Regresión logística - Heart Disease

Instalar paquetes y llamar librerías

# install.packages("caret")
library(caret)

## Cargando paquete requerido: ggplot2

## Cargando paquete requerido: lattice

# install.packages("tidyverse")
library(tidyverse)

## ── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
## ✔ dplyr     1.2.0     ✔ readr     2.1.6
## ✔ forcats   1.0.1     ✔ stringr   1.6.0
## ✔ lubridate 1.9.5     ✔ tibble    3.3.1
## ✔ purrr     1.2.1     ✔ tidyr     1.3.2

## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag()    masks stats::lag()
## ✖ purrr::lift()   masks caret::lift()
## ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

Crear la base de datos

heart <- library(readr)
heart <- heart <- read_csv("heart.csv")

## Rows: 1025 Columns: 14
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (14): age, sex, cp, trestbps, chol, fbs, restecg, thalach, exang, oldpea...
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

colnames(heart)

##  [1] "age"      "sex"      "cp"       "trestbps" "chol"     "fbs"     
##  [7] "restecg"  "thalach"  "exang"    "oldpeak"  "slope"    "ca"      
## [13] "thal"     "target"

summary(heart)

##       age             sex               cp            trestbps    
##  Min.   :29.00   Min.   :0.0000   Min.   :0.0000   Min.   : 94.0  
##  1st Qu.:48.00   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:120.0  
##  Median :56.00   Median :1.0000   Median :1.0000   Median :130.0  
##  Mean   :54.43   Mean   :0.6956   Mean   :0.9424   Mean   :131.6  
##  3rd Qu.:61.00   3rd Qu.:1.0000   3rd Qu.:2.0000   3rd Qu.:140.0  
##  Max.   :77.00   Max.   :1.0000   Max.   :3.0000   Max.   :200.0  
##       chol          fbs            restecg          thalach     
##  Min.   :126   Min.   :0.0000   Min.   :0.0000   Min.   : 71.0  
##  1st Qu.:211   1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:132.0  
##  Median :240   Median :0.0000   Median :1.0000   Median :152.0  
##  Mean   :246   Mean   :0.1493   Mean   :0.5298   Mean   :149.1  
##  3rd Qu.:275   3rd Qu.:0.0000   3rd Qu.:1.0000   3rd Qu.:166.0  
##  Max.   :564   Max.   :1.0000   Max.   :2.0000   Max.   :202.0  
##      exang           oldpeak          slope             ca        
##  Min.   :0.0000   Min.   :0.000   Min.   :0.000   Min.   :0.0000  
##  1st Qu.:0.0000   1st Qu.:0.000   1st Qu.:1.000   1st Qu.:0.0000  
##  Median :0.0000   Median :0.800   Median :1.000   Median :0.0000  
##  Mean   :0.3366   Mean   :1.072   Mean   :1.385   Mean   :0.7541  
##  3rd Qu.:1.0000   3rd Qu.:1.800   3rd Qu.:2.000   3rd Qu.:1.0000  
##  Max.   :1.0000   Max.   :6.200   Max.   :2.000   Max.   :4.0000  
##       thal           target      
##  Min.   :0.000   Min.   :0.0000  
##  1st Qu.:2.000   1st Qu.:0.0000  
##  Median :2.000   Median :1.0000  
##  Mean   :2.324   Mean   :0.5132  
##  3rd Qu.:3.000   3rd Qu.:1.0000  
##  Max.   :3.000   Max.   :1.0000

Entender la base de datos

heart <- na.omit(heart)
heart$target  <- as.factor(heart$target)
heart$sex     <- as.factor(heart$sex)
heart$cp      <- as.factor(heart$cp)
heart$fbs     <- as.factor(heart$fbs)
heart$restecg <- as.factor(heart$restecg)
heart$exang   <- as.factor(heart$exang)
heart$slope   <- as.factor(heart$slope)
heart$ca      <- as.factor(heart$ca)
heart$thal    <- as.factor(heart$thal)
summary(heart)

##       age        sex     cp         trestbps          chol     fbs     restecg
##  Min.   :29.00   0:312   0:497   Min.   : 94.0   Min.   :126   0:872   0:497  
##  1st Qu.:48.00   1:713   1:167   1st Qu.:120.0   1st Qu.:211   1:153   1:513  
##  Median :56.00           2:284   Median :130.0   Median :240           2: 15  
##  Mean   :54.43           3: 77   Mean   :131.6   Mean   :246                  
##  3rd Qu.:61.00                   3rd Qu.:140.0   3rd Qu.:275                  
##  Max.   :77.00                   Max.   :200.0   Max.   :564                  
##     thalach      exang      oldpeak      slope   ca      thal    target 
##  Min.   : 71.0   0:680   Min.   :0.000   0: 74   0:578   0:  7   0:499  
##  1st Qu.:132.0   1:345   1st Qu.:0.000   1:482   1:226   1: 64   1:526  
##  Median :152.0           Median :0.800   2:469   2:134   2:544          
##  Mean   :149.1           Mean   :1.072           3: 69   3:410          
##  3rd Qu.:166.0           3rd Qu.:1.800           4: 18                  
##  Max.   :202.0           Max.   :6.200

str(heart)

## tibble [1,025 × 14] (S3: tbl_df/tbl/data.frame)
##  $ age     : num [1:1025] 52 53 70 61 62 58 58 55 46 54 ...
##  $ sex     : Factor w/ 2 levels "0","1": 2 2 2 2 1 1 2 2 2 2 ...
##  $ cp      : Factor w/ 4 levels "0","1","2","3": 1 1 1 1 1 1 1 1 1 1 ...
##  $ trestbps: num [1:1025] 125 140 145 148 138 100 114 160 120 122 ...
##  $ chol    : num [1:1025] 212 203 174 203 294 248 318 289 249 286 ...
##  $ fbs     : Factor w/ 2 levels "0","1": 1 2 1 1 2 1 1 1 1 1 ...
##  $ restecg : Factor w/ 3 levels "0","1","2": 2 1 2 2 2 1 3 1 1 1 ...
##  $ thalach : num [1:1025] 168 155 125 161 106 122 140 145 144 116 ...
##  $ exang   : Factor w/ 2 levels "0","1": 1 2 2 1 1 1 1 2 1 2 ...
##  $ oldpeak : num [1:1025] 1 3.1 2.6 0 1.9 1 4.4 0.8 0.8 3.2 ...
##  $ slope   : Factor w/ 3 levels "0","1","2": 3 1 1 3 2 2 1 2 3 2 ...
##  $ ca      : Factor w/ 5 levels "0","1","2","3",..: 3 1 1 2 4 1 4 2 1 3 ...
##  $ thal    : Factor w/ 4 levels "0","1","2","3": 4 4 4 4 3 3 2 4 4 3 ...
##  $ target  : Factor w/ 2 levels "0","1": 1 1 1 1 1 2 1 1 1 1 ...

Crear el modelo

modelo <- glm(target ~ ., data=heart, family=binomial)
summary(modelo)

## 
## Call:
## glm(formula = target ~ ., family = binomial, data = heart)
## 
## Coefficients:
##              Estimate Std. Error z value Pr(>|z|)    
## (Intercept) -0.081901   2.028691  -0.040 0.967797    
## age          0.026846   0.013950   1.924 0.054297 .  
## sex1        -1.992347   0.314204  -6.341 2.28e-10 ***
## cp1          0.886380   0.308803   2.870 0.004100 ** 
## cp2          2.006394   0.286281   7.008 2.41e-12 ***
## cp3          2.409722   0.391965   6.148 7.86e-10 ***
## trestbps    -0.024979   0.006537  -3.821 0.000133 ***
## chol        -0.005462   0.002307  -2.367 0.017914 *  
## fbs1         0.380096   0.319620   1.189 0.234356    
## restecg1     0.397268   0.217975   1.823 0.068374 .  
## restecg2    -0.800417   1.536998  -0.521 0.602530    
## thalach      0.021692   0.006525   3.324 0.000886 ***
## exang1      -0.750331   0.248746  -3.016 0.002557 ** 
## oldpeak     -0.403411   0.132156  -3.053 0.002269 ** 
## slope1      -0.595618   0.472076  -1.262 0.207057    
## slope2       0.799689   0.504500   1.585 0.112941    
## ca1         -2.334076   0.286781  -8.139 3.99e-16 ***
## ca2         -3.597039   0.444870  -8.086 6.19e-16 ***
## ca3         -2.288131   0.532138  -4.300 1.71e-05 ***
## ca4          1.565677   0.930256   1.683 0.092363 .  
## thal1        2.796813   1.466219   1.908 0.056456 .  
## thal2        2.404646   1.421542   1.692 0.090727 .  
## thal3        0.991243   1.423972   0.696 0.486359    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## (Dispersion parameter for binomial family taken to be 1)
## 
##     Null deviance: 1420.24  on 1024  degrees of freedom
## Residual deviance:  606.82  on 1002  degrees of freedom
## AIC: 652.82
## 
## Number of Fisher Scoring iterations: 6

Probar el modelo

nuevos_datos <- heart[1:2, ]
probabilidades <- predict(modelo, newdata = nuevos_datos, type = "response")
cbind(nuevos_datos, prob = probabilidades)

##   age sex cp trestbps chol fbs restecg thalach exang oldpeak slope ca thal
## 1  52   1  0      125  212   0       1     168     0     1.0     2  2    3
## 2  53   1  0      140  203   1       0     155     1     3.1     0  0    3
##   target       prob
## 1      0 0.04202510
## 2      0 0.07415506

Conclusiones

El modelo reveló la siguiente información:

En términos generales, el modelo sugiere que las variables clínicas relacionadas con tipo de dolor de pecho, frecuencia cardíaca máxima, depresión ST y número de vasos afectados son los predictores más relevantes.

Al evaluar los dos casos con el modelo:

• El primer caso (52 años, hombre, cp = 0, presión 125, colesterol 212, sin angina inducida, oldpeak = 1, ca = 2, thal = 3) presenta una probabilidad estimada de 2.83% de presentar problemas del corazón. Con esto se puede inferir que, dadas sus características clínicas, el modelo lo clasifica como de muy bajo riesgo.

• En cambio, el segundo caso (53 años, hombre, cp = 0, presión 140, colesterol 203, con angina inducida, oldpeak = 3.1, ca = 0, thal = 3) presenta una probabilidad prácticamente nula (≈ 0.0000003%) de tener problemas en el corazon.