Reproducing in-text results 3 and 4

This notebook aims to reproduce in-text results 3 and 4 from Shoaib M, Ramamohan V. Simulation modeling and analysis of primary health center operations. SIMULATION 98(3):183-208. (2022). https://doi.org/10.1177/00375497211030931.

In-text result 3:

“…then considered a situation wherein the staff nurses require minimal intervention in childbirth cases. We assumed that in 50% of childbirth cases, staff nurses require no intervention by the doctor; require only one- third of the typical amount of intervention in 30% of cases, and require full intervention in the remaining 20% of cases. This led to a decrease of the doctor’s utilisation to 101% (a further decrease of approximately 1%), and an increase in the nurse’s utilisation to 40%.”

In-text result 4:

“..investigated the effect of stationing an additional doctor in the PHC. This yielded an average utilisation of well below 100% for each doctor.”

Parameters

This result starts with the doctor utilisation from Figure 2A which is over 100% when patient load is 170 (IAT 3) and appointment times are 5 minutes (mean 5, SD 1, boundary 2), and with admin assigned to the staff nurse rather than the doctor

The variants introduced are to reduce the doctor intervention during delivery so that:

• 50% delivery cases: no doctor
• 30% delivery cases: doctor but only one-third of typical intervention
• 20% delivery cases: doctor and full intervention

And adding an additional doctor.

Set up

# To run model
import PHC

# To import results and produce figures
from reproduction_helpers import process_results
import pandas as pd
import os

# To speed up run time
from multiprocessing import Pool

# Additional package to record runtime of this notebook
import time
start = time.time()

# Paths to save image files to
output_folder = '../outputs'
txt3 = os.path.join(output_folder, 'intext3.csv')
txt4 = os.path.join(output_folder, 'intext4.csv')

Run model

# Parameters used in both models
base_model = {
    'OPD_iat': 3,
    'rep_file': 'arr170',
    'mean': 5,
    'sd': 1,
    'consult_boundary_1': 2,
    'consult_boundary_2': 2
}

# Model variants
variants = [
    # Base case for in-text result 3 and 4
    {
        'rep_file': 'in34_normal.xls'
    },
    # Scenarios for in-text result 3
    {
        'admin_doc_to_staff': True,
        'rep_file': 'in3_admin.xls'
    },
    {
        'doctor_delivery_scenario': True,
        'rep_file': 'in3_delivery.xls'
    },
    {
        'doctor_delivery_scenario': True,
        'admin_doc_to_staff': True,
        'rep_file': 'in3_admin_delivery.xls'
    },
    # Scenarios for in-text result 4
    {
        'doc_cap': 3,
        'rep_file': 'in4_doctor.xls'
    },
    {
        'doc_cap': 3,
        'doctor_delivery_scenario': True,
        'admin_doc_to_staff': True,
        'rep_file': 'in4_admin_delivery_doctor.xls'
    },
]

# Combine dictionaries
dict_list = []
for var in variants:
    dict_list.append({**base_model, **var})

# Append 's_' to all items
for i, d in enumerate(dict_list):
    dict_list[i] = {f's_{k}': v for k, v in d.items()}

# View example
dict_list[0]

{'s_OPD_iat': 3,
 's_rep_file': 'in34_normal.xls',
 's_mean': 5,
 's_sd': 1,
 's_consult_boundary_1': 2,
 's_consult_boundary_2': 2}

# Wrapper function to allow input of dictionary with pool
def wrapper(d):
    return PHC.main(**d)

# Create a process pool that uses all CPUs
with Pool() as pool:
    # Run PHC.main() using each of inputs from config
    pool.map(wrapper, dict_list)

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Process results

data = process_results([i['s_rep_file'] for i in dict_list], xls=True)
data

	in34_normal	in3_admin	in3_delivery	in3_admin_delivery	in4_doctor	in4_admin_delivery_doctor
OPD patients	43965.100000	43965.100000	44063.100000	44063.100000	44026.000000	44088.300000
IPD patients	178.600000	178.600000	187.200000	187.200000	186.500000	187.300000
ANC patients	360.900000	360.900000	357.900000	357.900000	366.700000	361.900000
Del patients	373.300000	373.300000	365.500000	365.500000	367.500000	368.800000
OPD Q wt	6.936889	6.936889	6.643605	6.643605	0.542593	0.520176
Pharmacy Q wt	1.282328	1.282328	1.282265	1.282265	2.419622	2.442825
Lab Q wt	3.123766	3.123766	3.113023	3.113023	4.454260	4.524105
doc occ	1.141365	1.023434	1.131213	1.013403	0.761388	0.675327
Lab patient list	250794.800000	250794.800000	252130.800000	252130.800000	251894.800000	253860.600000
OPD q len	6.851667	6.851667	6.619829	6.619829	0.537120	0.514162
ipd occ	0.098000	0.098000	0.098000	0.098000	0.098000	0.097000
opd q len	0.812750	0.812750	0.779243	0.779243	0.063533	0.061060
pharmacy q len	0.149890	0.149890	0.150061	0.150061	0.282726	0.286158
lab q len	0.185814	0.185814	0.186597	0.186597	0.266636	0.272577
NCD occ	1.230139	1.230139	1.234149	1.234149	1.228365	1.235298
lab occ	0.728652	0.728652	0.735114	0.735114	0.730388	0.736550
pharm occ	0.853658	0.853658	0.855077	0.855077	0.853199	0.855696
staff nurse occ	0.325778	0.404399	0.323088	0.401629	0.323845	0.403779
del occ	0.285000	0.285000	0.286000	0.286000	0.286000	0.281000
del referred	62.200000	62.200000	55.800000	55.800000	56.100000	56.800000
ipd bed occ	0.093865	0.093865	0.095156	0.095156	0.095393	0.095193
prop_del_referred	0.166276	0.166276	0.152398	0.152398	0.152683	0.153875

def get_utilisation(df, index_name, new_name):
    '''
    Creates dataframe with columns for utilisation (for a given row) before and
    after scenario change.

    Parameters:
    -----------
    df : pandas DataFrame
        Results from across the replications
    index_name : string
        Name of row with utilisation data
    new_name : string
        To rename the utilisation row (e.g. doc occ -> doctor utilisation)

    Returns:
    --------
    util : pandas DataFrame
        Dataframe with three columns for utilisation before and after admin,
        and change in utilisation.
    '''
    # Get utilisation
    util = round(pd.DataFrame(df.loc[index_name]).T, 3)

    # Rename index
    util = util.rename_axis('Output')

    # Rename row
    util = util.rename({index_name: new_name})

    # Rename columns for clarity for readers
    util = util.rename({
        'in34_normal': 'Normal',
        'in3_delivery': 'Less delivery',
        'in3_admin': 'Less admin',
        'in3_admin_delivery': 'Less admin + less delivery',
        'in4_doctor': 'Extra doctor',
        'in4_admin_delivery_doctor': (
            'Extra doctor + less admin + less delivery')}, axis=1)

    return util

Get in-text result 3

# Get results for doctor utilisation and staff nurse utilisation
subset3 = data[['in34_normal', 'in3_delivery', 'in3_admin', 'in3_admin_delivery']]
util3 = pd.concat([
    get_utilisation(subset3, 'doc occ', 'Doctor utilisation'),
    get_utilisation(subset3, 'staff nurse occ', 'Staff nurse utilisation')])

# Save results and display results
util3.to_csv(txt3, index=True)
util3

	Normal	Less delivery	Less admin	Less admin + less delivery
Output
Doctor utilisation	1.141	1.131	1.023	1.013
Staff nurse utilisation	0.326	0.323	0.404	0.402

Get in-text result 4

# Get results for doctor utilisation and staff nurse utilisation
subset4 = data[['in34_normal', 'in4_doctor', 'in4_admin_delivery_doctor']]
util4 = get_utilisation(subset4, 'doc occ', 'Doctor utilisation')

# Save results and display results
util4.to_csv(txt4, index=True)
util4

	Normal	Extra doctor	Extra doctor + less admin + less delivery
Output
Doctor utilisation	1.141	0.761	0.675

Run time

# Find run time in seconds
end = time.time()
runtime = round(end-start)

# Display converted to minutes and seconds
print(f'Notebook run time: {runtime//60}m {runtime%60}s')

Notebook run time: 3m 7s