bootnum=100) \n",
    "bootmodel.run()\n",
    "\n",
    "# Boostrap Evaluate Model (include Test Dataset)\n",
    "bootmodel.evaluate(trainset=EvalTrain, testset=EvalTest)  "
   ]
  },
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    "### 7. Export Results"
   ]
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    "home = 'results/'\n",
    "file = 'PCR_MTBLS404.xlsx'\n",
    "\n",
    "bootmodel.save_results(home + file)"
   ]
  },
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