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Merge pull request #14 from pythonhealthdatascience/init
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‎content/14_initial_conditions.ipynb‎

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@@ -5,20 +5,39 @@
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"id": "0be7dabf-cb34-4faf-abb1-e2c8e735beda",
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"metadata": {},
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"source": [
8-
"# Setting initial conditions\n",
8+
"# Setting Initial Conditions\n",
99
"\n",
10+
"An alternative to including a warm-up period in a model is to set initial conditions. In our stroke example this would mean adding patients to beds and if required the admission queue. \n",
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"\n",
11-
"**IMPORTANT: There is still an initialisation bias problem:**\n",
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"🎓 **Why use Initial-Conditions over a Warm-Up?**\n",
13+
"\n",
14+
"* While warm-up periods are simpler to code, they can also increase how long it takes to run your model. Setting initial conditions is in theory computationally more efficient (no wasted run-time).\n",
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"\n",
16+
"* Setting initial-conditions also allows you to test specific starting scenarios, such as \"What happens if the day begins with a full ward?\"\n",
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"\n",
18+
"**In general, adding initial conditions is more complex than including a warm-up period.**\n",
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"\n",
20+
"Initial conditions could be \n",
21+
"\n",
22+
"1. Fixed i.e. the same number of patients for each replication.\n",
23+
"2. Random i.e. sampled from a discrete distribution specified by a user.\n",
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"\n",
25+
"In this notebook we will learn how to add initial conditions to a SimPy model. We will again use the acute stroke pathway model from the warm-up example notebook. Our initial conditions approach will load stroke patients to the queue before the simulation begins.\n",
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"\n",
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"<img src=\"img/acute_stroke_pathway.png\" alt=\"stroke pathway\" width=\"400\"/>\n",
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"\n",
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"\n",
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"## IMPORTANT: There is still an initialisation bias problem\n",
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"\n",
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"* We load patients into the model before we begin the run. \n",
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"* If there are $n$ acute stroke beds then the first $n$ patients loaded into the queue will begin service immediately and have a zero queuing time.\n",
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"* This applies if we have one queue in the model or if we have multiple queues and activities: the time in system metrics will be biased for initial condition patients.\n",
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"* This is the same problem faced when starting the model from time zero with no patients.\n",
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"\n",
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"**Some Options:**\n",
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"* Include a setting in a process to switch results collection on and off.\n",
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"* Code a seperate process for initial conditions that does not include results collection.\n",
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"* Mixed initial conditions and (a shorter) warm-up period.\n",
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"1. Include a setting in a process to switch results collection on and off.\n",
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"2. Code a seperate process for initial conditions that does not include results collection.\n",
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"3. Mixed initial conditions and (a shorter) warm-up period.\n",
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" * You will need to do some analysis to ensure this is working acceptably.\n",
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" * The warm-up pushes patients into service and also resets results collection. (deletes an initial transient)."
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]
@@ -83,7 +102,7 @@
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"\n",
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"# Acute LoS (Lognormal)\n",
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"ACUTE_LOS_MEAN = 7.0\n",
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"ACUTE_LOC_STD = 1.0\n",
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"ACUTE_LOS_STD = 1.0\n",
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"\n",
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"# initial conditions for acute queue + service \n",
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"# if there are 9 beds then 10 = 1 queuing\n",
@@ -93,11 +112,12 @@
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"\n",
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"INIT_COND_PARAMS = {\n",
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" \"mode\": \"fixed\",\n",
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" \"fixed\": 8,\n",
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" \"fixed\": 10,\n",
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" \"rnd\": {\n",
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" \"values\":[8, 9, 10, 11, 12, 13],\n",
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" \"freq\":[25, 25, 2, 1, 1, 1]\n",
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" }\n",
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" \"freq\":[15, 15, 25, 20, 5, 5]\n",
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" },\n",
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" \"collect_results\": False\n",
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"}\n",
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" \n",
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"# sampling settings\n",
@@ -129,7 +149,7 @@
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"source": [
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"def trace(msg):\n",
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" \"\"\"\n",
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" Turing printing of events on and off.\n",
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" Turning printing of events on and off.\n",
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"\n",
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" Params:\n",
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" -------\n",
@@ -159,14 +179,17 @@
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" \"\"\"\n",
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" Encapsulates the concept of an experiment 🧪 for the stroke pathway\n",
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" bed blocking simulator. Manages parameters, PRNG streams and results.\n",
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"\n",
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" There is a new parameter `init_cond_params` that stores the initial\n",
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" conditions to use in an experiment.\n",
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" \"\"\"\n",
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" def __init__(\n",
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" self,\n",
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" random_number_set=DEFAULT_RND_SET,\n",
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" n_streams=N_STREAMS,\n",
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" iat_strokes=IAT_STROKES,\n",
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" acute_los_mean=ACUTE_LOS_MEAN,\n",
169-
" acute_los_std=ACUTE_LOC_STD,\n",
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" acute_los_std=ACUTE_LOS_STD,\n",
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" n_acute_beds=N_ACUTE_BEDS,\n",
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" init_cond_params=INIT_COND_PARAMS, \n",
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" ):\n",
@@ -182,7 +205,7 @@
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" self.acute_los_mean = acute_los_mean\n",
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" self.acute_los_std = acute_los_std\n",
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"\n",
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" # stored initial conditions\n",
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" # ---- stored initial conditions -------\n",
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" self.init_cond_params = init_cond_params\n",
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"\n",
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" # place holder for resources\n",
@@ -198,8 +221,9 @@
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" def set_random_no_set(self, random_number_set):\n",
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" \"\"\"\n",
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" Controls the random sampling\n",
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" \n",
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" Parameters:\n",
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" ----------\n",
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" -----------\n",
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" random_number_set: int\n",
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" Used to control the set of pseudo random numbers used by\n",
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" the distributions in the simulation.\n",
@@ -231,12 +255,14 @@
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" self.init_conds = FixedDistribution(\n",
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" self.init_cond_params[\"fixed\"]\n",
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" )\n",
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" else:\n",
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" elif self.init_cond_params[\"mode\"] == \"rnd\":\n",
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" self.init_conds = DiscreteEmpirical(\n",
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" values = self.init_cond_params[\"rnd\"][\"values\"],\n",
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" freq = self.init_cond_params[\"rnd\"][\"freq\"],\n",
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" random_seed=self.seeds[2]\n",
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" )\n",
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" else:\n",
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" raise ValueError(\"Initial conditions mode must be 'fixed' or 'rnd'\")\n",
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" \n",
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"\n",
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" def init_results_variables(self):\n",
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" Parameters:\n",
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" ----------\n",
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" warm_up_period: float\n",
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" Duration of warm-up period in simultion time units\n",
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" Duration of warm-up period in simulation time units\n",
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"\n",
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" env: simpy.Environment\n",
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" The simpy environment\n",
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"\n",
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"The key things to recognise are \n",
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"\n",
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"* We include a optional parameter called `collection_results` that defaults to `True`. We may set this `False` in our functions that setup initial conditions"
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"* We include a optional parameter called `collect_results` that defaults to `True`. We may set this `False` in our functions that setup initial conditions"
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]
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},
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{
@@ -307,8 +333,7 @@
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"outputs": [],
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"source": [
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"def acute_stroke_pathway(patient_id, env, args, collect_results=True):\n",
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" \"\"\"Process a patient through the acute ward\n",
311-
" Simpy generator function.\n",
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" \"\"\"Process a patient through the acute ward. Simpy generator function.\n",
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" \n",
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" Parameters:\n",
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" -----------\n",
@@ -329,6 +354,7 @@
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" acute_admit_time = env.now\n",
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" wait_for_acute = acute_admit_time - arrival_time\n",
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"\n",
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" # used to avoid collecting stats from initial conditions...\n",
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" if collect_results:\n",
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" args.results['waiting_acute'].append(wait_for_acute)\n",
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" \n",
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"source": [
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"def setup_initial_conditions(\n",
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" env: simpy.Environment, \n",
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" args: Experiment,\n",
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" collect_results: bool = False,\n",
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" args: Experiment\n",
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"):\n",
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" \"\"\"Set up initial conditions with patients already in the acute\n",
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" stroke queue\n",
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" \"\"\"Set up initial conditions with patients already in the acute stroke queue\n",
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"\n",
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" Parmaters:\n",
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" ---------\n",
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" Parameters:\n",
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" -----------\n",
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" env: simpy.Environment\n",
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" The simpy environment for the simulation\n",
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"\n",
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" args: Experiment\n",
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" The settings and input parameters for the simulation.\n",
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"\n",
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" collect_results: bool, optional (default = False)#\n",
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" Should results be collected for initial conditions patients?\n",
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" \n",
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" The settings and input parameters for the simulation. \n",
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" \"\"\"\n",
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" # sample the no. patients to load into queue\n",
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" patients_to_load = args.init_conds.sample()\n",
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" trace(f\"Patient to load: {patients_to_load}\")\n",
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"\n",
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" # collect results or not?\n",
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" collect_results = args.init_cond_params[\"collect_results\"]\n",
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" \n",
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" for initial_id in range(1, patients_to_load+1):\n",
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" # Create patients with negative IDs to distinguish them as init cond.\n",
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" # we may or may not want collect results for initial conditions\n",
@@ -477,15 +501,19 @@
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" # simpy resources\n",
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" experiment.acute_ward = simpy.Resource(env, experiment.n_acute_beds)\n",
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"\n",
480-
" # load the acute stroke queue\n",
481-
" setup_initial_conditions(env, experiment)\n",
504+
" trace(\"--- Pre-Simulation Actions ---\")\n",
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"\n",
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" # schedule a warm_up period\n",
484507
" env.process(warmup_complete(wu_period, env, experiment))\n",
485508
" \n",
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" # load the acute stroke queue\n",
510+
" setup_initial_conditions(env, experiment)\n",
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" \n",
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" # we pass all arrival generators to simpy \n",
487513
" env.process(stroke_arrivals_generator(env, experiment))\n",
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"\n",
515+
" trace(\"--- Start Simulation ---\")\n",
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" \n",
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" # run model\n",
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" env.run(until=wu_period+rc_period)\n",
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"\n",
@@ -501,123 +529,47 @@
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"execution_count": null,
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"id": "caf52390-5455-4fa1-bb22-60b5b91ad8d0",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"0.00: Patient -1 loaded into queue\n",
513-
"0.00: Patient -2 loaded into queue\n",
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"0.00: Patient -3 loaded into queue\n",
515-
"0.00: Patient -4 loaded into queue\n",
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"0.00: Patient -5 loaded into queue\n",
517-
"0.00: Patient -6 loaded into queue\n",
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"0.00: Patient -7 loaded into queue\n",
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"0.00: Patient -8 loaded into queue\n",
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"0.00: Patient -9 loaded into queue\n",
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"0.00: Patient -10 loaded into queue\n",
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"0.00: Patient -1 admitted to acute ward.(waited 0.00 days)\n",
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"0.00: Patient -2 admitted to acute ward.(waited 0.00 days)\n",
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"0.00: Patient -3 admitted to acute ward.(waited 0.00 days)\n",
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"0.00: Patient -4 admitted to acute ward.(waited 0.00 days)\n",
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"0.00: Patient -5 admitted to acute ward.(waited 0.00 days)\n",
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"0.00: Patient -6 admitted to acute ward.(waited 0.00 days)\n",
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"0.00: Patient -7 admitted to acute ward.(waited 0.00 days)\n",
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"0.00: Patient -8 admitted to acute ward.(waited 0.00 days)\n",
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"0.00: Patient -9 admitted to acute ward.(waited 0.00 days)\n",
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"0.00: 🥵 Warm up complete.\n",
532-
"2.74: Patient 1. Stroke arrival.\n",
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"2.78: Patient 2. Stroke arrival.\n",
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"3.36: Patient 3. Stroke arrival.\n",
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"4.42: Patient 4. Stroke arrival.\n",
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"4.68: Patient 5. Stroke arrival.\n",
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"5.80: Patient -3 discharged.\n",
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"5.80: Patient -10 admitted to acute ward.(waited 5.80 days)\n",
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"5.80: Patient -8 discharged.\n",
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"5.80: Patient 1 admitted to acute ward.(waited 3.06 days)\n",
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"5.97: Patient 6. Stroke arrival.\n",
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"6.08: Patient -6 discharged.\n",
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"6.08: Patient 2 admitted to acute ward.(waited 3.30 days)\n",
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"6.22: Patient -7 discharged.\n",
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"6.22: Patient 3 admitted to acute ward.(waited 2.86 days)\n",
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"6.33: Patient 7. Stroke arrival.\n",
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"7.28: Patient 8. Stroke arrival.\n",
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"7.41: Patient -4 discharged.\n",
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"7.41: Patient 4 admitted to acute ward.(waited 2.99 days)\n",
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"7.43: Patient 9. Stroke arrival.\n",
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"7.55: Patient 10. Stroke arrival.\n",
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"7.94: Patient -5 discharged.\n",
553-
"7.94: Patient 5 admitted to acute ward.(waited 3.26 days)\n",
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"8.11: Patient -2 discharged.\n",
555-
"8.11: Patient 6 admitted to acute ward.(waited 2.14 days)\n",
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"8.26: Patient 11. Stroke arrival.\n",
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"8.42: Patient 12. Stroke arrival.\n",
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"8.68: Patient 13. Stroke arrival.\n",
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"8.72: Patient 14. Stroke arrival.\n",
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"8.82: Patient -9 discharged.\n",
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"8.82: Patient 7 admitted to acute ward.(waited 2.50 days)\n",
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"8.95: Patient 15. Stroke arrival.\n",
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"9.18: Patient 16. Stroke arrival.\n",
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"9.87: Patient -1 discharged.\n",
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"9.87: Patient 8 admitted to acute ward.(waited 2.58 days)\n",
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"9.92: Patient 17. Stroke arrival.\n"
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]
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},
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{
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"data": {
571-
"text/plain": [
572-
"{'mean_acute_wait': 2.8362718457918676}"
573-
]
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},
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"execution_count": 11,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"TRACE = True\n",
538+
"\n",
539+
"# settings dictionary\n",
582540
"init_cond_params = INIT_COND_PARAMS.copy()\n",
583541
"init_cond_params[\"mode\"] = \"fixed\"\n",
584542
"\n",
585-
"# uncomment to vary the fixed amount 10 = 1 in queue.\n",
543+
"# vary the fixed amount. Interpretation 10 = 1 in queue.\n",
586544
"init_cond_params[\"fixed\"] = 10\n",
587545
"\n",
546+
"# vary if we collect results from initial condition stroke patients\n",
547+
"init_cond_params[\"collect_results\"] = False\n",
548+
"\n",
549+
"# create experiment and pass in initial conditions\n",
588550
"experiment = Experiment(init_cond_params=init_cond_params)\n",
551+
"\n",
589552
"results = single_run(experiment, rep=1, wu_period=0.0, rc_period=10.0)\n",
590553
"results"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"execution_count": null,
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"id": "0aaef408-09ca-49e0-8d39-f4a088a4ef1b",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"{'n_arrivals': 17,\n",
603-
" 'waiting_acute': [3.0586175577655674,\n",
604-
" 3.303449502025928,\n",
605-
" 2.857579305401165,\n",
606-
" 2.9908615153438225,\n",
607-
" 3.2622390398417513,\n",
608-
" 2.136685286636955,\n",
609-
" 2.496306611009193,\n",
610-
" 2.58443594831056]}"
611-
]
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},
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"execution_count": 12,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"outputs": [],
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"source": [
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"experiment.results"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "9d5266e1-d8f3-4755-838b-89b9b416faef",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {

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