Stroke

class: center, middle, inverse, title-slide

.title[
# Stroke
]
.subtitle[
## What leads to a stroke?
]
.author[
### Connor McKee
]
.institute[
### West Chester University of Pennsylvania
]
.date[
### May 3, 2023
]

---

.center[
## What is a stroke?
]

**Mayo Clinic** defines a stroke to be when the blood supply to part of the brain is interrupted or reduced, preventing brain tissue from getting oxygen and nutrients. Brain cells begin to die in minutes.

**WebMd** states major attributes that lead to strokes are:

- High blood pressure
- Carotid or coronary artery disease
- Others

---

.center[
## What attributes lead to strokes?
]

This data set consists of 4795 unique individuals, and we have 10 possible variables to analyze these individuals on.

The variables include:

1. Gender (Male/Female)
2. Age
3. Hypertension (No/Yes)
4. Heart_disease (No/Yes)
5. Ever_married (No/Yes)
6. Work_type (Children, Self-employed, Private, Goverment)
7. Residence_type (Rural/Urban)
8. Average glucose level
9. BMI
10. Smoking_status (Formerly/Never/Smokes/Unknown)
11. Stroke (No/Yes)

.center[
** 249 patients recorded having a stroke which is 5% of the sample. **
]

---

.center[
## Exploratory Analysis
]

```
## NULL
```

---

.center[
## Full Model
]

<table class="table" style="font-size: 7px; margin-left: auto; margin-right: auto;">
<caption style="font-size: initial !important;">Summary of inferential statistics of the full model</caption>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> Estimate </th>
   <th style="text-align:right;"> Std. Error </th>
   <th style="text-align:right;"> z value </th>
   <th style="text-align:right;"> Pr(&gt;|z|) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> (Intercept) </td>
   <td style="text-align:right;"> -6.2178587 </td>
   <td style="text-align:right;"> 1.061345e+00 </td>
   <td style="text-align:right;"> -5.8584728 </td>
   <td style="text-align:right;"> 0.0000000 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> genderMale </td>
   <td style="text-align:right;"> -0.0728082 </td>
   <td style="text-align:right;"> 1.516328e-01 </td>
   <td style="text-align:right;"> -0.4801611 </td>
   <td style="text-align:right;"> 0.6311128 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> genderOther </td>
   <td style="text-align:right;"> -0.5942210 </td>
   <td style="text-align:right;"> 1.077026e+04 </td>
   <td style="text-align:right;"> -0.0000552 </td>
   <td style="text-align:right;"> 0.9999560 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> grp.age21-24 </td>
   <td style="text-align:right;"> 0.0104641 </td>
   <td style="text-align:right;"> 9.558103e+02 </td>
   <td style="text-align:right;"> 0.0000109 </td>
   <td style="text-align:right;"> 0.9999913 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> grp.age25-30 </td>
   <td style="text-align:right;"> 0.1043019 </td>
   <td style="text-align:right;"> 8.486763e+02 </td>
   <td style="text-align:right;"> 0.0001229 </td>
   <td style="text-align:right;"> 0.9999019 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> grp.age31-40 </td>
   <td style="text-align:right;"> 14.9125675 </td>
   <td style="text-align:right;"> 6.087398e+02 </td>
   <td style="text-align:right;"> 0.0244974 </td>
   <td style="text-align:right;"> 0.9804558 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> grp.age41-50 </td>
   <td style="text-align:right;"> 15.9398410 </td>
   <td style="text-align:right;"> 6.087397e+02 </td>
   <td style="text-align:right;"> 0.0261850 </td>
   <td style="text-align:right;"> 0.9791098 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> grp.age50 + </td>
   <td style="text-align:right;"> 17.2267749 </td>
   <td style="text-align:right;"> 6.087397e+02 </td>
   <td style="text-align:right;"> 0.0282991 </td>
   <td style="text-align:right;"> 0.9774236 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: black !important;background-color: yellow !important;"> hypertension1 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.6272358 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 1.718666e-01 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 3.6495493 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0002627 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: black !important;background-color: yellow !important;"> heart_disease1 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.6452723 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 2.012008e-01 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 3.2071066 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0013408 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> ever_marriedYes </td>
   <td style="text-align:right;"> -0.3057168 </td>
   <td style="text-align:right;"> 2.445262e-01 </td>
   <td style="text-align:right;"> -1.2502415 </td>
   <td style="text-align:right;"> 0.2112114 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> work_typeGovt_job </td>
   <td style="text-align:right;"> -13.4838709 </td>
   <td style="text-align:right;"> 6.087405e+02 </td>
   <td style="text-align:right;"> -0.0221504 </td>
   <td style="text-align:right;"> 0.9823279 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> work_typeNever_worked </td>
   <td style="text-align:right;"> -13.2717808 </td>
   <td style="text-align:right;"> 2.286195e+03 </td>
   <td style="text-align:right;"> -0.0058052 </td>
   <td style="text-align:right;"> 0.9953682 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> work_typePrivate </td>
   <td style="text-align:right;"> -13.2311130 </td>
   <td style="text-align:right;"> 6.087404e+02 </td>
   <td style="text-align:right;"> -0.0217352 </td>
   <td style="text-align:right;"> 0.9826592 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> work_typeSelf-employed </td>
   <td style="text-align:right;"> -13.3618875 </td>
   <td style="text-align:right;"> 6.087405e+02 </td>
   <td style="text-align:right;"> -0.0219501 </td>
   <td style="text-align:right;"> 0.9824878 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> Residence_typeUrban </td>
   <td style="text-align:right;"> 0.0410236 </td>
   <td style="text-align:right;"> 1.473891e-01 </td>
   <td style="text-align:right;"> 0.2783355 </td>
   <td style="text-align:right;"> 0.7807548 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: black !important;background-color: yellow !important;"> avg_glucose_level </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0055324 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 1.285500e-03 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 4.3038432 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0000168 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> bmi </td>
   <td style="text-align:right;"> -0.0187560 </td>
   <td style="text-align:right;"> 1.160620e-02 </td>
   <td style="text-align:right;"> -1.6160276 </td>
   <td style="text-align:right;"> 0.1060883 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> smoking_statusnever smoked </td>
   <td style="text-align:right;"> -0.0665951 </td>
   <td style="text-align:right;"> 1.851887e-01 </td>
   <td style="text-align:right;"> -0.3596067 </td>
   <td style="text-align:right;"> 0.7191413 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> smoking_statussmokes </td>
   <td style="text-align:right;"> 0.0844136 </td>
   <td style="text-align:right;"> 2.234039e-01 </td>
   <td style="text-align:right;"> 0.3778517 </td>
   <td style="text-align:right;"> 0.7055407 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> smoking_statusUnknown </td>
   <td style="text-align:right;"> -0.2635420 </td>
   <td style="text-align:right;"> 2.439421e-01 </td>
   <td style="text-align:right;"> -1.0803465 </td>
   <td style="text-align:right;"> 0.2799879 </td>
  </tr>
</tbody>
</table>

---

.center[
## Manual Model
]

<table>
<caption>Summary of inferential statistics of the reduced model</caption>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> Estimate </th>
   <th style="text-align:right;"> Std. Error </th>
   <th style="text-align:right;"> z value </th>
   <th style="text-align:right;"> Pr(&gt;|z|) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> (Intercept) </td>
   <td style="text-align:right;"> -3.451502 </td>
   <td style="text-align:right;"> 0.0876580 </td>
   <td style="text-align:right;"> -39.374652 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> hypertension1 </td>
   <td style="text-align:right;"> 1.307380 </td>
   <td style="text-align:right;"> 0.1666566 </td>
   <td style="text-align:right;"> 7.844756 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> heart_disease1 </td>
   <td style="text-align:right;"> 1.407844 </td>
   <td style="text-align:right;"> 0.1970324 </td>
   <td style="text-align:right;"> 7.145241 </td>
   <td style="text-align:right;"> 0 </td>
  </tr>
</tbody>
</table>

---

.center[
## Stepwise Model
]

<table>
<caption>Summary of inferential statistics of the final model</caption>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> Estimate </th>
   <th style="text-align:right;"> Std. Error </th>
   <th style="text-align:right;"> z value </th>
   <th style="text-align:right;"> Pr(&gt;|z|) </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> (Intercept) </td>
   <td style="text-align:right;"> -6.8909795 </td>
   <td style="text-align:right;"> 1.0339416 </td>
   <td style="text-align:right;"> -6.6647667 </td>
   <td style="text-align:right;"> 0.0000000 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: black !important;background-color: yellow !important;"> hypertension1 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.6515714 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.1705278 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 3.8209100 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0001330 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: black !important;background-color: yellow !important;"> heart_disease1 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.6680755 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.1980582 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 3.3731278 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0007432 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> grp.age21-24 </td>
   <td style="text-align:right;"> -12.6870260 </td>
   <td style="text-align:right;"> 741.5158532 </td>
   <td style="text-align:right;"> -0.0171096 </td>
   <td style="text-align:right;"> 0.9863492 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> grp.age25-30 </td>
   <td style="text-align:right;"> -12.6779784 </td>
   <td style="text-align:right;"> 592.3335413 </td>
   <td style="text-align:right;"> -0.0214034 </td>
   <td style="text-align:right;"> 0.9829238 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: black !important;background-color: yellow !important;"> grp.age31-40 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 2.0147358 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 1.1009074 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 1.8300685 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0672397 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: black !important;background-color: yellow !important;"> grp.age41-50 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 2.9866882 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 1.0392570 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 2.8738687 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0040548 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: black !important;background-color: yellow !important;"> grp.age50 + </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 4.2528703 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 1.0095812 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 4.2125095 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0000253 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: black !important;background-color: yellow !important;"> avg_glucose_level </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0054563 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0012784 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 4.2680899 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0000197 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> bmi </td>
   <td style="text-align:right;"> -0.0187445 </td>
   <td style="text-align:right;"> 0.0115840 </td>
   <td style="text-align:right;"> -1.6181364 </td>
   <td style="text-align:right;"> 0.1056332 </td>
  </tr>
</tbody>
</table>

---

.center[
## Goodness of Fit Measures
]

<table>
<caption>Comparison of global goodness-of-fit statistics</caption>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> Deviance.residual </th>
   <th style="text-align:right;"> Null.Deviance.Residual </th>
   <th style="text-align:right;"> AIC </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> full.model </td>
   <td style="text-align:right;"> 1409.708 </td>
   <td style="text-align:right;"> 1718.347 </td>
   <td style="text-align:right;"> 1451.708 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> reduced.model </td>
   <td style="text-align:right;"> 1610.339 </td>
   <td style="text-align:right;"> 1718.347 </td>
   <td style="text-align:right;"> 1616.339 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: black !important;background-color: yellow !important;"> final.model </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 1415.833 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 1718.347 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 1435.833 </td>
  </tr>
</tbody>
</table>

---

.center[
## Interpretting the Odds Ratio
]

<table>
<caption>Summary Stats with Odds Ratios</caption>
 <thead>
  <tr>
   <th style="text-align:left;">   </th>
   <th style="text-align:right;"> Estimate </th>
   <th style="text-align:right;"> Std. Error </th>
   <th style="text-align:right;"> z value </th>
   <th style="text-align:right;"> Pr(&gt;|z|) </th>
   <th style="text-align:right;"> odds.ratio </th>
  </tr>
 </thead>
<tbody>
  <tr>
   <td style="text-align:left;"> (Intercept) </td>
   <td style="text-align:right;"> -6.8909795 </td>
   <td style="text-align:right;"> 1.0339416 </td>
   <td style="text-align:right;"> -6.6647667 </td>
   <td style="text-align:right;"> 0.0000000 </td>
   <td style="text-align:right;"> 0.0010169 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> hypertension1 </td>
   <td style="text-align:right;"> 0.6515714 </td>
   <td style="text-align:right;"> 0.1705278 </td>
   <td style="text-align:right;"> 3.8209100 </td>
   <td style="text-align:right;"> 0.0001330 </td>
   <td style="text-align:right;"> 1.9185533 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> heart_disease1 </td>
   <td style="text-align:right;"> 0.6680755 </td>
   <td style="text-align:right;"> 0.1980582 </td>
   <td style="text-align:right;"> 3.3731278 </td>
   <td style="text-align:right;"> 0.0007432 </td>
   <td style="text-align:right;"> 1.9504800 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> grp.age21-24 </td>
   <td style="text-align:right;"> -12.6870260 </td>
   <td style="text-align:right;"> 741.5158532 </td>
   <td style="text-align:right;"> -0.0171096 </td>
   <td style="text-align:right;"> 0.9863492 </td>
   <td style="text-align:right;"> 0.0000031 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> grp.age25-30 </td>
   <td style="text-align:right;"> -12.6779784 </td>
   <td style="text-align:right;"> 592.3335413 </td>
   <td style="text-align:right;"> -0.0214034 </td>
   <td style="text-align:right;"> 0.9829238 </td>
   <td style="text-align:right;"> 0.0000031 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: black !important;background-color: yellow !important;"> grp.age31-40 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 2.0147358 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 1.1009074 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 1.8300685 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0672397 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 7.4987462 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: black !important;background-color: yellow !important;"> grp.age41-50 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 2.9866882 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 1.0392570 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 2.8738687 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0040548 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 19.8199344 </td>
  </tr>
  <tr>
   <td style="text-align:left;font-weight: bold;color: black !important;background-color: yellow !important;"> grp.age50 + </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 4.2528703 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 1.0095812 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 4.2125095 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 0.0000253 </td>
   <td style="text-align:right;font-weight: bold;color: black !important;background-color: yellow !important;"> 70.3069241 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> avg_glucose_level </td>
   <td style="text-align:right;"> 0.0054563 </td>
   <td style="text-align:right;"> 0.0012784 </td>
   <td style="text-align:right;"> 4.2680899 </td>
   <td style="text-align:right;"> 0.0000197 </td>
   <td style="text-align:right;"> 1.0054712 </td>
  </tr>
  <tr>
   <td style="text-align:left;"> bmi </td>
   <td style="text-align:right;"> -0.0187445 </td>
   <td style="text-align:right;"> 0.0115840 </td>
   <td style="text-align:right;"> -1.6181364 </td>
   <td style="text-align:right;"> 0.1056332 </td>
   <td style="text-align:right;"> 0.9814301 </td>
  </tr>
</tbody>
</table>

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.center[
## Summary and Conclusion
]

- **hypertension** and **heart disease** are considered to be major contributors to the risk of having a stroke by experts
- we obtain the final model with 5 variables, hypertension (1 dummy variable), heart disease (1 dummy variable), age ( 5 dummy variables), glucose, and BMI.
- our final conclusion from our data is that health factors are what lead to strokes.

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