Multivariate Logistic Regression for predicting probability of Heart Attacks

[j-craggy]

Authors

Jeff Craggy

Links

https://www.jeffcraggy.com

Full description

DATA:

Data is found in Data Mining for the Masses, 3rd Edition

• Chapter 9 Training
• Chapter 9 Scoring (test)

We have access to the company’s medical claims database. With this access, she is able to
generate two data sets for us. This first is a list of people who have suffered heart attacks, with an
attribute indicating whether or not they have had more than one; and the second is a list of those
who have had a first heart attack, but not a second. The former data set, comprised of 138
observations, will serve as our training data; while the latter, comprised of 690 peoples’ data, will be
for scoring. This data is used to help this latter group of people avoid becoming second heart attack
victims. In compiling the two data sets we have defined the following attributes:

• Age: The age in years of the person, rounded to the nearest whole year.
• Marital_Status: The person’s current marital status, indicated by a coded number:
  • 0 - Single, never married
  • 1 – Married
  • 2 - Divorced
  • 3 – Widowed
• Gender: The person’s gender:
  • 0 for female
  • 1 for male
• Weight_Category: The person’s weight categorized into one of three levels:
  • 0 for normal weight range
  • 1 for overweight
  • 2 for obese
• Cholesterol: The person’s cholesterol level, as recorded at the time of their treatment for their most recent heart attack (their only heart attack, in the case of those individuals in the scoring data set.)
• Stress_Management: A binary attribute indicating whether or not the person has previously attended a stress management course:
  • 0 for no
  • 1 for yes
• Trait_Anxiety: A score on a scale of 0 to 100 measuring the level of each person’s natural stress levels and abilities to cope with stress. A short time after each person in each of the two data sets had recovered from their first heart attack, they were administered a standard test of natural anxiety. Their scores are tabulated and recorded in this attribute along five point increments. A score of 0 would indicate that the person never feels anxiety, pressure or stress in any situation, while a score of 100 would indicate that the person lives in a constant state of being overwhelmed and unable to deal with his or her circumstances.
• 2nd_Heart_Attack: This attribute exists only in the training data set. It will be our label, the prediction or target attribute. In the training data set, the attribute is set to ‘yes’ for individuals who have suffered second heart attacks, and ‘no’ for those who have not.

Exploratory Data Analysis

Looking at the training data set, we can see that some statistically significant predictors of a heart attack are:

• Weight Category
• Marital Status
• Age

formula = "Q('2nd_Heart_Attack') ~ Age + Marital_Status + Gender + Weight_Category + Cholesterol + Stress_Management + Trait_Anxiety"
 
model = sm.formula.glm(
  formula=formula, 
  family=sm.families.Binomial(), 
  data=train
  ).fit()

print(model.summary())

=====================================================================================
                         coef    std err          z      P>|z|      [0.025      0.975]
-------------------------------------------------------------------------------------
Intercept            12.4191      4.690      2.648      0.008       3.226      21.612
Age                  -0.1193      0.078     -1.528      0.127.     -0.272       0.034
Marital_Status       -1.2784      0.531     -2.409      0.016*     -2.319      -0.238
Gender               -0.2148      0.851     -0.253      0.801      -1.882       1.453
Weight_Category      -4.0557      0.976     -4.154      0.000***   -5.969      -2.142
Cholesterol          -0.0086      0.015     -0.587      0.557      -0.037       0.020
Stress_Management     0.0707      0.949      0.074      0.941      -1.789       1.931
Trait_Anxiety         0.0536      0.065      0.818      0.413      -0.075       0.182
=====================================================================================

A second run narrowed by these three indicators show an even greater significance.

formula = "Q('2nd_Heart_Attack') ~ Age + Marital_Status + Weight_Category"

model = sm.formula.glm(
    formula=formula,
    family=sm.families.Binomial(),
    data=train
).fit()

print(model.summary())

===================================================================================
                      coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------
Intercept          12.8914      3.894      3.311      0.001       5.260      20.523
Age                -0.1075      0.062     -1.736      0.082*     -0.229       0.014
Marital_Status     -1.2398      0.443     -2.801      0.005**    -2.107      -0.372
Weight_Category    -3.9880      0.782     -5.098      0.000***   -5.521      -2.455
===================================================================================

References

North, A. Matthew (2012). Data Mining for the Masses. Global Text Project Book. Creative Commons Attribution 3.0 Licence

Code repository

Github: https://github.com/JBC-Inc/jbcPlotnine2
Plot: https://kraggle.shinyapps.io/jbcplotnine221/

[has2k1]

---

[EconomiCurtis]

Ahoy @j-craggy ,
I am one of the contest organizers.
If you'd like, we'd be happy to send you a little Plotnine and Posit care package of hex-shaped stickers. Just a small thanks for taking part. https://forms.gle/M8QmM286MSHbkDRd7

[has2k1]

@j-craggy, The winning submission has been announced here. Thank you again for taking part in the contest.