Hospital Readmissions Data Analysis and Recommendations for Reduction

Background

In October 2012, the US government's Center for Medicare and Medicaid Services (CMS) began reducing Medicare payments for Inpatient Prospective Payment System hospitals with excess readmissions. Excess readmissions are measured by a ratio, by dividing a hospital’s number of “predicted” 30-day readmissions for heart attack, heart failure, and pneumonia by the number that would be “expected,” based on an average hospital with similar patients. A ratio greater than 1 indicates excess readmissions.

Exercise Directions

In this exercise, you will:

critique a preliminary analysis of readmissions data and recommendations (provided below) for reducing the readmissions rate
construct a statistically sound analysis and make recommendations of your own

More instructions provided below. Include your work in this notebook and submit to your Github account.

Resources

Data source: https://data.medicare.gov/Hospital-Compare/Hospital-Readmission-Reduction/9n3s-kdb3
More information: http://www.cms.gov/Medicare/medicare-fee-for-service-payment/acuteinpatientPPS/readmissions-reduction-program.html
Markdown syntax: http://nestacms.com/docs/creating-content/markdown-cheat-sheet



In [32]:

    
%matplotlib inline

import pandas as pd
from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
import bokeh.plotting as bkp
from mpl_toolkits.axes_grid1 import make_axes_locatable



In [2]:

    
# read in readmissions data provided
hospital_read_df = pd.read_csv('data/cms_hospital_readmissions.csv')

Preliminary Analysis



In [3]:

    
# deal with missing and inconvenient portions of data 
clean_hospital_read_df = hospital_read_df[hospital_read_df['Number of Discharges'] != 'Not Available']
clean_hospital_read_df.loc[:, 'Number of Discharges'] = clean_hospital_read_df['Number of Discharges'].astype(int)
clean_hospital_read_df = clean_hospital_read_df.sort_values('Number of Discharges')









    



/Users/RyaniMac/anaconda/lib/python2.7/site-packages/pandas/core/indexing.py:517: SettingWithCopyWarning: 
A value is trying to be set on a copy of a slice from a DataFrame.
Try using .loc[row_indexer,col_indexer] = value instead

See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/indexing.html#indexing-view-versus-copy
  self.obj[item] = s



In [4]:

    
# generate a scatterplot for number of discharges vs. excess rate of readmissions
# lists work better with matplotlib scatterplot function
x = [a for a in clean_hospital_read_df['Number of Discharges'][81:-3]]
y = list(clean_hospital_read_df['Excess Readmission Ratio'][81:-3])

fig, ax = plt.subplots(figsize=(8,5))
ax.scatter(x, y,alpha=0.2)

ax.fill_between([0,350], 1.15, 2, facecolor='red', alpha = .15, interpolate=True)
ax.fill_between([800,2500], .5, .95, facecolor='green', alpha = .15, interpolate=True)

ax.set_xlim([0, max(x)])
ax.set_xlabel('Number of discharges', fontsize=12)
ax.set_ylabel('Excess rate of readmissions', fontsize=12)
ax.set_title('Scatterplot of number of discharges vs. excess rate of readmissions', fontsize=14)

ax.grid(True)
fig.tight_layout()

Preliminary Report

Read the following results/report. While you are reading it, think about if the conclusions are correct, incorrect, misleading or unfounded. Think about what you would change or what additional analyses you would perform.

A. Initial observations based on the plot above

Overall, rate of readmissions is trending down with increasing number of discharges
With lower number of discharges, there is a greater incidence of excess rate of readmissions (area shaded red)
With higher number of discharges, there is a greater incidence of lower rates of readmissions (area shaded green)

B. Statistics

In hospitals/facilities with number of discharges < 100, mean excess readmission rate is 1.023 and 63% have excess readmission rate greater than 1
In hospitals/facilities with number of discharges > 1000, mean excess readmission rate is 0.978 and 44% have excess readmission rate greater than 1

C. Conclusions

There is a significant correlation between hospital capacity (number of discharges) and readmission rates.
Smaller hospitals/facilities may be lacking necessary resources to ensure quality care and prevent complications that lead to readmissions.

D. Regulatory policy recommendations

Hospitals/facilties with small capacity (< 300) should be required to demonstrate upgraded resource allocation for quality care to continue operation.
Directives and incentives should be provided for consolidation of hospitals and facilities to have a smaller number of them with higher capacity and number of discharges.



In [28]:

    
# A. Do you agree with the above analysis and recommendations? Why or why not?
import seaborn as sns

relevant_columns = clean_hospital_read_df[['Excess Readmission Ratio', 'Number of Discharges']][81:-3]

sns.regplot(relevant_columns['Number of Discharges'], relevant_columns['Excess Readmission Ratio'])









    Out[28]:





<matplotlib.axes._subplots.AxesSubplot at 0x114a2aa50>

Exercise

Include your work on the following in this notebook and submit to your Github account.

A. Do you agree with the above analysis and recommendations? Why or why not?

B. Provide support for your arguments and your own recommendations with a statistically sound analysis:

Setup an appropriate hypothesis test.
Compute and report the observed significance value (or p-value).
Report statistical significance for $\alpha$ = .01.
Discuss statistical significance and practical significance. Do they differ here? How does this change your recommendation to the client?
Look at the scatterplot above.
- What are the advantages and disadvantages of using this plot to convey information?
- Construct another plot that conveys the same information in a more direct manner.

You can compose in notebook cells using Markdown:

In the control panel at the top, choose Cell > Cell Type > Markdown
Markdown syntax: http://nestacms.com/docs/creating-content/markdown-cheat-sheet </div>

Overall, rate of readmissions is trending down with increasing number of discharges
- Agree, according to regression trend line shown above
With lower number of discharges, there is a greater incidence of excess rate of readmissions (area shaded red)
- Agree
With higher number of discharges, there is a greater incidence of lower rates of readmissions (area shaded green)
- Agree



In [43]:

    
rv =relevant_columns
print rv[rv['Number of Discharges'] < 100][['Excess Readmission Ratio']].mean()

print '\nPercent of subset with excess readmission rate > 1: ', len(rv[(rv['Number of Discharges'] < 100) & (rv['Excess Readmission Ratio'] > 1)]) / len(rv[relevant_columns['Number of Discharges'] < 100])

print '\n', rv[rv['Number of Discharges'] > 1000][['Excess Readmission Ratio']].mean()
print '\nPercent of subset with excess readmission rate > 1: ', len(rv[(rv['Number of Discharges'] > 1000) & (rv['Excess Readmission Ratio'] > 1)]) / len(rv[relevant_columns['Number of Discharges'] > 1000])









    



Excess Readmission Ratio    1.022618
dtype: float64

Percent of subset with excess readmission rate > 1:  0.632154882155

Excess Readmission Ratio    0.979073
dtype: float64

Percent of subset with excess readmission rate > 1:  0.445652173913

In hospitals/facilities with number of discharges < 100, mean excess readmission rate is 1.023 and 63% have excess readmission rate greater than 1
- Accurate
In hospitals/facilities with number of discharges > 1000, mean excess readmission rate is 0.978 and 44% have excess readmission rate greater than 1
- Correction: mean excess readmission rate is 0.979, and 44.565% have excess readmission rate > 1



In [47]:

    
np.corrcoef(rv['Number of Discharges'], rv['Excess Readmission Ratio'])









    Out[47]:





array([[ 1.        , -0.09309554],
       [-0.09309554,  1.        ]])

There is a significant correlation between hospital capacity (number of discharges) and readmission rates.
- The correlation coefficient shows a very, very weak correlation between the two variables. More evidence needed to establish a correlation.

Smaller hospitals/facilities may be lacking necessary resources to ensure quality care and prevent complications that lead to readmissions.
- More evidence needed to asses the veracity of this statement.



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