{ "cells": [ { "cell_type": "markdown", "id": "b0b168a1-b3e4-48a2-97ac-e24f9789f0f2", "metadata": {}, "source": [ "# Collett (2015): Survival Analysis\n", "\n", "The following presents some survival analysis methods framed as M-estimators. The described example and methods are detailed further in the book by Collett. In survival analysis, we are commonly interested in estimating the survival or risk at a particular time. However, some observations are censored (most commonly right censored, which is exclusively considered hereafter). Therefore, our data is composed of the observation time ($T^*$) and an event indicator ($\\Delta$). The observation time is usually framed as the minimum of the time-to-event ($T$) and time-to-censor ($C$). Herem we assume that each person has both times, but we only see $T^* = \\min(T,C)$. The event indicator tells us which of these two options occurred ($\\Delta = 1$ if it was the event). Therefore, survival analysis methods consider how to efficiently learn functions of the time-to-event variable with this partial missingness. See Collett for a more detailed review of survival analysis and its methods.\n", "\n", "## Setup" ] }, { "cell_type": "code", "execution_count": 1, "id": "ef73e682-8bd2-4bc1-a719-e64f9754a9ba", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "NumPy version: 2.3.5\n", "SciPy version: 1.16.3\n", "Pandas version: 2.3.3\n", "Delicatessen version: 4.1\n" ] } ], "source": [ "import numpy as np\n", "import scipy as sp\n", "import pandas as pd\n", "import matplotlib.pyplot as plt\n", "\n", "import delicatessen as deli\n", "from delicatessen import MEstimator\n", "from delicatessen import data\n", "from delicatessen.estimating_equations import ee_survival_model, ee_aft\n", "from delicatessen.utilities import survival_predictions, aft_predictions_function\n", "\n", "print(\"NumPy version: \", np.__version__)\n", "print(\"SciPy version: \", sp.__version__)\n", "print(\"Pandas version: \", pd.__version__)\n", "print(\"Delicatessen version:\", deli.__version__)" ] }, { "cell_type": "markdown", "id": "e4b59170-62f5-4978-8f9f-987016c866c7", "metadata": {}, "source": [ "Here, data on the survival times of 45 women with breast cancer in Middlesex Hospital July 1987 (Table 1.2) is used. Information was collected on whether tumors were positively or negatively stained with HPA. This will be the only covariate included in the analysis." ] }, { "cell_type": "code", "execution_count": 2, "id": "43725717-072f-47b4-b1f9-8c5057a08c3f", "metadata": {}, "outputs": [], "source": [ "times_to_predict = np.linspace(0.5, 230, 100) # For drawing survival functions" ] }, { "cell_type": "code", "execution_count": 3, "id": "1191d4c4-f1b3-4ee8-ae1b-637fdf2f7daf", "metadata": {}, "outputs": [], "source": [ "d = pd.DataFrame(data.load_breast_cancer(), columns=['status', 'time', 'stain'])\n", "d['C'] = 1" ] }, { "cell_type": "markdown", "id": "51b33557-cc2e-4fac-bdf9-43665d7d0913", "metadata": {}, "source": [ "Here, `time` is the observation time, `status` is the event indicator, and `stain` is whether the tumor was HPA stained positive or negative. This data set can also be loaded through `delicatessen.data.load_breast_cancer()`.\n", "\n", "## Chapter 5: Parametric Proportional Hazards Models \n", "\n", "To begin, we will simply model the survival times using parametric models without covariates. \n", "\n", "### Exponential\n", "\n", "The exponential model is a one parameter model that assumes the hazard is constant. It is the simplest of the survival models. This model is parameterized as \n", "$$ h(t) = \\lambda t $$\n", "The following code can be used to fit the exponential model" ] }, { "cell_type": "code", "execution_count": 4, "id": "51d43d97-eedc-486f-946a-84729864d558", "metadata": {}, "outputs": [], "source": [ "def psi(theta):\n", " return ee_survival_model(theta=theta, t=d['time'], delta=d['status'], \n", " distribution='exponential')" ] }, { "cell_type": "code", "execution_count": 5, "id": "b5093bf2-6db3-49ad-ae9b-197538585467", "metadata": {}, "outputs": [], "source": [ "estr = MEstimator(psi, init=[0.01, ])\n", "estr.estimate()" ] }, { "cell_type": "code", "execution_count": 6, "id": "9392bdd6-f596-46aa-b82d-5983cd4ef87b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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EstSELCLUCL
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" ], "text/plain": [ " Est SE LCL UCL\n", "Params \n", "Lambda 0.006 0.001 0.003 0.009" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Setting up a Table for the results\n", "results = pd.DataFrame()\n", "results['Params'] = [\"Lambda\", ]\n", "results = results.set_index('Params')\n", "results['Est'] = estr.theta\n", "results['SE'] = np.diag(estr.variance) ** 0.5\n", "ci = estr.confidence_intervals()\n", "results['LCL'] = ci[:, 0]\n", "results['UCL'] = ci[:, 1]\n", "\n", "results.round(3)" ] }, { "cell_type": "markdown", "id": "ee45d237-ca1f-47ef-b3b5-f80036ead136", "metadata": {}, "source": [ "So the estimated hazard at each time is simply $0.006$.\n", "\n", "Another more informative way to view the results from this model is to plot the estimated survival function. The following code generates the confidence intervals for the survival function at designated times using the Delta Method." ] }, { "cell_type": "code", "execution_count": 7, "id": "33e6eedf-5fa3-4657-890f-159fff947ec4", "metadata": {}, "outputs": [], "source": [ "surv = survival_predictions(times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='exponential')" ] }, { "cell_type": "code", "execution_count": 8, "id": "98d0d9cc-7dbd-4521-9507-59c9ea9ca0ac", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(times_to_predict, surv[:, 0], '-', color='k')\n", "plt.fill_between(times_to_predict, surv[:, 2], surv[:, 3], color='k', alpha=0.3)\n", "plt.ylim([0, 1])\n", "plt.ylabel(\"Survival\")\n", "plt.xlim([0, 235])\n", "plt.xlabel(\"Time (days)\")\n", "plt.title(\"Exponential\")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "3c3e0e81-d553-4169-8f1d-4af821c06774", "metadata": {}, "source": [ "### Weibull \n", "\n", "The Weibull model is a two parameter model that is an extension of the exponential model. Here, the Weibull model is parameterized as \n", "$$ h(t) = \\lambda \\gamma t^{\\gamma - 1} $$\n", "where $\\gamma$ is the shape parameter. This parameter allows for the hazard to increase or decrease monotonically. The following code is used to fit a Weibull model." ] }, { "cell_type": "code", "execution_count": 9, "id": "704306e8-483e-49ec-b295-a069f0c28990", "metadata": {}, "outputs": [], "source": [ "def psi(theta):\n", " return ee_survival_model(theta=theta, t=d['time'], delta=d['status'], \n", " distribution='weibull')" ] }, { "cell_type": "code", "execution_count": 10, "id": "e45c50ab-5b8b-424c-a433-7dd3ad47de59", "metadata": {}, "outputs": [], "source": [ "estr = MEstimator(psi, init=[0.01, 1.])\n", "estr.estimate()" ] }, { "cell_type": "code", "execution_count": 11, "id": "f43487e9-c196-4f58-8cdb-ffd786d4784c", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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EstSELCLUCL
Params
Lambda0.0100.005-0.0000.019
Gamma0.9040.1110.6861.122
\n", "
" ], "text/plain": [ " Est SE LCL UCL\n", "Params \n", "Lambda 0.010 0.005 -0.000 0.019\n", "Gamma 0.904 0.111 0.686 1.122" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Setting up a Table for the results\n", "results = pd.DataFrame()\n", "results['Params'] = [\"Lambda\", \"Gamma\"]\n", "results = results.set_index('Params')\n", "results['Est'] = estr.theta\n", "results['SE'] = np.diag(estr.variance) ** 0.5\n", "ci = estr.confidence_intervals()\n", "results['LCL'] = ci[:, 0]\n", "results['UCL'] = ci[:, 1]\n", "\n", "results.round(3)" ] }, { "cell_type": "markdown", "id": "7e8c009e-8acd-4ee4-ad1b-d899b563d633", "metadata": {}, "source": [ "Here, $\\gamma$ is near 1, which suggests that the Weibull isn't much better of a fit to the data. \n", "\n", "As before, we can plot the survival function to get a better idea what these parameters mean" ] }, { "cell_type": "code", "execution_count": 12, "id": "78893125-4708-4125-99bf-4f29db673137", "metadata": {}, "outputs": [], "source": [ "surv = survival_predictions(times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='weibull')" ] }, { "cell_type": "code", "execution_count": 13, "id": "d9847e23-8853-4804-8228-a730e94d2c57", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(times_to_predict, surv[:, 0], '-', color='k')\n", "plt.fill_between(times_to_predict, surv[:, 2], surv[:, 3], color='k', alpha=0.3)\n", "plt.ylim([0, 1])\n", "plt.ylabel(\"Survival\")\n", "plt.xlim([0, 235])\n", "plt.xlabel(\"Time (days)\")\n", "plt.title(\"Weibull\")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "30637114-0de0-4092-9259-259faca5275d", "metadata": {}, "source": [ "A disadvantage of the previous models is that they do not incorporate information on baseline covariates.\n", "\n", "## Chapter 6: Accelerated Failure Time and Other Parametric Models\n", "\n", "Now we will switch focus to modeling survival by baseline covariates. The following is a line-diagram which represents the follow-up time for each individual (horizontal line), their event indicator (open circles are censoring, x's are events), and the HPA stain status (shaded is negative)." ] }, { "cell_type": "code", "execution_count": 14, "id": "7f5d1ddf-7203-4e53-8a45-a4d9e975873d", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.fill_between([0, 230], [0, 0], [13.5, 13.5], alpha=0.2, color='k')\n", "plt.hlines(d.index + 1, xmin=0, xmax=d['time'], color='k')\n", "d1 = d.loc[d['status'] == 1].copy()\n", "d0 = d.loc[d['status'] == 0].copy()\n", "plt.plot(d0['time'], d0.index+1, 'o', color='w', markeredgecolor='k')\n", "plt.plot(d1['time'], d1.index+1, 'x', color='k')\n", "plt.xlim([0, 230])\n", "plt.xlabel(\"Time (days)\")\n", "plt.ylim([46, 0])\n", "plt.yticks([1, 10, 20, 30, 40, 45])\n", "plt.ylabel('IDs')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "9a1dfe53-124b-47f3-b85b-3a38b3fd5b36", "metadata": {}, "source": [ "In this case, we can see there seems to be some pattern in survival by HPA stain. However, there is censoring and our description here is pretty general. To help make our descriptions of survival differences more precise, we will use AFT models.\n", "\n", "Here, we consider use of accelerated failure time (AFT) models with right censored data. These parametric models allow us to study how baseline variables are related to survival. AFT models are named because their scale parameters can be interpreted as how a baseline variable 'accelerates' the outcome. This acceleration is the ratio between the times when the survival are equal for a one unit change in the covariate. Alternatively, we can think about the parameters of this model as the ratio of mean survival times by covariate values.\n", "\n", "The AFT model can be represented as a log-linear model:\n", "$$ \\log(T_i) = \\beta_0 + \\beta_1 X_i + \\sigma \\epsilon_i $$ \n", "where different distributions for $\\epsilon$ provide different parametric AFT models. Here, $\\sigma$ is the shape parameter. It will be the parameter that varies in meanining between the different parametric distributions. The $\\beta$'s are the scale factors which give us the acceleration factors, which can be interpreted as \"the time to death given $X=1$ is accelerated by a factor of $\\exp(-\\beta_1)$\".\n", "\n", "For further details on the structure and interpretation of AFT models, see the Collett book.\n", "\n", "### Exponential\n", "\n", "To start, we consider the exponential AFT model. The exponential AFT model assumes a constant hazard, which is likely too simple for most settings. However, it can be useful to use as a starting point. The following is code to fit this AFT model using the `ee_aft` built-in estimating equation" ] }, { "cell_type": "code", "execution_count": 15, "id": "83a91c20-c4c3-49ec-9c0e-fdbbebdff670", "metadata": {}, "outputs": [], "source": [ "def psi(theta):\n", " return ee_aft(theta=theta, t=d['time'], delta=d['status'], \n", " X=d[['C', 'stain', ]], \n", " distribution='exponential')" ] }, { "cell_type": "code", "execution_count": 16, "id": "afd371fd-c143-4c2a-b43a-09a7ef2c7a9a", "metadata": {}, "outputs": [], "source": [ "estr = MEstimator(psi, init=[6., 0.])\n", "estr.estimate()" ] }, { "cell_type": "code", "execution_count": 17, "id": "72b88f31-6798-4b35-8cbf-dfaab2141ec1", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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EstSELCLUCL
Params
Intercept5.8000.4314.9566.645
Stain-0.9520.497-1.9260.023
\n", "
" ], "text/plain": [ " Est SE LCL UCL\n", "Params \n", "Intercept 5.800 0.431 4.956 6.645\n", "Stain -0.952 0.497 -1.926 0.023" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Setting up a Table for the results\n", "results = pd.DataFrame()\n", "results['Params'] = [\"Intercept\", \"Stain\"]\n", "results = results.set_index('Params')\n", "results['Est'] = estr.theta\n", "results['SE'] = np.diag(estr.variance) ** 0.5\n", "ci = estr.confidence_intervals()\n", "results['LCL'] = ci[:, 0]\n", "results['UCL'] = ci[:, 1]\n", "results.round(3)" ] }, { "cell_type": "markdown", "id": "99d08e89-a9fc-44e3-9642-aa632ce07e4f", "metadata": {}, "source": [ "Here, $\\exp(0.952)$ would be the acceleration factor due to a positive HPA stain (note the cancellation of the negative signs).\n", "\n", "Another informative way to view these results is through a plot of the survival functions. The following code computes the survival function (at user-provided time points) for a specific covariate pattern. Here, we only consider HPA stain. The next block uses these predictions (and their confidence intervals) to plot the survival functions by HPA stain." ] }, { "cell_type": "code", "execution_count": 18, "id": "582ff16e-fd68-4d85-888d-25878d55b510", "metadata": {}, "outputs": [], "source": [ "surv_neg = aft_predictions_function(X=[[1, 0], ], times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='exponential')\n", "surv_pos = aft_predictions_function(X=[[1, 1], ], times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='exponential')" ] }, { "cell_type": "code", "execution_count": 19, "id": "0f36e185-6dec-4b26-acdb-0faf3b8ea8a0", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(times_to_predict, surv_neg[:, 0], '-', color='blue', label='Negative')\n", "plt.fill_between(times_to_predict, surv_neg[:, 2], surv_neg[:, 3], color='blue', alpha=0.3)\n", "plt.plot(times_to_predict, surv_pos[:, 0], '-', color='red', label='Positive')\n", "plt.fill_between(times_to_predict, surv_pos[:, 2], surv_pos[:, 3], color='red', alpha=0.3)\n", "plt.ylim([0, 1])\n", "plt.ylabel(\"Survival\")\n", "plt.xlim([0, 235])\n", "plt.xlabel(\"Time (days)\")\n", "plt.legend()\n", "plt.title(\"Exponential AFT\")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "8d9e2740-4fdf-4506-8c70-c4b625c312b3", "metadata": {}, "source": [ "This plot summarizes how survival unfolds over time. These plots can be helpful with interpreting or presenting results beyond the table of estimated parameters given previously.\n", "\n", "### Weibull\n", "\n", "The next model is the Weibull AFT model, which is a two-parameter generalization of the exponential model. In particular, it allows the hazard to vary in a specific monotonic way over time. To assess whether the exponential AFT model is reasonable, one can fit a Weibull model and assess whether the shape parameter ($\\sigma$) is different from 1.\n", "\n", "Below is how one can fit a Weibull AFT model with `ee_aft`" ] }, { "cell_type": "code", "execution_count": 20, "id": "593fbb5c-7e6b-4722-8021-8c4d2c966bfa", "metadata": {}, "outputs": [], "source": [ "def psi(theta):\n", " return ee_aft(theta=theta, t=d['time'], delta=d['status'], \n", " X=d[['C', 'stain', ]], \n", " distribution='weibull')" ] }, { "cell_type": "code", "execution_count": 21, "id": "2ecd8ce2-4596-4bd2-8772-f088a228898c", "metadata": {}, "outputs": [], "source": [ "estr = MEstimator(psi, init=[5., 0., 0.])\n", "estr.estimate()" ] }, { "cell_type": "code", "execution_count": 22, "id": "a8450359-0008-4c14-8d36-0ecb596de80b", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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EstSELCLUCL
Params
Intercept5.8540.4834.9096.800
Stain-0.9970.532-2.0390.046
Shape-0.0650.126-0.3110.182
\n", "
" ], "text/plain": [ " Est SE LCL UCL\n", "Params \n", "Intercept 5.854 0.483 4.909 6.800\n", "Stain -0.997 0.532 -2.039 0.046\n", "Shape -0.065 0.126 -0.311 0.182" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Setting up a Table for the results\n", "results = pd.DataFrame()\n", "results['Params'] = [\"Intercept\", \"Stain\", \"Shape\"]\n", "results = results.set_index('Params')\n", "results['Est'] = estr.theta\n", "results['SE'] = np.diag(estr.variance) ** 0.5\n", "ci = estr.confidence_intervals()\n", "results['LCL'] = ci[:, 0]\n", "results['UCL'] = ci[:, 1]\n", "results.round(3)" ] }, { "cell_type": "markdown", "id": "77af7df1-cfac-4b28-a830-42c7deefc51c", "metadata": {}, "source": [ "Note that the shape parameter here is the log-transformed version, so $\\exp(-0.065)$ is near one. This suggests that a Weibull AFT model provides a pretty similar fit to an exponential AFT model for this data. We can compare this to the results reported in Collett (pg 245). There we see that the intercept ($\\mu$ in Collett) and stain ($\\hat{\\alpha}$ in Collett) match to the reported number of decimal places. Note that the $\\sigma$ in `delicatessen` is the inverse of the one reported in Collett. \n", "\n", "Below is code to generate a plot of the survival functions. As the shape parameter is near one, this plot is expected to be similar to the exponential AFT model plot." ] }, { "cell_type": "code", "execution_count": 23, "id": "cfaf4cbc-5230-4398-9a5c-3bc2bc62ada7", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Computing predictions for survival functions\n", "surv_neg = aft_predictions_function(X=[[1, 0], ], times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='weibull')\n", "surv_pos = aft_predictions_function(X=[[1, 1], ], times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='weibull')\n", "\n", "# Plotting survival functions\n", "plt.plot(times_to_predict, surv_neg[:, 0], '-', color='blue', label='Negative')\n", "plt.fill_between(times_to_predict, surv_neg[:, 2], surv_neg[:, 3], color='blue', alpha=0.3)\n", "plt.plot(times_to_predict, surv_pos[:, 0], '-', color='red', label='Positive')\n", "plt.fill_between(times_to_predict, surv_pos[:, 2], surv_pos[:, 3], color='red', alpha=0.3)\n", "plt.ylim([0, 1])\n", "plt.ylabel(\"Survival\")\n", "plt.xlim([0, 235])\n", "plt.xlabel(\"Time (days)\")\n", "plt.legend()\n", "plt.title(\"Weibull AFT\")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "99a227bc-5372-43e8-92b5-1ad562dd9b3e", "metadata": {}, "source": [ "Other measures can also be plotted. Here, we plot the hazard functions shown in Figure 6.6 of Collett." ] }, { "cell_type": "code", "execution_count": 24, "id": "a03a559f-c33f-431c-8188-24afd046be75", "metadata": {}, "outputs": [ { "data": { "image/png": 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7DQAAKcAExaEt5CcovnDhglmQV9d2895M9uzmuQYsf3S/83ylNXxJne+PvqfOdeO8jjbtli1bNtnrnD9/3nywzpJqTFIMAECmWLhwoemSdfz48WTP0+5g77//vmu+lYAFuyNHjkh8fLxZ181Jnx84cMDva3R/as5P6ho5c+aU/Pnzp+o6ut6bpmW7aM1iqtEUCwBAAo8//rgJYFr09/P1119v1oq9dOnSNX1SjRs3lv3795vf2So2NjbR7361YsUKiYmJcc23EvDBE6FiwIABpgrULnv27En9RVh9AgCARFq2bGlC2LZt26RPnz4yZMgQeeedd67pk8qZM6cUL17cBMbkaPes3Llzu+ZbCViwK1y4sISFhSUajarP9YvwR/en5vykrqHNwL5Vs1e7TkREhGnXdpZUu+46z1anO2HKEwAAvL9j9XdwuXLl5OmnnzbdpXTd17///ls6d+4sBQoUMOHr7rvvNuHP9ueff8p9991njkdFRZnlxOzZMpxNsfq4a9eupmLGrh3U8OjbFPvII4+Y/vxO2n1LM8v48eO94wG0FU/7wkVGRpqBn19//XXQfJMBC3aapOvUqSPz5s3z7tMPS583atTI72t0v/N8NWfOnCTP90ffU9eNc15ny5Ytsnv37lRdJ02iokRKlvQ83rEjY98LAJC16djI06cDU65xXKYGJq2E0WbalStXmpCn/eB1vOc999xjwpbSqcu0D/yiRYtk3bp1ZkYMncbMX7OshjetlNGaQS19+/ZNdN6jjz5qZs04deqUd9+PP/4oZ86cMevPKg11GvJ00OaGDRvMTBuPPfaYmWVDsvpasTrVSZcuXaRu3bpSv35986HrqFdN1UpTeqlSpcyHqJ577jlp2rSpDB8+XFq1aiWTJk0yX/jYsWO91zx27JgJaTqFiR3alP5LQIu2tet0KfreBQsWNF+yjsLVUJfSEbHXRJtj9d50zdh69TL+/QAAWdOZMyJ+Qk6m0GCklRmppMFNK140TGnt3LRp02Tx4sUmmKkJEyaYPu66v127dub3vc5Fq/Paqor2YgB+KpP097/W1CXXOqcDMrXmb+rUqdKpUyezT2fRuP/++yVv3rwmRL755psyd+5cb2WQvucvv/win3zyickoWTrYaXXn4cOHZdCgQWbggk5LMnv2bO8ACf3CdKSsTb9Y/YBffvllGThwoFSqVMl8uTVq1PCeo6neDoaqQ4cOZqtz5dnVriNGjDDX1f8Z9EvSL/Kjjz7KnB9ag92iRZ5gBwAAzDRmWtOmNXHaeqdNojq/rO7XqdFsurBAlSpVZNOmTeb5v/71L9N0+9///tc03z744INy4403pvkTDQ8Pl4cfftgESA12Wtk0ffp0U5Gktm/fbmrv/vGPfyR4ndYu3nTTTUHxTQY02Klnn33WFH+0TdyXJnQtSdFqWy3J0flhdMULLZmOARQAgMygAwIcTYqZKpWDEe644w75+OOPTc1ayZIlTcDSipqrefLJJ03lzA8//GDC3dChQ02rnrbEpZU2x2rNmy6WoN29tFlYB3cou4lW309bFH37CQaDgAe7LIcpTwAAmUFHg6ahOTQQtPlTpzlx0oUDdMqTZcuWeZtijx49arpYVatWzXueNs0+9dRTpgwYMEA+/fRTv8FOQ6NOs3Y1+l56TV0da9asWaYySfvmK31fDXDaohgMza7+EOwyG5MUAwCQgl+XlaR169bSvXt3039N+7jpqlRaU6b7Va9evUxfvMqVK5sRtAsWLDCB0B8d/ao1btqHT0ey6ijbpKY50aZgHRyxdetWc02b3oMOutABE9pkrEuY6khb7QeoffZ13ECgMY9dZrOnPDl8WNc3y/S3BwAgVIwbN87MZnHvvfeawQo6uEKnM7Fr0LQGTkfGapjT5tLKlSsn2Wdea+K0Vk/79+vcdcOGDUu2OXbjxo0mRN5yyy0Jjr322mvyyiuvmGZf+321aVanP5GsvlZsKEvTWrE2HZGj8/GtWiVy880ZdYsAgCyEtWJDW8ivFZulMYACAABkAIJdINDPDgAAZACCXSAwMhYAAGQAgl0gEOwAAEAGINgFAsEOAABkAIJdIIPdgQMiJ08G5BYAAO7EZBehSefFSw9MUBwI0dEiRYp45rLbsUOkdu2A3AYAwD10bjdd5F7XYNd52vQxQiOI61qz+r3pOva6Qsa1INgFstZOg9327QQ7AMA1CwsLk9KlS8vevXtl165dfKIhRlfBKFu2rAl314JgF8hgt3SpJ9gBAJAO8uTJY5biunjxIp9niIXy8PDwdKllJdgFCgMoAAAZFBK0IGti8ESgJyneti1gtwAAANyFYBco1NgBAIB0RrALdLDbt0/k9OmA3QYAAHAPgl2gFCggUrCg5/EffwTsNgAAgHsQ7AKJ5lgAAJCOCHaBVKWKZ7toUUBvAwAAuAPBLpA6dPBs//MflhYDAADXjGAXSC1bemrtTpwQiY0N6K0AAIDQR7AL6KefXeS55zyPP/hAJD4+oLcDAABCG8Eu0Dp39oyQ3bFD5IcfAn03AAAghBHsAi0qSiQmxvP4/fcDfTcAACCEEeyCQY8eurifyIIFIr/9Fui7AQAAIYpgFwzKlBFp1+5KXzsAAIA0INgFi169PNuJE0UOHgz03QAAgBBEsAsWDRqINGwocuGCyMcfB/puAABACCLYBZPnn/dsNdidOxfouwEAACGGYBdM2rb19Lc7dEjkyy8DfTcAACDEEOyCSXi4SM+enscDBtDXDgAApArBLtg8+6xIjRqeUNeli8jly4G+IwAAECIIdsEmMlJk0iTP9scfRd57L9B3BAAAQgTBLhhVr35lFQptkl2xItB3BAAAQgDBLlh17y7y4IMily6JdOwocuJEoO8IAAAEOYJdsMqWTeTTT0XKlhXZsUPkmWdELCvQdwUAAIIYwS6YFSjgmfZE15GdMEFk/PhA3xEAAAhiBLtg17ixyJAhnscxMSLffRfoOwIAAEGKYBcKdABFu3ae5ca039033wT6jgAAQBAi2IUCbYqdOFHkkUc8gynatxeZPDnQdwUAAIIMwS6UVqXQPnadO4vEx3tC3hdfBPquAABAECHYhVrN3bhxIt26eVak0JCnzwEAAAh2ISh7dpGxY0Weesoz/ckTT4j06SNy8WKg7wwAAAQYNXahGu4++kjkxRc9z3XZsdtuE9m9O9B3BgAAAohgF8oTGL/1lsjUqSLR0SK//ipy000iM2cG+s4AAECAEOxCXZs2IqtXi9SpI3LsmEirVp7pUXRqFAAAkKUQ7NygYkWRxYtFnn3W81xr8rT2btGiQN8ZAADIRAQ7t4iIEPnwQ5GvvhIpUkRk40aRpk09gyuOHAn03QEAgExAsHMbXaFi82bP8mNKp0OpUkXk//0/zxQpAADAtQh2blSwoMgnn3iaZ2+80dP37sknPf3wfvjBM00KAABwHYKdmzVuLLJqlcjw4SJ584r89pvIvfeK3HKLyIIFgb47AACQzgh2WWEpst69Rf74Q+SFF0QiI0WWLhVp1kykeXORn3+mBg8AAJcg2GUVhQuLDBsmsmOHZ/Rsjhwi8+Z5JjZu0EBk8mSRS5cCfZcAAOAaEOyymhIlPKNnt23zDLDQ0bQrVoh06CBy3XWeVSzi4gJ9lwAAIA0IdllVuXKeARa6DNmQIZ4pUvSxrjtbqpRIt26e1SwYaAEAQMgg2GV1RYuKDB7sCXWffipSrZrI6dMi//mPSKNGnlG1H3zgGVkLAACCGsEOHrlyeaZEWb/es2JF586effq8Vy9PE+4DD3gmQD5zhk8NAIAglM2yaGtLixMnTkh0dLTExcVJvnz5xJWOHxeZONFTk6dTpdjy5PGsUduxo2dkbc6cgbxLAABc7UQqMkfAa+xGjx4t5cuXl1y5ckmDBg1k+fLlyZ4/ZcoUqVq1qjm/Zs2aMnPmzATHNacOGjRISpQoIZGRkdK8eXPZpgMFHLZu3SqtW7eWwoULmw+oSZMmsoB53RLLn1/kmWdE1qwRWbtWZMAAkfLlRU6dEvniC5FWrTxNuY8+KvL11579AAAgYAIa7CZPniy9e/eWwYMHy+rVq6VWrVrSokULOXTokN/zlyxZIh07dpRu3brJmjVrpE2bNqas1+bC/xk2bJiMHDlSxowZI8uWLZOoqChzzXPnznnPuffee+XSpUsyf/58WbVqlXlf3XfgwIFM+blDUs2aIm++6ZkPb8kSz5QpxYp5RtBqrZ4uZaZTqtx3n8jYsSJ79gT6jgEAyHIC2hSrNXT16tWTUaNGmeeXL1+WMmXKSM+ePaV///6Jzm/fvr2cPn1aZsyY4d3XsGFDqV27tgly+qOULFlS+vTpI3379jXHtdqyWLFiEhsbKx06dJAjR45IkSJFZNGiRXLrrbeac06ePGlq7ubMmWNq+FIiSzTFXo2uPasjZ6dO9RSdI8+pRg2Ru+/2FF3tgiZbAADc2RR74cIFU1vmDFLZs2c3z5fqygh+6H7f4KW1cfb5O3fuNLVuznP0g9AAaZ9TqFAhqVKliowfP96ERK25++STT6Ro0aJSR9dSTcL58+fNB+ssWV727J5ly955xzMv3rp1Iq+95hlNq8e0JlWP6SoXun6tNt3qPHnarKuhEAAApKtwCRCtOYuPjze1aU76fPPmzX5fo6HN3/l2E6q9Te6cbNmyydy5c00Tbt68eU2Y1FA3e/ZsKVCgQJL3O3ToUHn11VfT+NNmAdmyeWrotLz8ssjRoyL//a/IrFkis2eLHD4sov0h7T6ROm/eHXeING3qWf1Cp1nRMAgAANIsy/0m1ebaHj16mDD3888/m8EaGvLuu+8+2b9/f5KvGzBggKkCtcse+pAlr1Ahz6jZ8eM1cXsGYLz7rkjLliK5c3uCnk6d0qOHp/+eBj0daTt8uKd59/z5dP/uAQBwu4DV2OmI1LCwMDl48GCC/fq8ePHifl+j+5M7397qPh0V6zxH++EpHTChffT+/vtvbzv1Rx99ZPrXffbZZ3779qmIiAhTkAZaE6efvxZd2eLCBZFly0QWLvTMmaeDMXQC5OnTPcXzgYvUretp1tXmXl3PtmRJPn4AAIKxxi5nzpymT9s8XYj+f3TwhD5vpL/M/dD9zvOVBjL7/AoVKphw5zxH+8Lp6Fj7nDP/m1xXm2Cd9Lm+PzKBDqLQgSuvvKJfoGe+PK2lGzZMhyx7avu0xm7xYk8tX9u2nmXOSpf2PB46VES/Y30dAAC4wgqgSZMmWREREVZsbKy1ceNGKyYmxsqfP7914MABc7xTp05W//79vecvXrzYCg8Pt959911r06ZN1uDBg60cOXJY69at857z1ltvmWtMnz7dWrt2rdW6dWurQoUK1tmzZ83xw4cPW4UKFbLatm1r/fbbb9aWLVusvn37muvo85SKi4vT0cRmi3R2+bJlbd1qWbGxlvXPf1pWzZqWlT27Dt9OXCpWtKx27Sxr6FDL+vFHyzp0iK8DAOAqqckcAWuKtacvOXz4sJlQWAc3aHOpDmKwBz/s3r07Qc1a48aNZeLEifLyyy/LwIEDpVKlSjJt2jSpoR32/6dfv35mtGtMTIwcP37cTD6s19QJje0mYH3+0ksvSbNmzeTixYtSvXp1mT59upnPDkEyEKNSJU/p0sWzT9evXb1aRCewtsuuXZ559bRMmXLl9dpkq9+lFm3+1e3114uEB/R/dwAAMhxLiqUR89gFAe2Xp4MyNPCtWuUp27f7P1f77N1wg2eghhb9x0D16iJlyniCJAAALsgcBLtM+JCRiU6e9Myn9/vvnqJr3Orz//WtTETXvdXApyFPp1zRx1WrepZOo4YPABAECHZB9iEjwHRQzM6dngmTNeRp0cdbt4pcupT0AA9tCtaQV6WKSOXKV4oO7gAAIJMQ7ILsQ0aQunjR03S7caOnbNggopNjb9ki4lhbOBENdnYfQO27p8V+nMwk1wAApAXBLhMQ7Fxew7d7tyfkbdrkqdmzy969yb9Wg13FiiLXXecp+tguOl0LzbsAgFQi2GUCgl0WpaNztZZPQ55u7aJr5SazcokRFiZStqxOuOgp2o/PLuXKeUbz6jkAAKQxczD/A5AaUVFXplLxF/rs6Vd27LhStH+fTs2iK27oYy1+/zSGe2r1NPxp0LO3OnJXH+s2b16+LwBAkgh2QHqGPns6FX/Nu1qjp6HPDnp//unZatGmXx3IYT9PSv78noCnRUOgFudjXaGD8AcAWRbTnaQRTbFIV/HxnuCnAU8Dnxb78Z49npLSJdQ02Nkhzy7azOssuq5yjhx8iQAQAuhjF2QfMpBuc/RpwNPAp4M4nEX3//WXSFxcyq6lkzIXLuwJeSVKJC4a/Oxt7tx8gQAQQAS7IPuQgUxz6pQn4GnY0+2+fYm3WjOY1Px9SdUAasCziy75p8X5WEvRoiKRkRn50wFAlnSCwRNAFqUraeiEylqSov39jhzxBDwtdtjTcuDAlcdadD4/rSnUoiN/UxICNeDZQc9ZihRJuNX5AJn+BQDSFYMngKwme/YrYcvf6F6bZXkCnYY9Zzl48MrWWXTUrx0CdTRwShQs6Al6dtHmYd+ts+gAFdb2BYAkEewA+KcBSrsZaNGl1JKjIfDECZFDhzwhz94ePux5rEUf2/uOHvW85tgxT9HVPlIiIsJT06chz7n1fWwXDY46kljDLABkAQQ7AOkTAqOjPUWXV0vJKGANdHbw06ZhfazFfqxbu+jz8+c9RZuOtaSUhjpdEURDnh32nMU+5rtPC03FAEIMwQ5A5tMVNuzm12rVrn6+1u6dOXOltk+LBj7n1ne/BkcdTKJ9Cu1jKekn6Ntn0A55SRWtEfT3OGfONH88AJBWBDsAoVEjqP3rtOgSbCmlNXx//30l2Olju/nXLr779bE9bYzdZ1CnmEktHSGsQS+5Ytdy+nus08zQnxBAKhHsALiX9smzp2lJDZ0ORieE1pBnFzv0+RY9zz5XtxoKtYbx7FlPudoawknRZmA77PkW7ffo77nvVkdJs/4wkKUQ7AAg0d+M4VdG4qaW9h/UgSQa8OzQZwc/3312EPTdavOxhku7pvFaaLizw55v0aZmf/vs/c5trlzUIAIhgGAHAOlJa8jsfnZpobV92jdQA15KioZIO0jaWy0XL3qup9eyJ66+1p/LN/QlVzRQJrVPt1qbCiDdEewAIJhovzo7COmav2ml/QudoU/7CtrPk9qnz+399jENhXZNpF3LmB50rWJn0LNLcs+1j6XzmLPoMWoVAYIdALiS1ojZI4+vhTYLa7izg54d+lJS7Nc5H+tqJkprFO1+iulFp7axQ54dAp1b3/3+jvnbrwNZGOWMEEGNHQAg+bBk978rVeraPyntO3j6dMKw5wyAesxuPrb3X22fDlKxQ6hd+5gR/S6dQS+lj5PbOgu1jUgnBDsAQOZxjvZNL9pMrPMcashzBj77sXPr+9jfc2fRIKp0a/dfzKgmeN+wl5qi0+v42/ruI0C6HsEOABDanAM70puugayh0V/o892vz+19zmO+++zztOj17UEz9vkZSQOkhjt/oc9Z/O1Lbn9SRZuwmY8xUxHsAABIigYTLTpxdEbQmkBtSvYNfHYI1GNX26fFuc/3sRZ7lLRzjsVrnUonJTTU2SFPA6Vv8HPuu9rj5LZ2ifzfc60ZzqKBkmAHAECgaADJqNpGJw12duCzg50zBPrucxZ/+5Lbr0UDpHM5QC2Z3Tc0l0/YS+p5So9p0UFJKdkfwHWmCXYAALidTi+jRQfBZDQNc9rEbIc8HQntDH3JPff32Hef7357n07xY9OBNIEIlM7uAXbYc4Y+38c1a4q88066vjXBDgAApB9tAtXQoiWjmrD90TB34ULSAVCLhj/7mL0/rfucgVK3dnO3c0DP1YJlBvSpJNgBAIDQ52x+DQQNc3bIc4ZAfWwHQ9/9hQql+20Q7AAAANKj+dUebRxA2QP67gAAAEg3BDsAAACXINgBAAC4BMEOAADAJQh2AAAALkGwAwAAcAmCHQAAgEsQ7AAAAFyCYAcAAOASBDsAAACXINgBAAC4BMEOAADAJQh2AAAALkGwAwAAcAmCHQAAgEsQ7AAAAFyCYAcAAOASBDsAAACXINgBAAC4BMEOAADAJQh2AAAALkGwAwAAcAmCHQAAgEsQ7AAAAFyCYAcAAOASBDsAAACXINgBAAC4BMEOAADAJQh2AAAAWS3YnThxIsUlNUaPHi3ly5eXXLlySYMGDWT58uXJnj9lyhSpWrWqOb9mzZoyc+bMBMcty5JBgwZJiRIlJDIyUpo3by7btm1LdJ0ffvjBvJ+eU6BAAWnTpk2q7hsAACBkg13+/PlNAEpJSanJkydL7969ZfDgwbJ69WqpVauWtGjRQg4dOuT3/CVLlkjHjh2lW7dusmbNGhPGtKxfv957zrBhw2TkyJEyZswYWbZsmURFRZlrnjt3znvON998I506dZKuXbvK77//LosXL5ZHHnkkxfcNAAAQjLJZWsWVAj/99JP38a5du6R///7y+OOPS6NGjcy+pUuXymeffSZDhw6VLl26pOjNtcasXr16MmrUKPP88uXLUqZMGenZs6e5vq/27dvL6dOnZcaMGd59DRs2lNq1a5sgpz9KyZIlpU+fPtK3b19zPC4uTooVKyaxsbHSoUMHuXTpkqkhfPXVV01ATCutmYyOjjbXz5cvX5qvAwAAkF6ZI1xSqGnTpt7H//d//yfvvfeeqT2z3X///aZpdOzYsSkKdhcuXJBVq1bJgAEDvPuyZ89umk41JPqj+7WGz0lr46ZNm2Ye79y5Uw4cOGCuYdMPQgOkvlaDndYM/vXXX+a9brrpJnO+BsN33nlHatSokeT9nj9/3hRbapucAQAAgnLwhIakunXrJtqv+67WR8525MgRiY+PN7VpTvpcw5Y/uj+58+1tcuf88ccfZjtkyBB5+eWXTe2fNh/ffvvtcuzYsSTvV2siNSTaRWsWAQAAQj7Yaaj59NNPE+3/97//HfSBR5t71UsvvSQPPvig1KlTR8aNGyfZsmUzAzOSojWLWgVqlz179mTiXQMAAFxdiptinUaMGGFC0axZs0wzp9KaOh19qgMTUqJw4cISFhYmBw8eTLBfnxcvXtzva3R/cufbW92no2Kd52hzq7L3V6tWzXs8IiJCKlasKLt3707yfvUcLQAAAK6qsbvnnntMiNN+ddp8qeW+++6TrVu3mmMpkTNnTlNbNm/evAS1afrcHpDhS/c7z1dz5szxnl+hQgUT7pznaF84HR1rn6PvqQFty5Yt3nMuXrxoBoSUK1culZ8EAABAELFS6cKFC1azZs2srVu3Wtdq0qRJVkREhBUbG2tt3LjRiomJsfLnz28dOHDAHO/UqZPVv39/7/mLFy+2wsPDrXfffdfatGmTNXjwYCtHjhzWunXrvOe89dZb5hrTp0+31q5da7Vu3dqqUKGCdfbsWe85zz33nFWqVCnrxx9/tDZv3mx169bNKlq0qHXs2LEU33tcXJyOJjZbAACAjJKazJHqptgcOXLI2rVr0yVU6vQlhw8fNhMK26NTZ8+e7R38oE2jOnrV1rhxY5k4caIZ9DBw4ECpVKmSGRHrHM3ar18/MyVKTEyMHD9+XJo0aWKuqRMa23QEbHh4uJnL7uzZs6Y5ef78+amagw8AACBk57Fzev75501z5ltvvSVZFfPYAQCAkJ3Hzkkn+f3Pf/4jc+fONX3WdHUHJ53jDgAAAJkrTcFOl/C6+eabzWMdMOGk04YAAAAgRILdggUL0v9OAAAAkPnTnQAAAMAlNXZq5cqV8tVXX5mRq7ruq9O3336bHvcGAACAjK6xmzRpkpl6ZNOmTTJ16lQzwe+GDRvMlCE6agMAAAAhEuzefPNNs6zY999/b1aQ+OCDD2Tz5s3y8MMPS9myZdP/LgEAAJAxwW7Hjh3SqlUr81iDnU4IrKNhdX67sWPHpuWSAAAACESw0xUaTp48aR6XKlXKTH+idKWHM2fOXOs9AQAAILMGT9x2220yZ84cqVmzprRr106ee+45079O9915551puSQAAAACEexGjRol586dM49feukls37skiVL5MEHHzTruAIAACBE1ooFa8UCAIDgWys2TX3smjVrJq+++mqi/X///bc5BgAAgBBpil24cKGsW7dO1qxZIxMmTJCoqCizXycq/umnn9L7HgEAAJCRS4rNnTtXDhw4IA0bNpRdu3al9TIAAAAIdLArUaKEqZ3TkbH16tUztXgAAAAIsWCnkxGriIgImThxopnupGXLlvLRRx+l9/0BAAAgI/vY+Q6k1SlObrjhBunSpUtaLgcAAIBABbudO3dKkSJFEuzTOeyqVKkiq1atSo/7AgAAQCoxj10mzCkDAACQGZkjTTV2auXKlfLVV1/J7t27zTQnTt9++21aLwsAAIDMHDwxadIkady4sWzatEmmTp0qFy9elA0bNpj1YjVRAgAAIESC3ZtvvikjRoyQ77//XnLmzCkffPCBbN68WR5++GEpW7Zs+t8lAAAAMibY7dixQ1q1amUea7A7ffq0mQLl+eefl7Fjx6blkgAAAAhEsCtQoICcPHnSPC5VqpSsX7/ePD5+/LicOXPmWu8JAAAAaZCmwRO33XabzJkzx6w60a5dOzNBsfav03133nlnWi4JAACAQAS7UaNGyblz58zjl156SXLkyCFLliwxc9npZMUAAAAI8nnsdB6VlMgK87oxjx0AAAjpeezy58/vXSc2OfHx8am5LAAAANJBqoLdggULvI+1ou+ee+6Rf//732YABQAAAEIo2DVt2jTB87CwMGnYsKFUrFgxve8LAAAAmTHdCQAAAIIPwQ4AAMAlrjnYpWQwBQAAAIKsj13btm0TPNe57J566imJiopKsP/bb79Nn7sDAABAxgQ7nUPF6bHHHkvNywEAABAswW7cuHEZdycAAAC4JgyeAAAAcAmCHQAAgEsQ7AAAAFyCYAcAAOASBDsAAACXINgBAAC4BMEOAADAJQh2AAAALkGwAwAAcAmCHQAAgEsQ7AAAAFyCYAcAAOASBDsAAACXINgBAAC4BMEOAADAJQh2AAAALkGwAwAAcAmCHQAAgEsQ7AAAAFyCYAcAAOASBDsAAACXCIpgN3r0aClfvrzkypVLGjRoIMuXL0/2/ClTpkjVqlXN+TVr1pSZM2cmOG5ZlgwaNEhKlCghkZGR0rx5c9m2bZvfa50/f15q164t2bJlk99++y1dfy4AAIAsFewmT54svXv3lsGDB8vq1aulVq1a0qJFCzl06JDf85csWSIdO3aUbt26yZo1a6RNmzamrF+/3nvOsGHDZOTIkTJmzBhZtmyZREVFmWueO3cu0fX69esnJUuWlMxw4UKmvA0AAMiisllavRVAWkNXr149GTVqlHl++fJlKVOmjPTs2VP69++f6Pz27dvL6dOnZcaMGd59DRs2NLVuGuT0x9Gg1qdPH+nbt685HhcXJ8WKFZPY2Fjp0KGD93WzZs0yofKbb76R6tWrm6Co10mJEydOSHR0tLl2vnz5kj33zBmRbt1EZs8W2blTJH/+FH88AAAgizuRiswR0Bq7CxcuyKpVq0xTqfeGsmc3z5cuXer3Nbrfeb7S2jj7/J07d8qBAwcSnKMfhgZI5zUPHjwo3bt3l88//1xy584tGSkyUkQrFI8fF/n66wx9KwAAkIUFNNgdOXJE4uPjTW2akz7XcOaP7k/ufHub3Dlaq/f444/LU089JXXr1k3RvWpfPE3MzpJS2bKJPPaY5/EXX6T4ZQAAAKHVxy4QPvzwQzl58qQMGDAgxa8ZOnSoqfmzizYXp8Yjj3i2P/0ksnt3au8YAAAgyINd4cKFJSwszDSLOunz4sWL+32N7k/ufHub3Dnz5883zbIRERESHh4u119/vdmvtXddunTx+74aArVt2y579uxJ1c+qOfD22z2PJ0xI1UsBAACCP9jlzJlT6tSpI/PmzfPu08ET+rxRo0Z+X6P7neerOXPmeM+vUKGCCXDOc7TZVEfH2ufoiNnff//dTG+ixZ4uRUfovvHGG37fV0Ogdlh0ltSym2M//1ybg1P9cgAAgGSFS4DpqFStJdPasvr168v7779vRr127drVHO/cubOUKlXKNIWq5557Tpo2bSrDhw+XVq1ayaRJk2TlypUyduxYc1zno+vVq5e8/vrrUqlSJRP0XnnlFTNSVqdFUWXLlk1wD3ny5DHb6667TkqXLp1hP+tDD4n06CGyaZOITpl3000Z9lYAACALCniw0+lLDh8+bCYU1sENOt3I7NmzvYMfdu/ebUbK2ho3biwTJ06Ul19+WQYOHGjC27Rp06RGjRoJ5qbTcBgTEyPHjx+XJk2amGvqhMaBFB0tcv/9OsGyZxAFwQ4AALhqHrusMKeM03ffibRurX0BRfbuFQkLy9DbBAAAIS5k5rHLilq2FClYUKdlEfHpKggAAHBNCHaZLGdObX72PGZOOwAAkJ4IdgHQqZNn++23IqdPB+IOAACAGxHsAqBhQ5GKFT2hbvr0QNwBAABwI4JdALDEGAAAyAgEuwB59FHP9r//1VUxAnUXAADATQh2AVK5skj9+iLx8SIxMSJnzwbqTgAAgFsQ7ALo9dc9o2R1brt//EPk2LFA3g0AAAh1BLsA0jCnTbG6IsXixSK33iqyZ08g7wgAAIQygl2ANW0q8vPPIqVKiWzcKNKokcj69YG+KwAAEIoIdkGgZk2RJUtEbrhB5K+/RJo0EZk6VYTF3gAAQGoQ7IJE2bIiv/wicsstInFxIm3beppmtYkWAAAgJQh2QUTXkJ0zR2TAAJHISE+o09q7Nm08zbQAAADJIdgFGQ10b74psm2bSPfuItmze1an0ObaRx4RmT9f5PLlQN8lAAAIRgS7IKWDKcaOFdmwQeSBBzxh7ssvRe68U+T660Vee40RtAAAIKFslkUX/bQ4ceKEREdHS1xcnOTLl08y2qpVIp9+6gl3J05cWZqsWTOR++8Xufdez/qzAAAg62YOgl0mfMjp6cwZkW+/FfnPf0QWLEh4rFo1T8C75x6Rhg1FIiIy7bYAAEAGIdi5ONg5/fGHyLRpIjNmiCxa5FmezKahTsPdbbd5is6PFxUVkNsEAADXgGCXRYKd0/HjIj/+6Al5uprFoUMJj4eHi9SoIVKvnkjdup6iz3VJMwAAELwIdkH2IWc27TW5daunFk/LTz/5H2ihoa56dc+IW2cpUcLTfw8AAAQewS7IPuRgoMFu5UqRFSs8Wy1//+3/3Pz5RapWFalSxbPVUrmyZ3BGrlyZfecAAGRtJxg8EVwfcjDSWr2dO0XWrhVZt+5K0Zq+5ObJK11a5LrrrpTy5a+U4sU98+4BAID0Q7DLBKEe7JJy7pxncuTNm0W2bPFstWjgO3ky+ddq064ujaalTBlP0SBob0uWFClUiGZeAAAyKnOEp+rKcD1tarX72vnW8B05IrJjR8Ly558iu3aJ7N0rcuGCyPbtnpJc+NOApxMwa18+u2htn70tVkykcGGRHDky/McFAMBVCHZIER1MUaSIp+g0Kr4uXRL56y9PyNP+fL5Fj2kw1PCn52i5Gq3dK1rUE/Ts9/YtGgC16LmM8AUAZHUEO6TP/0jhIuXKeUpSzp8X2b9fZN8+T9Gwd/CgZ9+BA1e2hw97+vkdPeopmzal7B7y5vUEPC0FCybeFiiQeKsDRXR9XgAA3IBgh0yjkybbAy2SY4c6DX06H59uNezZRffpVmsA7fCnr9E+gFpSUhvoe192yHOW6OgrW39FuznoVgOlBlsAAAKNX0cIOjqy1m5qTQkNdTpBsx30jh1LvNWpXXTrfKyv0ddqTaLWFGpJq9y5r4Q8DXzObXIlT57EW61BZB5BAEBaEOzgiiCoTataUkND3alTnqCnIc/exsV5tnbR575F92vtoI4ittfw1aLNyddKQ50GPLvoUnC+j3WbXNGg6ftYtzo4htAIAO5FsEOWDoRaq6Ylub6BydHBIBrwTpzwBD77sb21HzuL7tNAqY91az8+ffrKCGT73PSmoU4Dnl20dtD53He/c+v72F/R4Oh8zLyGAJC5CHbANdCRuPaAjWulNYha62eHPWfg06LPnduUFLsmUZub7dBoH8sM2n/RDnu+oc93v73PWezXJ7XPfuxvq4VgCSCrIdgBQUJDiN3kmt50OpqzZz0hT0Od/dguvvv0sb3PLs5jWrQZ2nncLvpeNg2UWrQ2MxB0LkQ75DkDn7/ndtGwnty+qz12bv091nuiORxARiHYAVmAjtq1B2xkNA12ztDnGwD1uV3sfRr+nPvtY/722/ucx5z7tFbSdvGip2gtZzDRcOcb+lJa7Nde7bnvNqljV9unRf//IYwCoYFgByB9/1IJz7iax6vRUKdBzg55viHQ3pfSon0o/T137tfHye3XEh+f8D7twJlZTeLpwQ55zuIMf9dS9P+Z5J5fbV9yW+frfPcTVuFGBDsArqG/qO3aqWCiwU7DnoY53xCo+3wDon2e7z7nfvt19j7ntZ3nJrW1Hzv32499g6iyj7tJWFjiAOjvcXLHfM9LqqT0vJQUve+U7EvuXEKtexHsACCD6S9SHVEcKnQgjzap+wZCZ/G3L61F3yu558md42+/7z5/QVXp/qSOZYU+vc7g5wyAV3uc3D7nNrlj13qO7/60Pg+7yn4toTYIi2AHAEhAf5EFY83ntTTRa4BzBj597hsMfffZW+d+5zFnSWqf/b5J7fd9H3/nOfcnt08f++5PLrxrOMfVae1mUqEvJcEwucBYs6bIiBGSrgh2AADX/2K2a5h0NHRWYte+OoOkbzD0DYR2kHWe53s8tft8j/ue5yzJvSa5x0ntu5TMc/vx1f5hYN9rerOnokpPBDsAAFxe+4qrB+DkwuLVSlpeo6VwYUl3BDsAACBZPQBnz+4Z5BLqQqxLIAAAAJJCsAMAAHAJgh0AAIBLEOwAAABcgmAHAADgEgQ7AAAAlyDYAQAAuATBDgAAwCUIdgAAAC5BsAMAAHAJgh0AAIB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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Computing predictions for survival functions\n", "haz_neg = aft_predictions_function(X=[[1, 0], ], times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='weibull', measure='hazard')\n", "haz_pos = aft_predictions_function(X=[[1, 1], ], times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='weibull', measure='hazard')\n", "\n", "# Plotting hazard functions\n", "plt.plot(times_to_predict, haz_neg[:, 0], '-', color='blue', label='Negative')\n", "plt.plot(times_to_predict, haz_pos[:, 0], '-', color='red', label='Positive')\n", "plt.ylim([0, 0.011])\n", "plt.ylabel(\"Hazard\")\n", "plt.xlim([-5, 235])\n", "plt.xlabel(\"Time (days)\")\n", "plt.legend()\n", "plt.title(\"Weibull AFT\")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "ab917294-1a9d-43bf-b91d-d411fbcde96a", "metadata": {}, "source": [ "Note that the approximation near $t=0$ is less precise for the given spacing used. One could improve its appearance relative to the book by using a finer resolution.\n", "\n", "### Log-Normal\n", "\n", "Another option is the log-normal AFT model. The following is how `ee_aft` can be used to fit the log-normal AFT model" ] }, { "cell_type": "code", "execution_count": 25, "id": "8c90a596-8f52-45a2-bb10-d3c91b406659", "metadata": {}, "outputs": [], "source": [ "def psi(theta):\n", " return ee_aft(theta=theta, t=d['time'], delta=d['status'], \n", " X=d[['C', 'stain', ]], \n", " distribution='log-normal')" ] }, { "cell_type": "code", "execution_count": 26, "id": "246fd76f-95e3-4785-a821-1fd93085233e", "metadata": {}, "outputs": [], "source": [ "estr = MEstimator(psi, init=[5., 0., 0.])\n", "estr.estimate()" ] }, { "cell_type": "code", "execution_count": 27, "id": "9b372105-8be3-429e-b8e8-482c783347c3", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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EstSELCLUCL
Params
Intercept5.4920.4504.6096.374
Stain-1.1510.498-2.127-0.176
Shape-0.3070.134-0.571-0.043
\n", "
" ], "text/plain": [ " Est SE LCL UCL\n", "Params \n", "Intercept 5.492 0.450 4.609 6.374\n", "Stain -1.151 0.498 -2.127 -0.176\n", "Shape -0.307 0.134 -0.571 -0.043" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Setting up a Table for the results\n", "results = pd.DataFrame()\n", "results['Params'] = [\"Intercept\", \"Stain\", \"Shape\"]\n", "results = results.set_index('Params')\n", "results['Est'] = estr.theta\n", "results['SE'] = np.diag(estr.variance) ** 0.5\n", "ci = estr.confidence_intervals()\n", "results['LCL'] = ci[:, 0]\n", "results['UCL'] = ci[:, 1]\n", "results.round(3)" ] }, { "cell_type": "code", "execution_count": 28, "id": "029e39cb-734a-49ad-95ff-775bf0a99361", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Computing predictions for survival functions\n", "surv_neg = aft_predictions_function(X=[[1, 0], ], times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='log-normal')\n", "surv_pos = aft_predictions_function(X=[[1, 1], ], times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='log-normal')\n", "\n", "# Plotting survival functions\n", "plt.plot(times_to_predict, surv_neg[:, 0], '-', color='blue', label='Negative')\n", "plt.fill_between(times_to_predict, surv_neg[:, 2], surv_neg[:, 3], color='blue', alpha=0.3)\n", "plt.plot(times_to_predict, surv_pos[:, 0], '-', color='red', label='Positive')\n", "plt.fill_between(times_to_predict, surv_pos[:, 2], surv_pos[:, 3], color='red', alpha=0.3)\n", "plt.ylim([0, 1])\n", "plt.ylabel(\"Survival\")\n", "plt.xlim([0, 235])\n", "plt.xlabel(\"Time (days)\")\n", "plt.legend()\n", "plt.title(\"Log-Normal AFT\")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "8d116a53-f186-4536-82e0-0f90c378a4c2", "metadata": {}, "source": [ "### Log-Logistic\n", "\n", "The final option available in `delicatessen` is the log-logistic AFT model. The following is how `ee_aft` can be used to fit this model" ] }, { "cell_type": "code", "execution_count": 29, "id": "0822db04-bb6e-4b04-85ba-c47192768b86", "metadata": {}, "outputs": [], "source": [ "def psi(theta):\n", " return ee_aft(theta=theta, t=d['time'], delta=d['status'], \n", " X=d[['C', 'stain', ]], \n", " distribution='log-logistic')" ] }, { "cell_type": "code", "execution_count": 30, "id": "57e934c1-cf27-4fef-8eae-0c07eb6e8186", "metadata": {}, "outputs": [], "source": [ "estr = MEstimator(psi, init=[5., 0., 0.])\n", "estr.estimate()" ] }, { "cell_type": "code", "execution_count": 31, "id": "5ff2ef63-0fe2-4773-9e2f-faa0aebbf235", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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EstSELCLUCL
Params
Intercept5.4610.4454.5896.334
Stain-1.1490.505-2.139-0.159
Shape0.2170.145-0.0670.502
\n", "
" ], "text/plain": [ " Est SE LCL UCL\n", "Params \n", "Intercept 5.461 0.445 4.589 6.334\n", "Stain -1.149 0.505 -2.139 -0.159\n", "Shape 0.217 0.145 -0.067 0.502" ] }, "execution_count": 31, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Setting up a Table for the results\n", "results = pd.DataFrame()\n", "results['Params'] = [\"Intercept\", \"Stain\", \"Shape\"]\n", "results = results.set_index('Params')\n", "results['Est'] = estr.theta\n", "results['SE'] = np.diag(estr.variance) ** 0.5\n", "ci = estr.confidence_intervals()\n", "results['LCL'] = ci[:, 0]\n", "results['UCL'] = ci[:, 1]\n", "results.round(3)" ] }, { "cell_type": "markdown", "id": "c016aa4c-1554-4981-9e78-7a4c3db69c3b", "metadata": {}, "source": [ "These parameter estimates are the same as those reported in Collett (except $\\sigma$ due to a differing parameterization). " ] }, { "cell_type": "code", "execution_count": 32, "id": "2b776f67-aa4c-42e3-a947-479289d9157f", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Computing predictions for survival functions\n", "surv_neg = aft_predictions_function(X=[[1, 0], ], times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='log-logistic')\n", "surv_pos = aft_predictions_function(X=[[1, 1], ], times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='log-logistic')\n", "\n", "# Plotting survival functions\n", "plt.plot(times_to_predict, surv_neg[:, 0], '-', color='blue', label='Negative')\n", "plt.fill_between(times_to_predict, surv_neg[:, 2], surv_neg[:, 3], color='blue', alpha=0.3)\n", "plt.plot(times_to_predict, surv_pos[:, 0], '-', color='red', label='Positive')\n", "plt.fill_between(times_to_predict, surv_pos[:, 2], surv_pos[:, 3], color='red', alpha=0.3)\n", "plt.ylim([0, 1])\n", "plt.ylabel(\"Survival\")\n", "plt.xlim([0, 235])\n", "plt.xlabel(\"Time (days)\")\n", "plt.legend()\n", "plt.title(\"Log-Logistic AFT\")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "6cec0eea-3636-4ba0-9ff2-a73608cc0a93", "metadata": {}, "source": [ "Again, we can also plot the hazard functions over time and compare them to the book (Figure 6.7)." ] }, { "cell_type": "code", "execution_count": 33, "id": "155a611d-4ba4-4941-92da-49f707bb8fb6", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Computing predictions for survival functions\n", "haz_neg = aft_predictions_function(X=[[1, 0], ], times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='log-logistic', measure='hazard')\n", "haz_pos = aft_predictions_function(X=[[1, 1], ], times=times_to_predict, \n", " theta=estr.theta, covariance=estr.variance, \n", " distribution='log-logistic', measure='hazard')\n", "\n", "# Plotting hazard functions\n", "plt.plot(times_to_predict, haz_neg[:, 0], '-', color='blue', label='Negative')\n", "plt.plot(times_to_predict, haz_pos[:, 0], '-', color='red', label='Positive')\n", "# Note: the book's figure seems to have an issue. If you plot the equation given in the book,\n", "# (commented below), it overlaps perfectly with this output. The book's figures seem to have\n", "# some sort of issue? Should check against the 2023 edition when available to me.\n", "# h1 = 1.243 * (times_to_predict)**-1 / (1 + times_to_predict**-1.243 * np.exp(6.787 - 1.428))\n", "# plt.plot(times_to_predict, h1, '--', color='green')\n", "# h1 = 1.243 * (times_to_predict)**-1 / (1 + times_to_predict**-1.243 * np.exp(6.787))\n", "# plt.plot(times_to_predict, h1, '--', color='green')\n", "plt.ylim([0, 0.011])\n", "plt.ylabel(\"Hazard\")\n", "plt.xlim([-5, 235])\n", "plt.xlabel(\"Time (days)\")\n", "plt.legend()\n", "plt.title(\"Log-Logistic AFT\")\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "69f7d4cf-ea14-44fa-88f4-385659643254", "metadata": {}, "source": [ "Consistent with the other results, the log-logistic AFT model does not differ substantially from the other AFT models.\n", "\n", "Here, we applied some of the parametric survival models described at length in Collett using the M-estimation framework. As these models are all finite dimension parameter vectors, standard M-estimation theory straightforwardly applies. A benefit in this context is the ease that variance estimation can be accomplished to create plots with point-wise confidence intervals.\n", "\n", "## References\n", "\n", "Collett, D. (2015). Survival analysis. In *Modelling survival data in medical research*. 3rd Ed. Chapman and Hall/CRC. pg 6-7\n", "\n", "Collett, D. (2015). Accelerated failure time and other parametric models. In *Modelling survival data in medical research*. 3rd Ed. Chapman and Hall/CRC. pg 221-274" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.7" } }, "nbformat": 4, "nbformat_minor": 5 }