"
],
"text/plain": [
" 0 1 2 3 4 \\\n",
"Stroke type \n",
"pre_stroke_nlvo 0.582881 0.745419 0.848859 0.951082 0.993055 \n",
"pre_stroke_nlvo_ivt_deaths 0.576469 0.737219 0.839522 0.940620 0.982131 \n",
"pre_stroke_lvo 0.417894 0.560853 0.679283 0.843494 0.957269 \n",
"pre_stroke_lvo_ivt_deaths 0.403644 0.541728 0.656119 0.814731 0.924626 \n",
"pre_stroke_lvo_mt_deaths 0.401178 0.538419 0.652112 0.809754 0.918978 \n",
"no_treatment_nlvo 0.197144 0.460000 0.580032 0.707768 0.855677 \n",
"no_effect_nlvo_ivt_deaths 0.197271 0.460000 0.577583 0.702252 0.845244 \n",
"t0_treatment_nlvo_ivt 0.429808 0.630000 0.738212 0.848427 0.929188 \n",
"no_treatment_lvo 0.050000 0.129000 0.265000 0.429000 0.676000 \n",
"no_effect_lvo_ivt_deaths 0.047898 0.123576 0.253858 0.410962 0.647576 \n",
"no_effect_lvo_mt_deaths 0.047534 0.122637 0.251930 0.407841 0.642658 \n",
"t0_treatment_lvo_ivt 0.112916 0.200000 0.327377 0.484757 0.698212 \n",
"t0_treatment_lvo_mt 0.312767 0.434474 0.552066 0.709276 0.849898 \n",
"\n",
" 5 6 \n",
"Stroke type \n",
"pre_stroke_nlvo 1.000000 1.0 \n",
"pre_stroke_nlvo_ivt_deaths 0.989000 1.0 \n",
"pre_stroke_lvo 1.000000 1.0 \n",
"pre_stroke_lvo_ivt_deaths 0.965900 1.0 \n",
"pre_stroke_lvo_mt_deaths 0.960000 1.0 \n",
"no_treatment_nlvo 0.917702 1.0 \n",
"no_effect_nlvo_ivt_deaths 0.904454 1.0 \n",
"t0_treatment_nlvo_ivt 0.956300 1.0 \n",
"no_treatment_lvo 0.811000 1.0 \n",
"no_effect_lvo_ivt_deaths 0.776900 1.0 \n",
"no_effect_lvo_mt_deaths 0.771000 1.0 \n",
"t0_treatment_lvo_ivt 0.811443 1.0 \n",
"t0_treatment_lvo_mt 0.912750 1.0 "
]
},
"execution_count": 19,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mrs_cprob_all = pd.read_csv(\n",
" './outcome_utilities/mrs_dist_probs_cumsum.csv', index_col='Stroke type')\n",
"\n",
"mrs_cprob_all"
]
},
{
"cell_type": "markdown",
"id": "845665ac-869f-48e9-950d-ae758d7b333d",
"metadata": {},
"source": [
"Pick out these values for the examples here:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "b0c44d22-0ae3-4a7c-a404-7d4c31acf2f1",
"metadata": {},
"outputs": [],
"source": [
"A = df_constants['lvo_mt_A']\n",
"b = df_constants['lvo_mt_b']"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "22708609-d08f-4406-a623-800234a60151",
"metadata": {},
"outputs": [],
"source": [
"mRS_prob_cumsum_t0_treatment = mrs_cprob_all.loc['t0_treatment_lvo_mt'].values\n",
"mRS_prob_cumsum_no_effect = mrs_cprob_all.loc['no_effect_lvo_mt_deaths'].values"
]
},
{
"cell_type": "markdown",
"id": "9336991d-1dc7-4904-bdbb-8a0dbf7e1bdb",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"## Why do the probability lines bend differently?"
]
},
{
"cell_type": "markdown",
"id": "cd8c6f4f-48a5-410a-bfe7-5edf7a3f6c72",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"In the graph of probability with time, the lines for each mRS follow a different path. The gradient of the bottom mRS$\\leq$0 line becomes less negative with increasing time, as though gradually curving upwards, whereas the top mRS$\\leq$4 line has a gradient becoming more negative with time, as though curving downwards. \n",
"\n",
"The reason for this is best explained by showing a similar line, another logistic function, with a new parameter $v=-b(t+\\frac{A}{b})$, so \n",
"\n",
"$$ P(v) = \\frac{1}{1+e^{v}} $$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "64d8c628-9a21-4e7f-9dae-e3484a090d60",
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Define some new parameter \"v\" for the x-axis:\n",
"v = np.linspace(-4,4,100)\n",
"\n",
"# Add a couple of key lines:\n",
"plt.axhline(0.5,color='Gainsboro')\n",
"plt.axvline(0.0,color='Gainsboro')\n",
"\n",
"# Plot probability as a function of \"v\":\n",
"p_v = 1.0/(1.0+np.exp(v))\n",
"plt.plot(v,p_v)\n",
"\n",
"# Draw the straight line connection:\n",
"plt.plot([v[0],v[-1]], [p_v[0],p_v[-1]],\n",
" color='k',linestyle=':')\n",
"\n",
"# The usual setup:\n",
"plt.ylabel('P(v)')\n",
"plt.xlabel('v')\n",
"plt.title('Probability', fontsize=15)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "195f7320-eb7c-44e3-b8b3-40318a4a0ba7",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"The bend of $P(v)$ changes at $v=0$, where $P(v)=0.5$. The $P(\\mathrm{mRS})$ lines are different shapes because some of them show mostly the $v>0$ curve (i.e. mRS=0,1), and the rest the $v<0$ part (i.e. mRS$\\geq$2). This can be viewed as the $v$-axis here being offset to the right in the $P(t)$ plots above. The size of the offset is different for each mRS line.\n",
"\n",
"The find the offset, we can convert from $v$ to $t$. Because $v=-b(t+\\frac{A}{b}) =-(A+bt)$, then $t=-\\frac{1}{b}(v+A)$. On the $t$-axis, the key point corresponding to $v=0$ is $t_k=-\\frac{A}{b}$. This $t_k$ is different for each of the mRS lines, which is why each $P(t)$ line shows a different shift sideways from $P(v)$. \n",
"\n",
"We can plot the $P(t)$ lines again and add the key points where the bend changes:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "24ff7218-312e-4a76-9b90-65107bf71726",
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t = np.arange(0,t_ne+0.1,0.1)\n",
"t_long = np.arange(-6, t_ne+12)\n",
"\n",
"# Store the key times t_k in this list:\n",
"tk_list = []\n",
"\n",
"# Use a wider figure than usual:\n",
"plt.figure(figsize=(10,5))\n",
"for i,A_i in enumerate(A): \n",
" # Plot probability:\n",
" p_i = np.exp(A_i + b[i]*t)/(1+np.exp(A_i + b[i]*t))\n",
" l, = plt.plot(t, p_i, '-', label = f'mRS <= {i}')\n",
" colour = l.get_color()\n",
" \n",
" # Plot probability over the longer time range:\n",
" p_long = np.exp(A_i + b[i]*t_long)/(1+np.exp(A_i + b[i]*t_long))\n",
" plt.plot(t_long, p_long, color=colour, linestyle=':')\n",
" \n",
" # Mark t=0 and t=t_ne data:\n",
" plt.scatter(0, mRS_prob_cumsum_t0_treatment[i], color=colour)\n",
" plt.scatter(t_ne, mRS_prob_cumsum_no_effect[i], color=colour)\n",
" \n",
" # Calculate the key time and store it:\n",
" t_k = -A_i/b[i]\n",
" tk_list.append(t_k)\n",
" plt.scatter(t_k, np.exp(A_i + b[i]*t_k)/(1+np.exp(A_i + b[i]*t_k)),\n",
" facecolor=colour, edgecolor='k', \n",
" marker='X', s=70, zorder=3)\n",
" \n",
"# # Add vertical lines at valid time boundaries:\n",
"# for v_pos in [0.0, t_ne]:\n",
"# plt.axvline(v_pos, lw=1, color='Gainsboro', zorder=0)\n",
" \n",
"# Add a horizontal line at P=0.5:\n",
"plt.axhline(0.5, lw=1, color='k', zorder=0)\n",
"\n",
"# The usual setup:\n",
"plt.ylim(0,1)\n",
"plt.ylabel('Probability')\n",
"plt.xlabel('Onset to treatment time (hours)')\n",
"plt.legend(loc='best')\n",
"plt.title('Probability', fontsize=15)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "1e75ed6d-af91-45f2-9b5e-91639b4bde91",
"metadata": {
"pycharm": {
"name": "#%% md\n"
}
},
"source": [
"Note that the scattered points above at $t=t_k$ all share a probability $P(t=t_k)=0.5$.\n",
"\n",
"Print the key times:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "b4a179aa-8c46-40a5-bc0a-a690323ab2c4",
"metadata": {
"pycharm": {
"name": "#%%\n"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mRS | Key time\n",
" 0 | -2 hours 51 mins\n",
" 1 | -1 hours 14 mins\n",
" 2 | 1 hours 17 mins\n",
" 3 | 5 hours 38 mins\n",
" 4 | 12 hours 6 mins\n",
" 5 | 16 hours 34 mins\n"
]
}
],
"source": [
"print('mRS | Key time')\n",
"for i in range(6):\n",
" print(f' {i} | {int(tk_list[i]):2.0f} hours '+\n",
" f'{np.abs(np.array(tk_list[i]))%1 *60.0:2.0f} mins')"
]
},
{
"cell_type": "markdown",
"id": "8d65acef-b5a7-49f6-b8b3-be5fa2d457f5",
"metadata": {},
"source": [
"## What do $A$ and $b$ mean for probability?"
]
},
{
"cell_type": "markdown",
"id": "f4d635c6-4128-4a38-ac7f-b88a34cd2f2f",
"metadata": {},
"source": [
"We have defined probability as a logistic function:\n",
"\n",
"$$ P = \\frac{1}{1+e^{-b\\left(t +\\frac{A}{b}\\right)}} $$\n",
"\n",
"Changing _A_ and _b_ then changes the slope of the function and its offset left and right. "
]
},
{
"cell_type": "markdown",
"id": "c7112411-85c0-46eb-8e42-3cb260aae271",
"metadata": {},
"source": [
"To see these changes, we'll plot a logistic function with an arbitrary _A_ and _b_:"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "47269d5c-ffc1-4712-a2a7-e8ee9fa125c0",
"metadata": {},
"outputs": [],
"source": [
"A_start = -0.91 \n",
"b_start = -0.5"
]
},
{
"cell_type": "markdown",
"id": "4bf5aeb1-64b1-4c90-ac3b-d05b556f3fd5",
"metadata": {},
"source": [
"And compare it with probability data $P(\\mathrm{mRS}\\leq \\mathrm{mRS}_x)$ for this value of mRS$_x$ where we know the target values of _A_ and _b_:"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "4adbb75f-4b11-4873-8b45-e52c8d67b973",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.8918699522503979 -0.1580959999968494\n"
]
}
],
"source": [
"mRS_x = 3\n",
"\n",
"A_target = A[mRS_x]\n",
"b_target = b[mRS_x]\n",
"\n",
"print(A_target, b_target)"
]
},
{
"cell_type": "markdown",
"id": "12d80ea7-2607-4493-a4ed-4d43fe0e3424",
"metadata": {},
"source": [
"We'll also plot over this time range, which is longer than usual: "
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "b0f91114-69ca-42aa-9a21-5f627bedd958",
"metadata": {},
"outputs": [],
"source": [
"t = np.arange(-t_ne-0.1,t_ne+0.1,0.1)"
]
},
{
"cell_type": "markdown",
"id": "089e997f-f492-4fc1-b8a9-0b7ddc2b999e",
"metadata": {},
"source": [
"To save repeating some code, we'll put the plot setup into this function: "
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "e34220a9-cd36-4909-b76f-11d0eacbe139",
"metadata": {},
"outputs": [],
"source": [
"def plot_probs_logistic():\n",
" # Mark the central point of the standard logistic function:\n",
" plt.axvline(0.0, color='k', lw=1)\n",
" plt.axhline(0.5, color='k', lw=1)\n",
"\n",
" # Plot the two known data points for this mRS:\n",
" plt.scatter([0.0,t_ne], \n",
" [mRS_prob_cumsum_t0_treatment[mRS_x],\n",
" mRS_prob_cumsum_no_effect[mRS_x]], \n",
" label='Data', zorder=3)\n",
"\n",
" # The usual setup:\n",
" plt.ylim(0.0,1.0)\n",
" plt.ylabel('P(t)')\n",
" plt.xlabel('t (hours)')\n",
" plt.title('Probability', fontsize=15)"
]
},
{
"cell_type": "markdown",
"id": "f2f188ca-a6e2-41d3-a5cc-9d925e6f93ac",
"metadata": {},
"source": [
"First, we'll plot the effect of changing _A_. At time zero, $ P(t=0) = \\frac{1}{1+e^{-A}} $ so _A_ adjusts the x-offset of the curve. We can show this by plotting a series of curves where everything is identical except for _A_:"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "63c38e9e-b6b4-43fd-b90f-bc072396c0b6",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_probs_logistic()\n",
"\n",
"# Plot lines for this many values of A...\n",
"n_lines = 5\n",
"# ... in these colours:\n",
"colours = plt.get_cmap('viridis')(np.linspace(0,1,n_lines))\n",
"\n",
"# Plot probability as a function of time:\n",
"for i,A_line in enumerate(np.linspace(A_start, A_target, n_lines)):\n",
" p_t = 1.0/(1.0+np.exp(-b_start * (t + A_line/b_start)) )\n",
" plt.plot(t,p_t, color=colours[i], label=f'A = {A_line:1.2f}')\n",
"\n",
"plt.legend(bbox_to_anchor=[1.0,0.5,0.2,0.2]) # outside axis\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "f93a5bd5-b55c-4d57-9f48-46643dd5871a",
"metadata": {},
"source": [
"For the palest line, changing _A_ has fixed the probability line in the right spot at time zero. However, the line is currently nowhere near the data point at the no-effect time. To fix this, we have to change the value of _b_. \n",
"\n",
"Changing _b_ effectively changes two things simultaneously. It changes the slope of the line, so that the logistic function looks more flattened out or stretched tall. But since _b_ cannot change the value of the probability at time zero, changing _b_ must also move the probability line left or right to account for the changes. This is seen in the following plot, where every parameter of each curve is identical except for _b_. The palest yellow line is the same as in the previous plot."
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "f66f2b34-5eb0-4865-a909-68626c993238",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plot_probs_logistic()\n",
"\n",
"# Plot lines for this many values of b...\n",
"n_lines = 5\n",
"# ... in these colours:\n",
"colours = plt.get_cmap('viridis')(np.linspace(0,1,n_lines)[::-1])\n",
"\n",
"for i,b_line in enumerate(np.linspace(b_start, b_target, n_lines)):\n",
" # Plot probability as a function of time:\n",
" p_t = 1.0/(1.0+np.exp(-b_line * (t + A_target/b_line)) )\n",
" plt.plot(t,p_t, color=colours[i], label=f'b = {b_line:1.4f}')\n",
"\n",
"plt.legend(bbox_to_anchor=[1.0,0.5,0.2,0.2]) # outside axis\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "15205857-e828-4d8d-bd5c-ad725fab7ba0",
"metadata": {},
"source": [
"Each line has a different slope because of the changed _b_, but also a different x-offset - the lines cross $P(t)=0.5$ at different times. The darkest line uses the only combination of _A_ and _b_ that will pass through both data points simultaneously. "
]
},
{
"cell_type": "markdown",
"id": "56f97b84-7fd3-4355-9a67-53f53ae05c1a",
"metadata": {},
"source": [
"Since our calculated $P(\\mathrm{mRS})$ lines all use different values of _A_ and _b_, we end up plotting each line with a different slope and x-offset."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "41684fad-ab8d-4ab7-a76a-6f05c1638ceb",
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