{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Section 4. from \"Piecewise exponential models for survival data with covariates\" by Michael Friedman"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"from lifelines.datasets import load_lupus\n",
"\n",
"df = load_lupus()\n",
"\n",
"# preprocessing\n",
"T_col = 'time_between_diagnosis_and_last_observation_(years)'\n",
"E_col = 'dead'\n",
"df['time_elapsed_between_estimated_onset_and_diagnosis_binary'] = df['time_elapsed_between_estimated_onset_and_diagnosis_(months)'] <= 2*12\n",
"df['recent'] = df['year_month_of_diagnosis'] < '1951-07'\n",
"\n",
"columns = ['is_male', 'is_white', \n",
" 'age_at_diagnosis', \n",
" 'time_elapsed_between_estimated_onset_and_diagnosis_binary',\n",
" 'recent'] + [T_col, E_col]\n",
"\n",
"df = df[columns]\n",
"df = df.dropna() # drop the individual with NaN\n",
"\n",
"# these models can naturally handle 0 durations, so we fudge a bit.\n",
"df.loc[df[T_col] == 0, T_col] = 0.000001\n",
"# add a constant column (only needed for non-Cox models.)\n",
"df['constant'] = 1.\n"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"from lifelines import PiecewiseExponentialRegressionFitter, CoxPHFitter\n",
"\n",
"\n",
"breakpoints = [\n",
" [0.5, 0.8, 1.1, 1.7, 2.5, 3.1], \n",
" [0.3, 0.8, 1.0, 2.0, 3.0],\n",
" [0.4, 0.9, 1.5, 2.5],\n",
" [0.3, 1.0, 2.0, 3.0],\n",
" [0.4],\n",
" [0.3]\n",
"]\n",
"\n",
"results = dict()\n",
"for i, bp in enumerate(breakpoints, start=1):\n",
" # by forcing the penalizer to be 1000, the coefs between periods are constrainted to be identical. \n",
" pcf = PiecewiseExponentialRegressionFitter(penalizer=1000., breakpoints=bp)\n",
" pcf.fit(df, T_col, E_col)\n",
" # Note the negative sign. We use a different parameterization than the paper.\n",
" results[\"model %d\" % i] = -pcf.params_['lambda_0_'].drop('constant')\n",
" \n",
"cph = CoxPHFitter().fit(df.drop('constant', axis=1), T_col, E_col)\n",
"results['Cox'] = cph.params_"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"results = pd.DataFrame(results).T"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" is_male | \n",
" is_white | \n",
" age_at_diagnosis | \n",
" time_elapsed_between_estimated_onset_and_diagnosis_binary | \n",
" recent | \n",
"
\n",
" \n",
" \n",
" \n",
" | model 1 | \n",
" -0.454013 | \n",
" -0.660882 | \n",
" 0.001334 | \n",
" 0.472303 | \n",
" 1.096200 | \n",
"
\n",
" \n",
" | model 2 | \n",
" -0.449296 | \n",
" -0.664789 | \n",
" 0.001070 | \n",
" 0.435175 | \n",
" 1.174195 | \n",
"
\n",
" \n",
" | model 3 | \n",
" -0.415715 | \n",
" -0.667667 | \n",
" 0.000182 | \n",
" 0.497052 | \n",
" 1.086471 | \n",
"
\n",
" \n",
" | model 4 | \n",
" -0.423635 | \n",
" -0.637827 | \n",
" 0.001707 | \n",
" 0.409149 | \n",
" 1.247443 | \n",
"
\n",
" \n",
" | model 5 | \n",
" -0.455248 | \n",
" -0.647714 | \n",
" 0.001018 | \n",
" 0.462002 | \n",
" 1.145437 | \n",
"
\n",
" \n",
" | model 6 | \n",
" -0.445260 | \n",
" -0.638205 | \n",
" 0.001007 | \n",
" 0.456981 | \n",
" 1.189638 | \n",
"
\n",
" \n",
" | Cox | \n",
" -0.444981 | \n",
" -0.619252 | \n",
" 0.000664 | \n",
" 0.475423 | \n",
" 1.144530 | \n",
"
\n",
" \n",
"
\n",
"