%matplotlib inline

import pandas as pd
import numpy as np
import scikits.bootstrap as bt  
import scipy
import math
import pylab
import matplotlib.pyplot as plt
import bokeh.plotting as bkp
from mpl_toolkits.axes_grid1 import make_axes_locatable

# read in readmissions data provided
hospital_read_df = pd.read_csv('data/cms_hospital_readmissions.csv')
hospital_read_df.head(2)

"""
Explanation: 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
End of explanation
"""


# 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')


# 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()

"""
Explanation: Preliminary Analysis
End of explanation
"""


#Collect the entries with non-zero 'Number of Discharges' and not-null 'Excess Readmission Ratio' 
df = clean_hospital_read_df.loc[clean_hospital_read_df ['Number of Discharges']!=0,]
df1 = df.loc[df['Excess Readmission Ratio'].notnull(),]

"""
Explanation: 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.
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
End of explanation
"""


plt.hist(small['Excess Readmission Ratio'], 50, normed=1, alpha = 0.7, label = 'Small Hospitals')
plt.hist(large['Excess Readmission Ratio'], 50, normed=1, alpha = 0.7, label = 'Large Hospitals')
plt.legend(loc='upper right')
plt.title('Normalized histograms of excess readmission ratio for small and large hospitals')
plt.show()

stats.probplot(small['Excess Readmission Ratio'], dist="norm", plot=pylab)
pylab.title('Probability plot for the excess readmission ratio of small hospitals')
pylab.show()

stats.probplot(large['Excess Readmission Ratio'], dist="norm", plot=pylab)
pylab.title('Probability plot for the excess readmission ratio of large hospitals')
pylab.show()

#data = [small['Excess Readmission Ratio'], large['Excess Readmission Ratio']]
#plt.boxplot(data)

"""
Explanation: (1) Examine the distributions of excess readmission ratio for small and large hospitals using histograms and normal probability plots:
1. The distribution of excess readmission ratio for large hospitals follows a normal distribution, however, the distribution of excess readmission ratio for small hospitals deviates from a normal distribution with a long upper tail. 
2. The distribution of the excess readmission ratio for large hospitals is more spread-out compared to that for small hospitals. The mean of excess readmission ratio for larger hospitals seem to be somewhat lower than that for smaller hospitals.
End of explanation
"""


large = df1[df1['Number of Discharges']>=1000]
small = df1[df1['Number of Discharges']<100]

n_l = large['Number of Discharges'].count()
n_s = small['Number of Discharges'].count()
print('number of large hospitals: ' + str(n_l))
print('number of large hospitals: ' + str(n_s))

mean_l = np.mean(large['Excess Readmission Ratio'])
mean_s = np.mean(small['Excess Readmission Ratio'])

diff = mean_l - mean_s
md = stats.mannwhitneyu(small['Excess Readmission Ratio'],large['Excess Readmission Ratio'])
p_mw = md[1] 

print('The excess readmission ratio of large hospitals is ' + str(abs(diff)) + ' lower compared to that of small hospitals with p value ' + str(abs(p_mw)) )

CI_s = bt.ci(data=small['Excess Readmission Ratio'], statfunction=scipy.mean, alpha=0.1)  
CI_l = bt.ci(data=large['Excess Readmission Ratio'], statfunction=scipy.mean, alpha=0.1)  
print('90% confidence interval of excess readmission ratio for small hospitals:')
print(CI_s)
print('90% confidence interval of excess readmission ratio for large hospitals:')
print(CI_l)

"""
Explanation: (2) Since the distribution of the excess readmission ratio for small hospital deviates from normal distribution, a Mann–Whitney U test is performed here to test if there is a significant difference in excess readmission ratio $R$ between small (number of discharges < 100) and large (number of discharges > 1000) hospitals
$H_0: R_s = R_l$
$H_A: R_s \neq R_l$
In this case, the excess readmission ratio for small hospital is 0.044 higher than that for large hospital, with p value 3.50e-14 (<0.1). Therefore, we are able to reject the Hypothesis that the excess readmission ratio $R$ between small and large hospitals are the same. The 90% confidence interval of mean excess readmission ratio for small hospitals is [1.020, 1.026], and the 90% confidence interval of mean excess readmission ratio for large hospitals is [0.969, 0.987]. These confidence intervals were calculated using bootstrap.
End of explanation
"""


#Examine the distributions of 'Excess Readmission Ratio' and 'Number of Discharges'
excess_ratio = df1['Excess Readmission Ratio']
discharged = df1['Number of Discharges']

plt.hist(excess_ratio, 50)
plt.title('Histogram of excess readmission ratio')
plt.show()

stats.probplot(excess_ratio, dist="norm", plot=pylab)
pylab.title('Probability plot for the excess readmission ratio')
pylab.show()

plt.hist(discharged, 50)
plt.title('Histogram of number of discharges')
plt.show()

stats.probplot(discharged, dist="norm", plot=pylab)
pylab.title('Probability plot for number of discharges')
pylab.show()

#Since not both distributions are normal distributions, it is more appropriate to use Spearman rank correlation coefficient here.
sp = stats.spearmanr(discharged.as_matrix(), excess_ratio.as_matrix())
print('Spearman correlation coeffcient between number of discharges and excess readmission ratio: ')
print('correlation=' + str(sp[0]) + ' pvalue=' + str(sp[1]))


"""
Explanation: (3) Calculate the Correlation Coefficient

The distribution of the excess readmission ratio somewhat deviates from a normal distribution around its upper tail, and the distribution of the number of discharges is very right skew.  
The Spearman Correlation Coefficient between these two variables shows that there is a weak correlation (r=-0.077) between these two variables, and this weak correlation is not due to sampling errors (p=0.22e-16).
End of explanation
"""


