{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Piecewise exponential models and creating custom models\n",
"\n",
"This section will be easier if we recall our three mathematical \"creatures\" and the relationships between them. First is the survival function, $S(t)$, that represents the probability of living past some time, $t$. Next is the _always non-negative and non-decreasing_ cumulative hazard function, $H(t)$. Its relation to $S(t)$ is:\n",
"\n",
"$$ S(t) = \\exp\\left(-H(t)\\right)$$\n",
"\n",
"Finally, the hazard function, $h(t)$, is the derivative of the cumulative hazard: \n",
"\n",
"$$h(t) = \\frac{dH(t)}{dt}$$\n",
"\n",
"which has the immediate relation to the survival function:\n",
"\n",
"$$S(t) = \\exp\\left(-\\int_{0}^t h(s) ds\\right)$$\n",
"\n",
"Notice that any of the three absolutely defines the other two. Some situations make it easier to define one vs the others. For example, in the Cox model, it's easist to work with the hazard, $h(t)$. In this section on parametric univariate models, it'll be easiest to work with the cumulative hazard. This is because of an asymmetry in math: derivatives are much easier to compute than integrals. So, if we define the cumulative hazard, both the hazard and survival function are much easier to reason about versus if we define the hazard and ask questions about the other two.\n",
"\n",
"First, let's revisit some simpler parametric models. \n",
"\n",
"#### The Exponential model\n",
"\n",
"Recall that the Exponential model has a constant hazard, that is:\n",
"\n",
"$$ h(t) = \\frac{1}{\\lambda} $$\n",
"\n",
"which implies that the cumulative hazard, $H(t)$, has a pretty simple form: $H(t) = \\frac{t}{\\lambda}$. Below we fit this model to some survival data. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"%config InlineBackend.figure_format = 'retina'\n",
"\n",
"from matplotlib import pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"from lifelines.datasets import load_waltons\n",
"waltons = load_waltons()\n",
"T, E = waltons['T'], waltons['E']"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
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"metadata": {
"image/png": {
"height": 263,
"width": 608
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from lifelines import ExponentialFitter\n",
"\n",
"fig, ax = plt.subplots(nrows=1, ncols=2, figsize=(10, 4))\n",
"\n",
"epf = ExponentialFitter().fit(T, E)\n",
"epf.plot_hazard(ax=ax[0])\n",
"epf.plot_cumulative_hazard(ax=ax[1])\n",
"\n",
"ax[0].set_title(\"hazard\"); ax[1].set_title(\"cumulative_hazard\")\n",
"\n",
"epf.print_summary(3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This model does a poor job of fitting to our data. If I fit a _non-parametric_ model, like the Nelson-Aalen model, to this data, the Exponential's lack of fit is very obvious. "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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""
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
},
{
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},
"metadata": {
"image/png": {
"height": 316,
"width": 474
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from lifelines import NelsonAalenFitter\n",
"\n",
"ax = epf.plot(figsize=(8,5))\n",
"\n",
"naf = NelsonAalenFitter().fit(T, E)\n",
"ax = naf.plot(ax=ax)\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It should be clear that the single parameter model is just averaging the hazards over the entire time period. In reality though, the true hazard rate exhibits some complex non-linear behaviour.\n",
"\n",
"#### Piecewise Exponential models\n",
"\n",
"What if we could break out model into different time periods, and fit an exponential model to each of those? For example, we define the hazard as:\n",
"\n",
"$$ \n",
"h(t) = \\begin{cases}\n",
" \\lambda_0, & \\text{if $t \\le \\tau_0$} \\\\\n",
" \\lambda_1 & \\text{if $\\tau_0 < t \\le \\tau_1$} \\\\\n",
" \\lambda_2 & \\text{if $\\tau_1 < t \\le \\tau_2$} \\\\\n",
" ... \n",
" \\end{cases}\n",
"$$\n",
"\n",
"This model should be flexible enough to fit better to our dataset. \n",
"\n",
"The cumulative hazard is only slightly more complicated, but not too much and can still be defined in Python. In _lifelines_, univariate models are constructed such that one _only_ needs to define the cumulative hazard model with the parameters of interest, and all the hard work of fitting, creating confidence intervals, plotting, etc. is taken care. \n",
"\n",
"For example, _lifelines_ has implemented the `PiecewiseExponentialFitter` model. Internally, the code is a single function that defines the cumulative hazard. The user specifies where they believe the \"breaks\" are, and _lifelines_ estimates the best $\\lambda_i$. \n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
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]
},
"metadata": {
"image/png": {
"height": 277,
"width": 601
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from lifelines import PiecewiseExponentialFitter\n",
"\n",
"# looking at the above plot, I think there may be breaks at t=40 and t=60. \n",
"pf = PiecewiseExponentialFitter(breakpoints=[40, 60]).fit(T, E)\n",
"\n",
"fig, axs = plt.subplots(nrows=1, ncols=2, figsize=(10, 4))\n",
"\n",
"ax = pf.plot(ax=axs[1])\n",
"pf.plot_hazard(ax=axs[0])\n",
"\n",
"ax = naf.plot(ax=ax, ci_show=False)\n",
"axs[0].set_title(\"hazard\"); axs[1].set_title(\"cumulative_hazard\")\n",
"\n",
"pf.print_summary(3)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see a much better fit in this model. A quantitative measure of fit is to compare the log-likelihood between exponential model and the piecewise exponential model (higher is better). The log-likelihood went from -772 to -647, respectively. We could keep going and add more and more breakpoints, but that would end up overfitting to the data. \n",
"\n",
"#### Univarite models in _lifelines_\n",
"\n",
"I mentioned that the `PiecewiseExponentialFitter` was implemented using only its cumulative hazard function. This is not a lie. _lifelines_ has very general semantics for univariate fitters. For example, this is how the entire `ExponentialFitter` is implemented:\n",
"\n",
"```python\n",
"class ExponentialFitter(ParametricUnivariateFitter):\n",
"\n",
" _fitted_parameter_names = [\"lambda_\"]\n",
"\n",
" def _cumulative_hazard(self, params, times):\n",
" lambda_ = params[0]\n",
" return times / lambda_\n",
"```\n",
"\n",
"We only need to specify the cumulative hazard function because of the 1:1:1 relationship between the cumulative hazard function and the survival function and the hazard rate. From there, _lifelines_ handles the rest. \n",
"\n",
"\n",
"#### Defining our own survival models\n",
"\n",
"\n",
"To show off the flexability of _lifelines_ univariate models, we'll create a brand new, never before seen, survival model. Looking at the Nelson-Aalen fit, the cumulative hazard looks looks like their might be an asymptote at $t=80$. This may correspond to an absolute upper limit of subjects' lives. Let's start with that functional form.\n",
"\n",
"$$ H_1(t; \\alpha) = \\frac{\\alpha}{(80 - t)} $$\n",
"\n",
"We subscript $1$ because we'll investigate other models. In a _lifelines_ univariate model, this is defined in the following code. \n",
"\n",
"**Important**: in order to compute derivatives, you must use the numpy imported from the `autograd` library. This is a thin wrapper around the original numpy. Note the `import autograd.numpy as np` below. "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"from lifelines.fitters import ParametricUnivariateFitter\n",
"\n",
"import autograd.numpy as np\n",
"\n",
"class InverseTimeHazardFitter(ParametricUnivariateFitter):\n",
" \n",
" # we tell the model what we want the names of the unknown parameters to be\n",
" _fitted_parameter_names = ['alpha_']\n",
"\n",
" \n",
" # this is the only function we need to define. It always takes two arguments:\n",
" # params: an iterable that unpacks the parameters you'll need in the order of _fitted_parameter_names\n",
" # times: a vector of times that will be passed in.\n",
" def _cumulative_hazard(self, params, times):\n",
" alpha = params[0]\n",
" return alpha /(80 - times)"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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},
"metadata": {
"image/png": {
"height": 316,
"width": 474
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"itf = InverseTimeHazardFitter()\n",
"itf.fit(T, E)\n",
"itf.print_summary()\n",
"\n",
"ax = itf.plot(figsize=(8,5))\n",
"ax = naf.plot(ax=ax, ci_show=False)\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The best fit of the model to the data is:\n",
"\n",
"$$H_1(t) = \\frac{21.51}{80-t}$$\n",
"\n",
"Our choice of 80 as an asymptote was maybe mistaken, so let's allow the asymptote to be another parameter:\n",
"\n",
"$$ H_2(t; \\alpha, \\beta) = \\frac{\\alpha}{\\beta-t} $$\n",
"\n",
"If we define the model this way, we need to add a bound to the values that $\\beta$ can take. Obviously it can't be smaller than or equal to the maximum observed duration. Generally, the cumulative hazard _must be positive and non-decreasing_. Otherwise the model fit will hit convergence problems. "
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"class TwoParamInverseTimeHazardFitter(ParametricUnivariateFitter):\n",
" \n",
" _fitted_parameter_names = ['alpha_', 'beta_']\n",
" \n",
" # Sequence of (min, max) pairs for each element in x. None is used to specify no bound\n",
" _bounds = [(0, None), (75.0001, None)]\n",
" \n",
" def _cumulative_hazard(self, params, times):\n",
" alpha, beta = params\n",
" return alpha / (beta - times)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
"
]
},
"metadata": {
"image/png": {
"height": 316,
"width": 480
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"two_f = TwoParamInverseTimeHazardFitter()\n",
"two_f.fit(T, E)\n",
"two_f.print_summary()\n",
"\n",
"ax = itf.plot(ci_show=False, figsize=(8,5))\n",
"ax = naf.plot(ax=ax, ci_show=False)\n",
"two_f.plot(ax=ax)\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the output, we see that the value of 76.55 is the suggested asymptote, that is:\n",
"\n",
"$$H_2(t) = \\frac{16.50} {76.55 - t}$$\n",
"\n",
"The curve also appears to track against the Nelson-Aalen model better too. Let's try one additional parameter, $\\gamma$, some sort of measure of decay. \n",
"\n",
"$$H_3(t; \\alpha, \\beta, \\gamma) = \\frac{\\alpha}{(\\beta-t)^\\gamma} $$\n"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"from lifelines.fitters import ParametricUnivariateFitter\n",
"\n",
"class ThreeParamInverseTimeHazardFitter(ParametricUnivariateFitter):\n",
" \n",
" _fitted_parameter_names = ['alpha_', 'beta_', 'gamma_']\n",
" _bounds = [(0, None), (75.0001, None), (0, None)]\n",
" \n",
" # this is the only function we need to define. It always takes two arguments:\n",
" # params: an iterable that unpacks the parameters you'll need in the order of _fitted_parameter_names\n",
" # times: a numpy vector of times that will be passed in by the optimizer\n",
" def _cumulative_hazard(self, params, times):\n",
" a, b, c = params\n",
" return a / (b - times) ** c"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
"
]
},
"metadata": {
"image/png": {
"height": 316,
"width": 480
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"three_f = ThreeParamInverseTimeHazardFitter()\n",
"three_f.fit(T, E)\n",
"three_f.print_summary()\n",
"\n",
"ax = itf.plot(ci_show=False, figsize=(8,5))\n",
"ax = naf.plot(ax=ax, ci_show=False)\n",
"ax = two_f.plot(ax=ax, ci_show=False)\n",
"ax = three_f.plot(ax=ax)\n",
"plt.legend()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our new asymptote is at $t\\approx 100, \\text{c.i.}=(87, 112)$. The model appears to fit the early times better than the previous models as well, however our $\\alpha$ parameter has more uncertainty now. Continuing to add parameters isn't advisable, as we will overfit to the data. \n",
"\n",
"Why fit parametric models anyways? Taking a step back, we are fitting parametric models and comparing them to the non-parametric Nelson-Aalen. Why not just always use the Nelson-Aalen model? \n",
"\n",
"1) Sometimes we have scientific motivations to use a parametric model. That is, using domain knowledge, we may know the system has a parametric model and we wish to fit to that model. \n",
"\n",
"2) In a parametric model, we are borrowing information from _all_ observations to determine the best parameters. To make this more clear, imagine taking a single observation and changing it's value wildly. The fitted parameters would change as well. On the other hand, imagine doing the same for a non-parametric model. In this case, only the local survival function or hazard function would change. Because parametric models can borrow information from all observations, and there are much _fewer_ unknowns than a non-parametric model, parametric models are said to be more _statistically efficient._ \n",
"\n",
"3) Extrapolation: non-parametric models are not easily extended to values outside the observed data. On the other hand, parametric models have no problem with this. However, extrapolation outside observed values is a very dangerous activity. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
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\n",
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"
]
},
"metadata": {
"image/png": {
"height": 465,
"width": 427
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, axs = plt.subplots(3, figsize=(7, 8), sharex=True)\n",
"\n",
"new_timeline = np.arange(0, 85)\n",
"\n",
"three_f = ThreeParamInverseTimeHazardFitter().fit(T, E, timeline=new_timeline)\n",
"\n",
"three_f.plot_hazard(label='hazard', ax=axs[0]).legend()\n",
"three_f.plot_cumulative_hazard(label='cumulative hazard', ax=axs[1]).legend()\n",
"three_f.plot_survival_function(label='survival function', ax=axs[2]).legend()\n",
"\n",
"fig.subplots_adjust(hspace=0)\n",
"# Hide x labels and tick labels for all but bottom plot.\n",
"for ax in axs:\n",
" ax.label_outer()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 3-parameter Weibull distribution\n",
"\n",
"We can easily extend the built-in Weibull model (`lifelines.WeibullFitter`) to include a new _location_ parameter:\n",
"\n",
"$$ H(t) = \\left(\\frac{t - \\theta}{\\lambda}\\right)^\\rho $$\n",
"\n",
"(When $\\theta = 0$, this is just the 2-parameter case again). In *lifelines* custom models, this looks like:"
]
},
{
"cell_type": "code",
"execution_count": 90,
"metadata": {},
"outputs": [],
"source": [
"import autograd.numpy as np\n",
"from autograd.scipy.stats import norm\n",
"\n",
"# I'm shifting this to exaggerate the effect \n",
"T_ = T + 10\n",
"\n",
"class ThreeParameterWeibullFitter(ParametricUnivariateFitter):\n",
"\n",
" _fitted_parameter_names = [\"lambda_\", \"rho_\", \"theta_\"]\n",
" _bounds = [(0, None), (0, None), (0, T.min()-0.001)]\n",
"\n",
" def _cumulative_hazard(self, params, times):\n",
" lambda_, rho_, theta_ = params\n",
" return ((times - theta_) / lambda_) ** rho_\n"
]
},
{
"cell_type": "code",
"execution_count": 92,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
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]
},
"metadata": {
"image/png": {
"height": 316,
"width": 474
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"apg = APGWFitter()\n",
"apg.fit(T, E)\n",
"apg.print_summary(2)\n",
"ax = apg.plot_cumulative_hazard(figsize=(8,5))\n",
"ax = NelsonAalenFitter().fit(T, E).plot(ax=ax, ci_show=False)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Bounded lifetimes using the beta distribution\n",
"\n",
"Maybe your data is bounded between 0 and some (unknown) upperbound M? That is, lifetimes can't be more than M. Maybe you know M, maybe you don't."
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"n = 100\n",
"T = 5 * np.random.random(n)**2\n",
"T_censor = 10 * np.random.random(n)**2\n",
"E = T < T_censor\n",
"T_obs = np.minimum(T, T_censor)\n"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"from autograd_gamma import betainc\n",
"\n",
"class BetaFitter(ParametricUnivariateFitter):\n",
" _fitted_parameter_names = ['alpha_', 'beta_', \"m_\"]\n",
" _bounds = [(0, None), (0, None), (T.max(), None)]\n",
" \n",
" def _cumulative_density(self, params, times):\n",
" alpha_, beta_, m_ = params\n",
" return betainc(alpha_, beta_, times / m_)\n",
"\n",
" def _cumulative_hazard(self, params, times):\n",
" return -np.log(1-self._cumulative_density(params, times))"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/camerondavidson-pilon/code/lifelines/lifelines/fitters/__init__.py:936: StatisticalWarning: The diagonal of the variance_matrix_ has negative values. This could be a problem with BetaFitter's fit to the data.\n",
"\n",
"It's advisable to not trust the variances reported, and to be suspicious of the\n",
"fitted parameters too. Perform plots of the cumulative hazard to help understand\n",
"the latter's bias.\n",
"\n",
"To fix this, try specifying an `initial_point` kwarg in `fit`.\n",
"\n",
" warnings.warn(warning_text, utils.StatisticalWarning)\n",
"/Users/camerondavidson-pilon/code/lifelines/lifelines/fitters/__init__.py:460: RuntimeWarning: invalid value encountered in sqrt\n",
" np.einsum(\"nj,jk,nk->n\", gradient_at_times.T, self.variance_matrix_, gradient_at_times.T)\n"
]
},
{
"data": {
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model
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lifelines.BetaFitter
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number of observations
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100
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number of events observed
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log-likelihood
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hypothesis
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alpha_ != 1, beta_ != 1, m_ != 5.92869
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""
]
},
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\n",
"text/plain": [
""
]
},
"metadata": {
"image/png": {
"height": 251,
"width": 372
},
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"beta_fitter = BetaFitter().fit(T_obs, E)\n",
"beta_fitter.plot()\n",
"beta_fitter.print_summary()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Discrete survival models\n",
"\n",
"So far we have only been investigating continous time survival models, where times can take on any positive value. If we want to consider discrete survival times (for example, over the positive integers), we need to make a small adjustment. With discrete survival models, there is a slightly more complicated relationship between the hazard and cumulative hazard. This is because there are two ways to define the cumulative hazard. \n",
"\n",
"$$H_1(t) = \\sum_i^t h(t_i) $$ \n",
"\n",
"$$H_2(t) = -\\log(S(t))$$\n",
"\n",
"We also no longer have the relationship that $h(t) = \\frac{d H(t)}{dt}$, since $t$ is no longer continous. Instead, depending on which verion of the cumulative hazard you choose to use (inference will be the same), we have to redefine the hazard function in *lifelines*. \n",
"\n",
"$$ h(t) = H_1(t) - H_1(t-1) $$\n",
"$$ h(t) = 1 - \\exp(H_2(t) - H_2(t+1)) $$\n",
"\n",
"[Here is an example](https://stats.stackexchange.com/questions/417303/what-is-the-likelihood-for-this-process) of a discrete survival model, that may not look like a survival model at first, where we use a redefined `_hazard` function. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Looking for more examples of what you can build? See other unique survival models in the docs on [time-lagged survival](Modelling time-lagged conversion rates.ipynb)"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.7.3"
}
},
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"nbformat_minor": 2
}