diff --git a/notebooks/SuStaIn tutorial using simulated data with BIC comparison.ipynb b/notebooks/SuStaIn tutorial using simulated data with BIC comparison.ipynb new file mode 100644 index 0000000..fe5436d --- /dev/null +++ b/notebooks/SuStaIn tutorial using simulated data with BIC comparison.ipynb @@ -0,0 +1,28636 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# SuStaIn tutorial using simulated data\n", + "\n", + "Written by Alex Young in April 2020, last updated in October 2022. Please email alexandra.young@kcl.ac.uk with any questions.\n", + "\n", + "This tutorial demonstrates how to run Subtype and Stage Inference (SuStaIn) using simulated data. SuStaIn is an unsupervised learning algorithm that identifies subgroups of individuals with distinct biomarker progression patterns. See [Young et al. Nature Communications 2018](https://doi.org/10.1038/s41467-018-05892-0) for more details.\n", + "\n", + "SuStaIn is a generalisable algorithm in which you can choose how to model the progression of biomarkers within a subtype. In this tutorial I use the linear z-score model I used in [Young et al. 2018](https://doi.org/10.1038/s41467-018-05892-0), but it is possible to use other models of biomarker evolution, such as the event-based model.\n", + "\n", + "For a demonstration of the 'event-based'/mixture modelling version of SuStaIn (i.e. MixtureSustain), see simrun.py, available in the /sim subdirectory of the pySuStaIn package." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Installing SuStaIn and setting it up to run in a notebook\n", + "\n", + "To get SuStaIn up and running first you need to install the package. I'm using Anaconda and had some conflicts with existing packagaes so I had to create a new environment. For me the whole set up process looked like this...\n", + "\n", + "Step 1: Open up a terminal window and create a new environment \"sustain_env\" in anaconda that uses python 3.7 and activate the environment ready to install pySuStaIn.\n", + "```console\n", + "conda create --name sustain_tutorial_env python=3.7\n", + "conda activate sustain_tutorial_env\n", + "```\n", + "\n", + "Step 2: Use the terminal to install necessary packages for running the notebook and pySuStaIn within the environment.\n", + "```console\n", + "conda install -y ipython jupyter matplotlib statsmodels numpy pandas scipy seaborn pip\n", + "pip install git+https://github.com/ucl-pond/pySuStaIn\n", + "```\n", + "\n", + "Step 3: Use the terminal to run the notebook from inside the environment.\n", + "```console\n", + "jupyter notebook\n", + "```\n", + "\n", + "Once you've got your environment running the general workflow will be to open a terminal window and navigate to the directory with the notebook in, activate the envirnoment, open a jupyter notebook inside and use the notebook to run your analyses, then use the terminal deactivate the environment once you've finished running analyses.\n", + "```console\n", + "conda activate sustain_tutorial_env\n", + "jupyter notebook\n", + "conda deactivate\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Importing packages" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# import the python packages needed to generate simulated data for the tutorial\n", + "import os\n", + "import shutil\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import pickle\n", + "from pathlib import Path\n", + "import sklearn.model_selection\n", + "import pandas as pd\n", + "import pylab\n", + "import sys\n", + "import pySuStaIn\n", + "\n", + "# this needs to point to wherever the sim folder inside pySuStaIn is on your computer\n", + "sys.path.insert(0,'/Users/seymour/Downloads/pySuStaIn-1-master_2/sim')\n", + "# if you're running the notebook from within the existing structure you can use\n", + "# sys.path.insert(0,'../sim/')\n", + "from simfuncs import generate_random_Zscore_sustain_model, generate_data_Zscore_sustain" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The linear z-score model\n", + "\n", + "The linear z-score model I use in this tutorial describes a subtype progression pattern as the linear evolution of biomarkers between different z-scores. Figure 1 below shows an example of what this model looks like for a single subtype. The model is indexed by a set of discrete stages. Each stage corresponds to a biomarker reaching a new z-score from the set of z-scores for each biomarker, Z_vals. Each biomarker starts with a minimum value of 0 at stage 0 and reaches a maximum of Z_max at the final stage of the progression. The number of stages is determined by the number of biomarkers and z-scores in Z_vals. The SuStaIn algorithm identifies subgroups of individuals and their progression patterns - for the linear z-score model the progression pattern would be the ordering of the different biomarker z-scores in Z_vals - gt_sequence below.\n", + "\n", + "You can play around generating different sequences and altering the settings of the linear z-score model using the code below." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Simulated sequence: [ 2 1 7 9 4 6 3 0 13 19 11 14 20 10 8 5 16 17 12 15 18]\n", + "At the beginning of the progression (stage 0) the biomarkers have scores of 0\n", + "At the stages: [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21]\n", + "the biomarkers: [2 1 7 1 4 6 3 0 6 6 4 7 7 3 0 5 3 4 5 1 5]\n", + "reach z-scores of: [1 1 1 2 1 1 1 1 2 3 2 2 3 2 2 1 3 3 2 3 3]\n", + "At the end of the progression (stage 23 ) the biomarkers reach scores of: [3 5 2 5 5 5 5 5]\n", + "The z-score model assumes individuals belong to some unknown stage of this progression,\n", + "with gaussian noise with a standard deviation of 1 for each biomarker\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "N = 8 # number of biomarkers\n", + "\n", + "SuStaInLabels = []\n", + "for i in range(N):\n", + " SuStaInLabels.append( 'Biomarker '+str(i)) # labels of biomarkers for plotting\n", + " \n", + "Z_vals = np.array([[1,2,3]]*N) # Z-scores for each biomarker\n", + "Z_max = np.array([5]*N) # maximum z-score\n", + "\n", + "# To demonstrate how to set different biomarkers to have different z-scores,\n", + "# set biomarker 0 to have z-scores of 1 and 2 only and a maximum of 3\n", + "# to do this change the corresponding row of Z_vals to read 1 2 0\n", + "# and change the corresponding row of Z_max to 3\n", + "Z_vals[np.array(0),np.array(2)] = 0\n", + "Z_max[np.array(0)] = 3\n", + "\n", + "# and set biomarker 2 to have a z-score of 1 only and a maximum of 2\n", + "# to do this change the corresponding row of Z_vals to read 1 0 0 \n", + "# and change the corresponding row of Z_max to 2 \n", + "Z_vals[np.array(2),np.array([1,2])] = 0\n", + "Z_max[np.array(2)] = 2\n", + "\n", + "\n", + "# generate a random sequence for the linear z-score model\n", + "gt_sequence = generate_random_Zscore_sustain_model(Z_vals,\n", + " 1)\n", + "\n", + "# ignore this part, it's only necessary so that the generate_data_sustain function\n", + "# can be used in this demo setting\n", + "gt_stages = np.array([0])\n", + "gt_subtypes = np.array([0])\n", + "\n", + "# this code generates data from z-score sustain \n", + "# - here i've just output the z-score model itself rather than any datapoints\n", + "_, _, gt_stage_value = generate_data_Zscore_sustain(gt_subtypes,\n", + " gt_stages,\n", + " gt_sequence,\n", + " Z_vals,\n", + " Z_max)\n", + "\n", + "# ignore this part, just calculates some parameters of sustain to output below\n", + "stage_zscore = np.array([y for x in Z_vals.T for y in x])\n", + "stage_zscore = stage_zscore.reshape(1,len(stage_zscore))\n", + "IX_select = stage_zscore>0\n", + "stage_zscore = stage_zscore[IX_select]\n", + "stage_zscore = stage_zscore.reshape(1,len(stage_zscore))\n", + "num_zscores = Z_vals.shape[1]\n", + "IX_vals = np.array([[x for x in range(N)]] * num_zscores).T\n", + "stage_biomarker_index = np.array([y for x in IX_vals.T for y in x])\n", + "stage_biomarker_index = stage_biomarker_index.reshape(1,len(stage_biomarker_index))\n", + "stage_biomarker_index = stage_biomarker_index[IX_select]\n", + "stage_biomarker_index = stage_biomarker_index.reshape(1,len(stage_biomarker_index))\n", + "\n", + "# print out some of the values and plot a picture of the model\n", + "print('Simulated sequence:',(gt_sequence.astype(int).flatten()))\n", + "print('At the beginning of the progression (stage 0) the biomarkers have scores of 0')\n", + "print('At the stages:',1+np.arange(np.array(stage_zscore).shape[1]))\n", + "print('the biomarkers:',stage_biomarker_index[:,gt_sequence.astype(int).flatten()].flatten())\n", + "print('reach z-scores of:',stage_zscore[:,gt_sequence.astype(int).flatten()].flatten())\n", + "print('At the end of the progression (stage',np.array(stage_zscore).shape[1]+2,') the biomarkers reach scores of:',Z_max)\n", + "print('The z-score model assumes individuals belong to some unknown stage of this progression,')\n", + "print('with gaussian noise with a standard deviation of 1 for each biomarker')\n", + "\n", + "temp_stages = np.array(range(np.array(stage_zscore).shape[1]+2))\n", + "for b in range(N):\n", + " ax = plt.plot(temp_stages, gt_stage_value[b,:,:])\n", + "\n", + "_ = plt.xlabel('SuStaIn stage') \n", + "_ = plt.ylabel('Z-score') \n", + "_ = plt.legend(SuStaInLabels)\n", + "_ = plt.title('Figure 1')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Important note on the linear z-score model\n", + "\n", + "It's natural to think of the progression pattern in Figure 1 as linear in time but this isn't necessarily the case. For example, the time between stages 2 and 3 may be much longer than between stages 8 and 9. This means that the shape of the trajectories may look quite different if indexed by time (although the general order in which the biomarkers progress to different z-scores would remain the same). The linear z-score model simply describes the patient snapshots you would expect to see in a cross-sectional dataset for any particular subtype at a particular stage. The subtypes and stages are considered as hidden variables, which the SuStaIn algorithm identifies directly from the data." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Generating simulated data\n", + "\n", + "This section of code generates simulated data for the tutorial. Any variables labelled as 'gt' (ground truth) are for generating the simulated data only and would typically not be known beforehand in a real dataset.\n", + "\n", + "You can ignore many of the settings below for now, but in particular\n", + "- N_S_gt is the number of subtypes to simulate\n", + "- gt_f is the proportion of individuals belonging to each subtype\n", + "- gt_sequence is the order in which each biomarker approaches each z-score for each subtype\n", + "- gt_subtypes is the subtype of each individual\n", + "- gt_stages is the stage of each individual along the progression pattern of their subtype\n", + "\n", + "You can alter these to get a feel for how SuStaIn works on different simulated datasets." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "For subtype 0 ( 35.714285714285715 % of individuals)\n", + "Simulated sequence: [ 2 1 3 5 11 0 9 13 10 8 17 16 19 6 4 14 21 12 7 15 20 18 23 22]\n", + "At the beginning of the progression (stage 0) the biomarkers have scores of 0\n", + "At the stages: [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24]\n", + "the biomarkers: [2 1 3 5 3 0 1 5 2 0 1 0 3 6 4 6 5 4 7 7 4 2 7 6]\n", + "reach z-scores of: [1 1 1 1 2 1 2 2 2 2 3 3 3 1 1 2 3 2 1 2 3 3 3 3]\n", + "At the end of the progression (stage 26 ) the biomarkers reach scores of: [5 5 5 5 5 5 5 5]\n", + "\n", + "For subtype 1 ( 28.57142857142857 % of individuals)\n", + "Simulated sequence: [ 0 4 12 7 6 15 14 3 22 8 5 16 1 11 2 13 9 21 20 19 10 17 23 18]\n", + "At the beginning of the progression (stage 0) the biomarkers have scores of 0\n", + "At the stages: [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24]\n", + "the biomarkers: [0 4 4 7 6 7 6 3 6 0 5 0 1 3 2 5 1 5 4 3 2 1 7 2]\n", + "reach z-scores of: [1 1 2 1 1 2 2 1 3 2 1 3 1 2 1 2 2 3 3 3 2 3 3 3]\n", + "At the end of the progression (stage 26 ) the biomarkers reach scores of: [5 5 5 5 5 5 5 5]\n", + "\n", + "For subtype 2 ( 21.428571428571427 % of individuals)\n", + "Simulated sequence: [ 7 4 3 6 0 12 14 11 5 15 2 20 19 22 1 23 10 9 18 8 17 16 13 21]\n", + "At the beginning of the progression (stage 0) the biomarkers have scores of 0\n", + "At the stages: [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24]\n", + "the biomarkers: [7 4 3 6 0 4 6 3 5 7 2 4 3 6 1 7 2 1 2 0 1 0 5 5]\n", + "reach z-scores of: [1 1 1 1 1 2 2 2 1 2 1 3 3 3 1 3 2 2 3 2 3 3 2 3]\n", + "At the end of the progression (stage 26 ) the biomarkers reach scores of: [5 5 5 5 5 5 5 5]\n", + "\n", + "For subtype 3 ( 14.285714285714285 % of individuals)\n", + "Simulated sequence: [ 0 1 9 3 8 6 14 7 4 11 17 16 19 15 22 23 12 2 20 10 5 18 13 21]\n", + "At the beginning of the progression (stage 0) the biomarkers have scores of 0\n", + "At the stages: [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24]\n", + "the biomarkers: [0 1 1 3 0 6 6 7 4 3 1 0 3 7 6 7 4 2 4 2 5 2 5 5]\n", + "reach z-scores of: [1 1 2 1 2 1 2 1 1 2 3 3 3 2 3 3 2 1 3 2 1 3 2 3]\n", + "At the end of the progression (stage 26 ) the biomarkers reach scores of: [5 5 5 5 5 5 5 5]\n", + "\n" + ] + } + ], + "source": [ + "N = 8 # number of biomarkers\n", + "M = 500 # number of observations ( e.g. subjects )\n", + "M_control = 100 # number of these that are control subjects\n", + "N_S_gt = 4 # number of ground truth subtypes\n", + "\n", + "SuStaInLabels = []\n", + "for i in range(N):\n", + " SuStaInLabels.append( 'Biomarker '+str(i)) # labels of biomarkers for plotting\n", + " \n", + "Z_vals = np.array([[1,2,3]]*N) # Z-scores for each biomarker\n", + "Z_max = np.array([5]*N) # maximum z-score\n", + " \n", + "# ground truth proportion of individuals belonging to each subtype \n", + "gt_f = [1+0.5*x for x in range(N_S_gt)]\n", + "gt_f = [x/sum(gt_f) for x in gt_f][::-1]\n", + "\n", + "# ground truth sequence for each subtype\n", + "gt_sequence = generate_random_Zscore_sustain_model(Z_vals,\n", + " N_S_gt)\n", + "\n", + "# simulate subtypes and stages for individuals, including a control population at stage 0\n", + "N_k = np.sum(Z_vals>0)+1\n", + "gt_subtypes = np.random.choice(range(N_S_gt), M, replace=True, p=gt_f)\n", + "gt_stages_control = np.zeros((M_control,1))\n", + "gt_stages = np.concatenate((gt_stages_control,\n", + " np.ceil(np.random.rand(M-M_control,1)*N_k)),\n", + " axis=0)\n", + "\n", + "# generate simulated data\n", + "data, gt_data_denoised, gt_stage_value = generate_data_Zscore_sustain(gt_subtypes,\n", + " gt_stages,\n", + " gt_sequence,\n", + " Z_vals,\n", + " Z_max)\n", + "\n", + "# ignore this part, just calculates some parameters of sustain to output below\n", + "stage_zscore = np.array([y for x in Z_vals.T for y in x])\n", + "stage_zscore = stage_zscore.reshape(1,len(stage_zscore))\n", + "IX_select = stage_zscore>0\n", + "stage_zscore = stage_zscore[IX_select]\n", + "stage_zscore = stage_zscore.reshape(1,len(stage_zscore))\n", + "num_zscores = Z_vals.shape[1]\n", + "IX_vals = np.array([[x for x in range(N)]] * num_zscores).T\n", + "stage_biomarker_index = np.array([y for x in IX_vals.T for y in x])\n", + "stage_biomarker_index = stage_biomarker_index.reshape(1,len(stage_biomarker_index))\n", + "stage_biomarker_index = stage_biomarker_index[IX_select]\n", + "stage_biomarker_index = stage_biomarker_index.reshape(1,len(stage_biomarker_index))\n", + "\n", + "for s in range (N_S_gt):\n", + " # print out the parameters\n", + " print('For subtype',s,'(',gt_f[s]*100,'% of individuals)')\n", + " print('Simulated sequence:',(gt_sequence[s,:].astype(int).flatten()))\n", + " print('At the beginning of the progression (stage 0) the biomarkers have scores of 0')\n", + " print('At the stages:',1+np.arange(np.array(stage_zscore).shape[1]))\n", + " print('the biomarkers:',stage_biomarker_index[:,gt_sequence[s,:].astype(int).flatten()].flatten())\n", + " print('reach z-scores of:',stage_zscore[:,gt_sequence[s,:].astype(int).flatten()].flatten())\n", + " print('At the end of the progression (stage',np.array(stage_zscore).shape[1]+2,') the biomarkers reach scores of:',Z_max)\n", + " print('')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The SuStaIn algorithm\n", + "\n", + "SuStaIn identifies subtypes with distinct progression patterns from cross-sectional data. The algorithm proceeds hierarchically, first fitting a single subtype to the data, then two, then three, etc., up to a maximum number of subtypes chosen by the user. The fitting of the nth subtype model works but splitting each of the previous n-1 clusters into two and then using this as an initialisation to fit the n subtype model. For each of the n subtype models, SuStaIn uses MCMC sampling to estimate the uncertainty in the subtype progression patterns and the proportion of individuals that belong to each subtype. The optimal number of subtypes is selected by using cross-validation to compute the cross-validation information criterion (CVIC)." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Preparing data for SuStaIn\n", + "\n", + "The data for SuStaIn needs to be z-scored relative to a control population such that the mean of the control population is 0 and the standard deviation of the control population is 1. To do this simply subtract the mean of the control population from your data and divide by the standard deviation of the control population. Double check that if you apply this transformation to the control population only that the control population has a mean of 0 and a standard deviation of 1. The data further needs to be transformed to increase in z-score with disease progression. If the biomarkers you are using decrease with disease progression you need to multiply the data for those biomarkers by -1.\n", + "\n", + "I'd suggest the following workflow for getting your data ready to run SuStaIn on.\n", + "\n", + "1. Regress out the effects of covariates. Learn the effects of covariates in a control population and use this model to regress out the effect of covariates for all the subjects. Learning the model in the control population will avoid regressing out disease effects, which you want to keep in your dataset.\n", + "\n", + "2. Calculate the mean and standard deviation of each biomarker in your control dataset, mean_control and std_control.\n", + "\n", + "3. Z-score your data by taking (data-mean_control)/std_control.\n", + "\n", + "4. Identify any biomarkers that decrease with disease progression, these will have mean_data < mean_control. Multiply the data for these biomarkers by -1.\n", + "\n", + "Steps 2-4 are illustrated in the section below but will have little effect on the simulated data because it is generated as z-scores already." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Mean of controls is [ 1.33226763e-17 3.55271368e-17 5.55111512e-19 -8.43769499e-17\n", + " -4.66293670e-17 9.99200722e-18 -1.55431223e-17 4.16333634e-17]\n", + "Standard deviation of controls is [1. 1. 1. 1. 1. 1. 1. 1.]\n", + "Mean of whole dataset is [2.28861742 2.25994534 1.38195663 2.22569733 1.91812071 1.38720092\n", + " 1.73821978 1.68502206]\n", + "Standard deviation of whole dataset is [2.07976322 2.2021612 1.69421494 2.0081455 1.90085241 1.75828055\n", + " 1.8268627 1.99597538]\n" + ] + } + ], + "source": [ + "# extract data for control subjects\n", + "data_control = data[np.tile(gt_stages,(1,N))==0].reshape(M_control,N)\n", + "\n", + "# compute the mean and standard deviation of the control population\n", + "mean_control = np.mean(data_control,axis=0)\n", + "std_control = np.std(data_control,axis=0)\n", + "\n", + "# z-score the data\n", + "data = (data-mean_control)/std_control\n", + "data_control = (data_control-mean_control)/std_control\n", + "\n", + "# multiply data for decreasing biomarkers by -1\n", + "IS_decreasing = np.mean(data,axis=0)10 indicates very strong evidence of the models being different, 6-10 indicates strong evidence,\n", + "#2-6 indicates positive evidence and 0-2 indicates weak evidence.\n", + "#Ref: https://link.springer.com/article/10.3758/s13428-018-1188-3#:~:text=The%20difference%20between%20the%20BICs,model%20(Raftery%2C%201995).\n", + "\n", + "def BIC(logML, n,k):\n", + " res = k * np.log(n) -2*logML\n", + " return(res)\n", + "\n", + "\n", + "split1_BIC=BIC(-6966.32,data.shape[0],1)\n", + "split2_BIC=BIC(-6972.19,data.shape[0],2)\n", + "split3_BIC=BIC(-6966.21,data.shape[0],3)\n", + "split4_BIC=BIC(-6963.84,data.shape[0],4)\n", + "print(round(split1_BIC,3))\n", + "print(round(split2_BIC,3))\n", + "print(round(split3_BIC,3))\n", + "print(round(split4_BIC,3))" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "#Here we see strong evidence upto the 3rd split (4 subtypes) and weak evidence at the 4th split (5 subtypes)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "sustain_BIC", + "language": "python", + "name": "sustain_bic" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.5" + }, + "widgets": { + "application/vnd.jupyter.widget-state+json": { + "state": { + "000dd01423b0483a835db82a8a3353ed": 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